# Symbol API¶

## Overview¶

This document lists the routines of the symbolic expression package:

 mxnet.symbol Symbolic configuration API of MXNet.

The Symbol API, defined in the symbol (or simply sym) package, provides neural network graphs and auto-differentiation. A symbol represents a multi-output symbolic expression. They are composited by operators, such as simple matrix operations (e.g. “+”), or a neural network layer (e.g. convolution layer). An operator can take several input variables, produce more than one output variables, and have internal state variables. A variable can be either free, which we can bind with value later, or an output of another symbol.

>>> a = mx.sym.Variable('a')
>>> b = mx.sym.Variable('b')
>>> c = 2 * a + b
>>> type(c)
<class 'mxnet.symbol.Symbol'>
>>> e = c.bind(mx.cpu(), {'a': mx.nd.array([1,2]), 'b':mx.nd.array([2,3])})
>>> y = e.forward()
>>> y
[<NDArray 2 @cpu(0)>]
>>> y[0].asnumpy()
array([ 4.,  7.], dtype=float32)


A detailed tutorial is available at Symbol - Neural network graphs and auto-differentiation.

Note

most operators provided in symbol are similar to those in ndarray although there are few differences:

• symbol adopts declarative programming. In other words, we need to first compose the computations, and then feed it with data for execution whereas ndarray adopts imperative programming.
• Most binary operators in symbol such as + and > don’t broadcast. We need to call the broadcast version of the operator such as broadcast_plus explicitly.

In the rest of this document, we first overview the methods provided by the symbol.Symbol class, and then list other routines provided by the symbol package.

## The Symbol class¶

### Composition¶

Composite multiple symbols into a new one by an operator.

 Symbol.__call__ Composes symbol using inputs.

#### Arithmetic operations¶

 Symbol.__add__ x.__add__(y) <=> x+y Symbol.__sub__ x.__sub__(y) <=> x-y Symbol.__rsub__ x.__rsub__(y) <=> y-x Symbol.__neg__ x.__neg__() <=> -x Symbol.__mul__ x.__mul__(y) <=> x*y Symbol.__div__ x.__div__(y) <=> x/y Symbol.__rdiv__ x.__rdiv__(y) <=> y/x Symbol.__mod__ x.__mod__(y) <=> x%y Symbol.__rmod__ x.__rmod__(y) <=> y%x Symbol.__pow__ x.__pow__(y) <=> x**y

#### Comparison operators¶

 Symbol.__lt__ x.__lt__(y) <=> x x<=y Symbol.__gt__ x.__gt__(y) <=> x>y Symbol.__ge__ x.__ge__(y) <=> x>=y Symbol.__eq__ x.__eq__(y) <=> x==y Symbol.__ne__ x.__ne__(y) <=> x!=y

### Query information¶

 Symbol.name Gets name string from the symbol, this function only works for non-grouped symbol. Symbol.list_arguments Lists all the arguments in the symbol. Symbol.list_outputs Lists all the outputs in the symbol. Symbol.list_auxiliary_states Lists all the auxiliary states in the symbol. Symbol.list_attr Gets all attributes from the symbol. Symbol.attr Returns the attribute string for corresponding input key from the symbol. Symbol.attr_dict Recursively gets all attributes from the symbol and its children.

### Get internal and output symbol¶

 Symbol.__getitem__ x.__getitem__(i) <=> x[i] Symbol.__iter__ Returns a generator object of symbol. Symbol.get_internals Gets a new grouped symbol sgroup. Symbol.get_children Gets a new grouped symbol whose output contains inputs to output nodes of the original symbol.

### Inference type and shape¶

 Symbol.infer_type Infers the type of all arguments and all outputs, given the known types for some arguments. Symbol.infer_shape Infers the shapes of all arguments and all outputs given the known shapes of some arguments. Symbol.infer_shape_partial Infers the shape partially.

### Bind¶

 Symbol.bind Binds the current symbol to an executor and returns it. Symbol.simple_bind Bind current symbol to get an executor, allocate all the arguments needed.

### Save¶

 Symbol.save Saves symbol to a file. Symbol.tojson Saves symbol to a JSON string. Symbol.debug_str Gets a debug string of symbol.

## Symbol creation routines¶

 var Creates a symbolic variable with specified name. zeros Returns a new symbol of given shape and type, filled with zeros. ones Returns a new symbol of given shape and type, filled with ones. arange Returns evenly spaced values within a given interval.

## Symbol manipulation routines¶

### Changing shape and type¶

 cast Casts all elements of the input to a new type. reshape Reshapes the input array. flatten Flattens the input array into a 2-D array by collapsing the higher dimensions. expand_dims Inserts a new axis of size 1 into the array shape

### Expanding elements¶

 broadcast_to Broadcasts the input array to a new shape. broadcast_axes Broadcasts the input array over particular axes. repeat Repeats elements of an array. tile Repeats the whole array multiple times. pad Pads an input array with a constant or edge values of the array.

### Rearranging elements¶

 transpose Permutes the dimensions of an array. swapaxes Interchanges two axes of an array. flip Reverses the order of elements along given axis while preserving array shape.

### Joining and splitting symbols¶

 concat Joins input arrays along a given axis. split Splits an array along a particular axis into multiple sub-arrays.

### Indexing routines¶

 slice Slices a contiguous region of the array. slice_axis Slices along a given axis. take Takes elements from an input array along the given axis. batch_take Takes elements from a data batch. one_hot Returns a one-hot array.

## Mathematical functions¶

### Arithmetic operations¶

 broadcast_add Returns element-wise sum of the input arrays with broadcasting. broadcast_sub Returns element-wise difference of the input arrays with broadcasting. broadcast_mul Returns element-wise product of the input arrays with broadcasting. broadcast_div Returns element-wise division of the input arrays with broadcasting. broadcast_mod Returns element-wise modulo of the input arrays with broadcasting. negative Numerical negative of the argument, element-wise. reciprocal Returns the reciprocal of the argument, element-wise. dot Dot product of two arrays. batch_dot Batchwise dot product. add_n Adds all input arguments element-wise.

### Trigonometric functions¶

 sin Computes the element-wise sine of the input array. cos Computes the element-wise cosine of the input array. tan Computes the element-wise tangent of the input array. arcsin Returns element-wise inverse sine of the input array. arccos Returns element-wise inverse cosine of the input array. arctan Returns element-wise inverse tangent of the input array. hypot Given the “legs” of a right triangle, returns its hypotenuse. broadcast_hypot Returns the hypotenuse of a right angled triangle, given its “legs” with broadcasting. degrees Converts each element of the input array from radians to degrees. radians Converts each element of the input array from degrees to radians.

### Hyperbolic functions¶

 sinh Returns the hyperbolic sine of the input array, computed element-wise. cosh Returns the hyperbolic cosine of the input array, computed element-wise. tanh Returns the hyperbolic tangent of the input array, computed element-wise. arcsinh Returns the element-wise inverse hyperbolic sine of the input array, computed element-wise. arccosh Returns the element-wise inverse hyperbolic cosine of the input array, computed element-wise. arctanh Returns the element-wise inverse hyperbolic tangent of the input array, computed element-wise.

### Reduce functions¶

 sum Computes the sum of array elements over given axes. nansum Computes the sum of array elements over given axes treating Not a Numbers (NaN) as zero. prod Computes the product of array elements over given axes. nanprod Computes the product of array elements over given axes treating Not a Numbers (NaN) as one. mean Computes the mean of array elements over given axes. max Computes the max of array elements over given axes. min Computes the min of array elements over given axes. norm Flattens the input array and then computes the l2 norm.

### Rounding¶

 round Returns element-wise rounded value to the nearest integer of the input. rint Returns element-wise rounded value to the nearest integer of the input. fix Returns element-wise rounded value to the nearest integer towards zero of the input. floor Returns element-wise floor of the input. ceil Returns element-wise ceiling of the input. trunc Return the element-wise truncated value of the input.

### Exponents and logarithms¶

 exp Returns element-wise exponential value of the input. expm1 Returns exp(x) - 1 computed element-wise on the input. log Returns element-wise Natural logarithmic value of the input. log10 Returns element-wise Base-10 logarithmic value of the input. log2 Returns element-wise Base-2 logarithmic value of the input. log1p Returns element-wise log(1 + x) value of the input.

### Powers¶

 broadcast_power Returns result of first array elements raised to powers from second array, element-wise with broadcasting. sqrt Returns element-wise square-root value of the input. rsqrt Returns element-wise inverse square-root value of the input. square Returns element-wise squared value of the input.

### Logic functions¶

 broadcast_equal Returns the result of element-wise equal to (==) comparison operation with broadcasting. broadcast_not_equal Returns the result of element-wise not equal to (!=) comparison operation with broadcasting. broadcast_greater Returns the result of element-wise greater than (>) comparison operation with broadcasting. broadcast_greater_equal Returns the result of element-wise greater than or equal to (>=) comparison operation with broadcasting. broadcast_lesser Returns the result of element-wise lesser than (<) comparison operation with broadcasting. broadcast_lesser_equal Returns the result of element-wise lesser than or equal to (<=) comparison operation with broadcasting.

### Random sampling¶

 random_uniform Draw random samples from a uniform distribution. random_normal Draw random samples from a normal (Gaussian) distribution. random_gamma Draw random samples from a gamma distribution. random_exponential Draw random samples from an exponential distribution. random_poisson Draw random samples from a Poisson distribution. random_negative_binomial Draw random samples from a negative binomial distribution. random_generalized_negative_binomial Draw random samples from a generalized negative binomial distribution. sample_uniform Concurrent sampling from multiple uniform distributions on the intervals given by [low,high). sample_normal Concurrent sampling from multiple normal distributions with parameters mu (mean) and sigma (standard deviation). sample_gamma Concurrent sampling from multiple gamma distributions with parameters alpha (shape) and beta (scale). sample_exponential Concurrent sampling from multiple exponential distributions with parameters lambda (rate). sample_poisson Concurrent sampling from multiple Poisson distributions with parameters lambda (rate). sample_negative_binomial Concurrent sampling from multiple negative binomial distributions with parameters k (failure limit) and p (failure probability). sample_generalized_negative_binomial Concurrent sampling from multiple generalized negative binomial distributions with parameters mu (mean) and alpha (dispersion). mxnet.random.seed Seeds the random number generators in MXNet.

### Sorting and searching¶

 sort Returns a sorted copy of an input array along the given axis. topk Returns the top k elements in an input array along the given axis. argsort Returns the indices that would sort an input array along the given axis. argmax Returns indices of the maximum values along an axis. argmin Returns indices of the minimum values along an axis.

### Linear Algebra¶

 linalg_gemm Performs general matrix multiplication and accumulation. linalg_gemm2 Performs general matrix multiplication. linalg_potrf Performs Cholesky factorization of a symmetric positive-definite matrix. linalg_potri Performs matrix inversion from a Cholesky factorization. linalg_trmm Performs multiplication with a triangular matrix. linalg_trsm Solves matrix equations involving a triangular matrix. linalg_sumlogdiag Computes the sum of the logarithms of all diagonal elements in a matrix.

### Miscellaneous¶

 maximum Returns element-wise maximum of the input elements. minimum Returns element-wise minimum of the input elements. broadcast_maximum Returns element-wise maximum of the input arrays with broadcasting. broadcast_minimum Returns element-wise minimum of the input arrays with broadcasting. clip Clips (limits) the values in an array. abs Returns element-wise absolute value of the input. sign Returns element-wise sign of the input. gamma Returns the gamma function (extension of the factorial function to the reals) , computed element-wise on the input array. gammaln Returns element-wise log of the absolute value of the gamma function of the input.

## Neural network¶

### Basic¶

 FullyConnected Applies a linear transformation: $$Y = XW^T + b$$. Convolution Compute N-D convolution on (N+2)-D input. Activation Applies an activation function element-wise to the input. BatchNorm Batch normalization. Pooling Performs pooling on the input. SoftmaxOutput Computes the gradient of cross entropy loss with respect to softmax output. softmax Applies the softmax function. log_softmax Computes the log softmax of the input.

### More¶

 Correlation Applies correlation to inputs. Deconvolution Computes 2D transposed convolution (aka fractionally strided convolution) of the input tensor. RNN Applies a recurrent layer to input. Embedding Maps integer indices to vector representations (embeddings). LeakyReLU Applies Leaky rectified linear unit activation element-wise to the input. InstanceNorm Applies instance normalization to the n-dimensional input array. L2Normalization Normalize the input array using the L2 norm. LRN Applies local response normalization to the input. ROIPooling Performs region of interest(ROI) pooling on the input array. SoftmaxActivation Applies softmax activation to input. Dropout Applies dropout operation to input array. BilinearSampler Applies bilinear sampling to input feature map. GridGenerator Generates 2D sampling grid for bilinear sampling. UpSampling Performs nearest neighbor/bilinear up sampling to inputs. SpatialTransformer Applies a spatial transformer to input feature map. LinearRegressionOutput Computes and optimizes for squared loss during backward propagation. LogisticRegressionOutput Applies a logistic function to the input. MAERegressionOutput Computes mean absolute error of the input. SVMOutput Computes support vector machine based transformation of the input. softmax_cross_entropy Calculate cross entropy of softmax output and one-hot label. smooth_l1 Calculate Smooth L1 Loss(lhs, scalar) by summing IdentityAttachKLSparseReg Apply a sparse regularization to the output a sigmoid activation function. MakeLoss Make your own loss function in network construction. BlockGrad Stops gradient computation. Custom Apply a custom operator implemented in a frontend language (like Python).

## Contrib¶

Warning

This package contains experimental APIs and may change in the near future.

The contrib.symbol module contains many useful experimental APIs for new features. This is a place for the community to try out the new features, so that feature contributors can receive feedback.

 CTCLoss Connectionist Temporal Classification Loss. DeformableConvolution Compute 2-D deformable convolution on 4-D input. DeformablePSROIPooling Performs deformable position-sensitive region-of-interest pooling on inputs.The DeformablePSROIPooling operation is described in https://arxiv.org/abs/1703.06211 .batch_size will change to the number of region bounding boxes after DeformablePSROIPooling MultiBoxDetection Convert multibox detection predictions. MultiBoxPrior Generate prior(anchor) boxes from data, sizes and ratios. MultiBoxTarget Compute Multibox training targets MultiProposal Generate region proposals via RPN PSROIPooling Performs region-of-interest pooling on inputs. Proposal Generate region proposals via RPN count_sketch Apply CountSketch to input: map a d-dimension data to k-dimension data” ctc_loss Connectionist Temporal Classification Loss. dequantize Dequantize the input tensor into a float tensor. fft Apply 1D FFT to input” ifft Apply 1D ifft to input” quantize Quantize a input tensor from float to out_type, with user-specified min_range and max_range.

## API Reference¶

Symbolic configuration API of MXNet.

class mxnet.symbol.Symbol(handle)

Symbol is symbolic graph of the mxnet.

__repr__()

Gets a string representation of the symbol.

__iter__()

Returns a generator object of symbol.

One can loop through the returned object list to get outputs.

>>> a = mx.sym.Variable('a')
>>> b = mx.sym.Variable('b')
>>> c = a+b
>>> d = mx.sym.Variable('d')
>>> e = d+c
>>> out = e.get_children()
>>> out
<Symbol Grouped>
>>> for i in out:
...     i
...
<Symbol d>
<Symbol _plus0>

__add__(other)

__sub__(other)

x.__sub__(y) <=> x-y

__rsub__(other)

x.__rsub__(y) <=> y-x

Only NDArray is supported for now.

>>> x = mx.nd.ones((2,3))*3
>>> y = mx.nd.ones((2,3))
>>> x.__rsub__(y).asnumpy()
array([[-2., -2., -2.],
[-2., -2., -2.]], dtype=float32)

__mul__(other)

x.__mul__(y) <=> x*y

__div__(other)

x.__div__(y) <=> x/y

__rdiv__(other)

x.__rdiv__(y) <=> y/x

Only NDArray is supported for now.

>>> x = mx.nd.ones((2,3))*3
>>> y = mx.nd.ones((2,3))
>>> x.__rdiv__(y).asnumpy()
array([[ 0.33333334,  0.33333334,  0.33333334],
[ 0.33333334,  0.33333334,  0.33333334]], dtype=float32)

__mod__(other)

x.__mod__(y) <=> x%y

__rmod__(other)

x.__rmod__(y) <=> y%x

Only NDArray is supported for now.

>>> x = mx.nd.ones((2,3))*3
>>> y = mx.nd.ones((2,3))
>>> x.__rmod__(y).asnumpy()
array([[ 1.,  1.,  1.,
[ 1.,  1.,  1., dtype=float32)

__pow__(other)

x.__pow__(y) <=> x**y

__neg__()

x.__neg__() <=> -x

Numerical negative, element-wise.

>>> a = mx.sym.Variable('a')
>>> a
<Symbol a>
>>> -a
<Symbol _mulscalar0>
>>> a_neg = a.__neg__()
>>> c = a_neg*b
>>> ex = c.eval(ctx=mx.cpu(), a=mx.nd.ones([2,3]), b=mx.nd.ones([2,3]))
>>> ex[0].asnumpy()
array([[-1., -1., -1.],
[-1., -1., -1.]], dtype=float32)

__deepcopy__(_)

Returns a deep copy of the input object.

This function returns a deep copy of the input object including the current state of all its parameters such as weights, biases, etc.

Any changes made to the deep copy do not reflect in the original object.

>>> import copy
>>> data = mx.sym.Variable('data')
>>> data_1 = copy.deepcopy(data)
>>> data_1 = 2*data
>>> data_1.tojson()
>>> data_1 is data    # Data got modified
False

__eq__(other)

x.__eq__(y) <=> x==y

__ne__(other)

x.__ne__(y) <=> x!=y

__gt__(other)

x.__gt__(y) <=> x>y

__ge__(other)

x.__ge__(y) <=> x>=y

__lt__(other)

x.__lt__(y) <=> x<y

__le__(other)

x.__le__(y) <=> x<=y

__call__(*args, **kwargs)

Composes symbol using inputs.

x.__call__(y, z) <=> x(y,z)

This function internally calls _compose to compose the symbol and returns the composed symbol.

>>> data = mx.symbol.Variable('data')
>>> net1 = mx.symbol.FullyConnected(data=data, name='fc1', num_hidden=10)
>>> net2 = mx.symbol.FullyConnected(name='fc3', num_hidden=10)
>>> composed = net2(fc3_data=net1, name='composed')
>>> composed
<Symbol composed>
>>> called = net2.__call__(fc3_data=net1, name='composed')
>>> called
<Symbol composed>

Parameters: args – Positional arguments. kwargs – Keyword arguments. The resulting symbol.
__getitem__(index)

x.__getitem__(i) <=> x[i]

Returns a sliced view of the input symbol.

>>> a = mx.sym.var('a')
>>> a.__getitem__(0)
<Symbol a>
>>> a[0]
<Symbol a>

Parameters: index (int or str) – Indexing key
name

Gets name string from the symbol, this function only works for non-grouped symbol.

Returns: value – The name of this symbol, returns None for grouped symbol. str
attr(key)

Returns the attribute string for corresponding input key from the symbol.

This function only works for non-grouped symbols.

>>> data = mx.sym.Variable('data', attr={'mood': 'angry'})
>>> data.attr('mood')
'angry'

Parameters: key (str) – The key corresponding to the desired attribute. value – The desired attribute value, returns None if the attribute does not exist. str
list_attr(recursive=False)

Gets all attributes from the symbol.

>>> data = mx.sym.Variable('data', attr={'mood': 'angry'})
>>> data.list_attr()
{'mood': 'angry'}

Returns: ret – A dictionary mapping attribute keys to values. Dict of str to str
attr_dict()

Recursively gets all attributes from the symbol and its children.

>>> a = mx.sym.Variable('a', attr={'a1':'a2'})
>>> b = mx.sym.Variable('b', attr={'b1':'b2'})
>>> c = a+b
>>> c.attr_dict()
{'a': {'a1': 'a2'}, 'b': {'b1': 'b2'}}

Returns: ret – There is a key in the returned dict for every child with non-empty attribute set. For each symbol, the name of the symbol is its key in the dict and the correspond value is that symbol’s attribute list (itself a dictionary). Dict of str to dict
get_internals()

Gets a new grouped symbol sgroup. The output of sgroup is a list of outputs of all of the internal nodes.

Consider the following code:

>>> a = mx.sym.var('a')
>>> b = mx.sym.var('b')
>>> c = a + b
>>> d = c.get_internals()
>>> d
<Symbol Grouped>
>>> d.list_outputs()
['a', 'b', '_plus4_output']

Returns: sgroup – A symbol group containing all internal and leaf nodes of the computation graph used to compute the symbol. Symbol
get_children()

Gets a new grouped symbol whose output contains inputs to output nodes of the original symbol.

>>> x = mx.sym.Variable('x')
>>> y = mx.sym.Variable('y')
>>> z = mx.sym.Variable('z')
>>> a = y+z
>>> b = x+a
>>> b.get_children()
<Symbol Grouped>
>>> b.get_children().list_outputs()
['x', '_plus10_output']
>>> b.get_children().get_children().list_outputs()
['y', 'z']

Returns: sgroup – The children of the head node. If the symbol has no inputs then None will be returned. Symbol or None
list_arguments()

Lists all the arguments in the symbol.

>>> a = mx.sym.var('a')
>>> b = mx.sym.var('b')
>>> c = a + b
>>> c.list_arguments
['a', 'b']

Returns: args – List containing the names of all the arguments required to compute the symbol. list of string
list_outputs()

Lists all the outputs in the symbol.

>>> a = mx.sym.var('a')
>>> b = mx.sym.var('b')
>>> c = a + b
>>> c.list_outputs()
['_plus12_output']

Returns: List of all the outputs. For most symbols, this list contains only the name of this symbol. For symbol groups, this is a list with the names of all symbols in the group. list of str
list_auxiliary_states()

Lists all the auxiliary states in the symbol.

>>> a = mx.sym.var('a')
>>> b = mx.sym.var('b')
>>> c = a + b
>>> c.list_auxiliary_states()
[]


Example of auxiliary states in BatchNorm.

>>> data = mx.symbol.Variable('data')
>>> weight = mx.sym.Variable(name='fc1_weight')
>>> fc1  = mx.symbol.FullyConnected(data = data, weight=weight, name='fc1', num_hidden=128)
>>> fc2 = mx.symbol.BatchNorm(fc1, name='batchnorm0')
>>> fc2.list_auxiliary_states()
['batchnorm0_moving_mean', 'batchnorm0_moving_var']

Returns: aux_states – List of the auxiliary states in input symbol. list of str

Notes

Auxiliary states are special states of symbols that do not correspond to an argument, and are not updated by gradient descent. Common examples of auxiliary states include the moving_mean and moving_variance in BatchNorm. Most operators do not have auxiliary states.

list_inputs()

Lists all arguments and auxiliary states of this Symbol.

Returns: inputs – List of all inputs. list of str

Examples

>>> bn = mx.sym.BatchNorm(name='bn')
>>> bn.list_arguments()
['bn_data', 'bn_gamma', 'bn_beta']
>>> bn.list_auxiliary_states()
['bn_moving_mean', 'bn_moving_var']
>>> bn.list_inputs()
['bn_data', 'bn_gamma', 'bn_beta', 'bn_moving_mean', 'bn_moving_var']

infer_type(*args, **kwargs)

Infers the type of all arguments and all outputs, given the known types for some arguments.

This function takes the known types of some arguments in either positional way or keyword argument way as input. It returns a tuple of None values if there is not enough information to deduce the missing types.

Inconsistencies in the known types will cause an error to be raised.

>>> a = mx.sym.var('a')
>>> b = mx.sym.var('b')
>>> c = a + b
>>> arg_types, out_types, aux_types = c.infer_type(a='float32')
>>> arg_types
[<type 'numpy.float32'>, <type 'numpy.float32'>]
>>> out_types
[<type 'numpy.float32'>]
>>> aux_types
[]

Parameters: *args – Type of known arguments in a positional way. Unknown type can be marked as None. **kwargs – Keyword arguments of known types. arg_types (list of numpy.dtype or None) – List of argument types. The order is same as the order of list_arguments(). out_types (list of numpy.dtype or None) – List of output types. The order is same as the order of list_outputs(). aux_types (list of numpy.dtype or None) – List of auxiliary state types. The order is same as the order of list_auxiliary_states().
infer_shape(*args, **kwargs)

Infers the shapes of all arguments and all outputs given the known shapes of some arguments.

This function takes the known shapes of some arguments in either positional way or keyword argument way as input. It returns a tuple of None values if there is not enough information to deduce the missing shapes.

>>> a = mx.sym.var('a')
>>> b = mx.sym.var('b')
>>> c = a + b
>>> arg_shapes, out_shapes, aux_shapes = c.infer_shape(a=(3,3))
>>> arg_shapes
[(3L, 3L), (3L, 3L)]
>>> out_shapes
[(3L, 3L)]
>>> aux_shapes
[]
>>> c.infer_shape(a=(0,3)) # 0s in shape means unknown dimensions. So, returns None.
(None, None, None)


Inconsistencies in the known shapes will cause an error to be raised. See the following example:

>>> data = mx.sym.Variable('data')
>>> out = mx.sym.FullyConnected(data=data, name='fc1', num_hidden=1000)
>>> out = mx.sym.Activation(data=out, act_type='relu')
>>> out = mx.sym.FullyConnected(data=out, name='fc2', num_hidden=10)
>>> weight_shape= (1, 100)
>>> data_shape = (100, 100)
>>> out.infer_shape(data=data_shape, fc1_weight=weight_shape)
Error in operator fc1: Shape inconsistent, Provided=(1,100), inferred shape=(1000,100)

Parameters: *args – Shape of arguments in a positional way. Unknown shape can be marked as None. **kwargs – Keyword arguments of the known shapes. arg_shapes (list of tuple or None) – List of argument shapes. The order is same as the order of list_arguments(). out_shapes (list of tuple or None) – List of output shapes. The order is same as the order of list_outputs(). aux_shapes (list of tuple or None) – List of auxiliary state shapes. The order is same as the order of list_auxiliary_states().
infer_shape_partial(*args, **kwargs)

Infers the shape partially.

This functions works the same way as infer_shape, except that this function can return partial results.

In the following example, information about fc2 is not available. So, infer_shape will return a tuple of None values but infer_shape_partial will return partial values.

>>> data = mx.sym.Variable('data')
>>> prev = mx.sym.Variable('prev')
>>> fc1  = mx.sym.FullyConnected(data=data, name='fc1', num_hidden=128)
>>> fc2  = mx.sym.FullyConnected(data=prev, name='fc2', num_hidden=128)
>>> out  = mx.sym.Activation(data=mx.sym.elemwise_add(fc1, fc2), act_type='relu')
>>> out.list_arguments()
['data', 'fc1_weight', 'fc1_bias', 'prev', 'fc2_weight', 'fc2_bias']
>>> out.infer_shape(data=(10,64))
(None, None, None)
>>> out.infer_shape_partial(data=(10,64))
([(10L, 64L), (128L, 64L), (128L,), (), (), ()], [(10L, 128L)], [])
>>> # infers shape if you give information about fc2
>>> out.infer_shape(data=(10,64), prev=(10,128))
([(10L, 64L), (128L, 64L), (128L,), (10L, 128L), (128L, 128L), (128L,)], [(10L, 128L)], [])

Parameters: *args – Shape of arguments in a positional way. Unknown shape can be marked as None **kwargs – Keyword arguments of known shapes. arg_shapes (list of tuple or None) – List of argument shapes. The order is same as the order of list_arguments(). out_shapes (list of tuple or None) – List of output shapes. The order is same as the order of list_outputs(). aux_shapes (list of tuple or None) – List of auxiliary state shapes. The order is same as the order of list_auxiliary_states().
debug_str()

Gets a debug string of symbol.

It contains Symbol output, variables and operators in the computation graph with their inputs, variables and attributes.

Returns: Debug string of the symbol. string

Examples

>>> a = mx.sym.Variable('a')
>>> b = mx.sym.sin(a)
>>> c = 2 * a + b
>>> d = mx.sym.FullyConnected(data=c, num_hidden=10)
>>> d.debug_str()
>>> print d.debug_str()
Symbol Outputs:
output[0]=fullyconnected0(0)
Variable:a
--------------------
Op:_mul_scalar, Name=_mulscalar0
Inputs:
arg[0]=a(0) version=0
Attrs:
scalar=2
--------------------
Op:sin, Name=sin0
Inputs:
arg[0]=a(0) version=0
--------------------
Inputs:
arg[0]=_mulscalar0(0)
arg[1]=sin0(0)
Variable:fullyconnected0_weight
Variable:fullyconnected0_bias
--------------------
Op:FullyConnected, Name=fullyconnected0
Inputs:
arg[0]=_plus0(0)
arg[1]=fullyconnected0_weight(0) version=0
arg[2]=fullyconnected0_bias(0) version=0
Attrs:
num_hidden=10

save(fname)

Saves symbol to a file.

You can also use pickle to do the job if you only work on python. The advantage of load/save functions is that the file contents are language agnostic. This means the model saved by one language binding can be loaded by a different language binding of MXNet. You also get the benefit of being able to directly load/save from cloud storage(S3, HDFS).

Parameters: fname (str) – The name of the file. “s3://my-bucket/path/my-s3-symbol” “hdfs://my-bucket/path/my-hdfs-symbol” “/path-to/my-local-symbol”

symbol.load()
Used to load symbol from file.
tojson()

Saves symbol to a JSON string.

symbol.load_json()
Used to load symbol from JSON string.
simple_bind(ctx, grad_req='write', type_dict=None, group2ctx=None, shared_arg_names=None, shared_exec=None, shared_buffer=None, **kwargs)

Bind current symbol to get an executor, allocate all the arguments needed. Allows specifying data types.

This function simplifies the binding procedure. You need to specify only input data shapes. Before binding the executor, the function allocates arguments and auxiliary states that were not explicitly specified. Allows specifying data types.

>>> x = mx.sym.Variable('x')
>>> y = mx.sym.FullyConnected(x, num_hidden=4)
>>> exe = y.simple_bind(mx.cpu(), x=(5,4), grad_req='null')
>>> exe.forward()
[<NDArray 5x4 @cpu(0)>]
>>> exe.outputs[0].asnumpy()
array([[ 0.,  0.,  0.,  0.],
[ 0.,  0.,  0.,  0.],
[ 0.,  0.,  0.,  0.],
[ 0.,  0.,  0.,  0.],
[ 0.,  0.,  0.,  0.]], dtype=float32)
>>> exe.arg_arrays
[<NDArray 5x4 @cpu(0)>, <NDArray 4x4 @cpu(0)>, <NDArray 4 @cpu(0)>]
[<NDArray 5x4 @cpu(0)>, <NDArray 4x4 @cpu(0)>, <NDArray 4 @cpu(0)>]

bind(ctx, args, args_grad=None, grad_req='write', aux_states=None, group2ctx=None, shared_exec=None)

Binds the current symbol to an executor and returns it.

We first declare the computation and then bind to the data to run. This function returns an executor which provides method forward() method for evaluation and a outputs() method to get all the results.

>>> a = mx.sym.Variable('a')
>>> b = mx.sym.Variable('b')
>>> c = a + b
<Symbol _plus1>
>>> ex = c.bind(ctx=mx.cpu(), args={'a' : mx.nd.ones([2,3]), 'b' : mx.nd.ones([2,3])})
>>> ex.forward()
[<NDArray 2x3 @cpu(0)>]
>>> ex.outputs[0].asnumpy()
[[ 2.  2.  2.]
[ 2.  2.  2.]]


Notes

Auxiliary states are the special states of symbols that do not correspond to an argument, and do not have gradient but are still useful for the specific operations. Common examples of auxiliary states include the moving_mean and moving_variance states in BatchNorm. Most operators do not have auxiliary states and in those cases, this parameter can be safely ignored.

One can give up gradient by using a dict in args_grad and only specify gradient they interested in.

gradient(wrt)

Gets the autodiff of current symbol.

This function can only be used if current symbol is a loss function.

Note

This function is currently not implemented.

Parameters: wrt (Array of String) – keyword arguments of the symbol that the gradients are taken. grad – A gradient Symbol with returns to be the corresponding gradients. Symbol
eval(ctx=None, **kwargs)

Evaluates a symbol given arguments.

The eval method combines a call to bind (which returns an executor) with a call to forward (executor method). For the common use case, where you might repeatedly evaluate with same arguments, eval is slow. In that case, you should call bind once and then repeatedly call forward. This function allows simpler syntax for less cumbersome introspection.

>>> a = mx.sym.Variable('a')
>>> b = mx.sym.Variable('b')
>>> c = a + b
>>> ex = c.eval(ctx = mx.cpu(), a = mx.nd.ones([2,3]), b = mx.nd.ones([2,3]))
>>> ex
[<NDArray 2x3 @cpu(0)>]
>>> ex[0].asnumpy()
array([[ 2.,  2.,  2.],
[ 2.,  2.,  2.]], dtype=float32)

Parameters: ctx (Context) – The device context the generated executor to run on. kwargs (Keyword arguments of type NDArray) – Input arguments to the symbol. All the arguments must be provided. result (a list of NDArrays corresponding to the values taken by each symbol when) evaluated on given args. When called on a single symbol (not a group), the result will be a list with one element.
reshape(shape)

Shorthand for mxnet.sym.reshape.

Parameters: shape (tuple of int) – The new shape should not change the array size, namely np.prod(new_shape) should be equal to np.prod(self.shape). One shape dimension can be -1. In this case, the value is inferred from the length of the array and remaining dimensions. A reshaped symbol. Symbol
mxnet.symbol.var(name, attr=None, shape=None, lr_mult=None, wd_mult=None, dtype=None, init=None, **kwargs)

Creates a symbolic variable with specified name.

>>> data = mx.sym.Variable('data', attr={'a': 'b'})
>>> data
<Symbol data>

Parameters: name (str) – Variable name. attr (Dict of strings) – Additional attributes to set on the variable. Format {string : string}. shape (tuple) – The shape of a variable. If specified, this will be used during the shape inference. If one has specified a different shape for this variable using a keyword argument when calling shape inference, this shape information will be ignored. lr_mult (float) – The learning rate multiplier for input variable. wd_mult (float) – Weight decay multiplier for input variable. dtype (str or numpy.dtype) – The dtype for input variable. If not specified, this value will be inferred. init (initializer (mxnet.init.*)) – Initializer for this variable to (optionally) override the default initializer. kwargs (Additional attribute variables) – Additional attributes must start and end with double underscores. variable – A symbol corresponding to an input to the computation graph. Symbol
mxnet.symbol.Variable(name, attr=None, shape=None, lr_mult=None, wd_mult=None, dtype=None, init=None, **kwargs)

Creates a symbolic variable with specified name.

>>> data = mx.sym.Variable('data', attr={'a': 'b'})
>>> data
<Symbol data>

Parameters: name (str) – Variable name. attr (Dict of strings) – Additional attributes to set on the variable. Format {string : string}. shape (tuple) – The shape of a variable. If specified, this will be used during the shape inference. If one has specified a different shape for this variable using a keyword argument when calling shape inference, this shape information will be ignored. lr_mult (float) – The learning rate multiplier for input variable. wd_mult (float) – Weight decay multiplier for input variable. dtype (str or numpy.dtype) – The dtype for input variable. If not specified, this value will be inferred. init (initializer (mxnet.init.*)) – Initializer for this variable to (optionally) override the default initializer. kwargs (Additional attribute variables) – Additional attributes must start and end with double underscores. variable – A symbol corresponding to an input to the computation graph. Symbol
mxnet.symbol.Group(symbols)

Creates a symbol that contains a collection of other symbols, grouped together.

>>> a = mx.sym.Variable('a')
>>> b = mx.sym.Variable('b')
>>> mx.sym.Group([a,b])
<Symbol Grouped>

Parameters: symbols (list) – List of symbols to be grouped. sym – A group symbol. Symbol
mxnet.symbol.load(fname)

Loads symbol from a JSON file.

You can also use pickle to do the job if you only work on python. The advantage of load/save is the file is language agnostic. This means the file saved using save can be loaded by other language binding of mxnet. You also get the benefit being able to directly load/save from cloud storage(S3, HDFS).

Parameters: fname (str) – The name of the file, examples: s3://my-bucket/path/my-s3-symbol hdfs://my-bucket/path/my-hdfs-symbol /path-to/my-local-symbol sym – The loaded symbol. Symbol

Symbol.save()
Used to save symbol into file.
mxnet.symbol.load_json(json_str)

Parameters: json_str (str) – A JSON string. sym – The loaded symbol. Symbol

Symbol.tojson()
Used to save symbol into json string.
mxnet.symbol.pow(base, exp)

Returns element-wise result of base element raised to powers from exp element.

Parameters: base (Symbol or scalar) – The base symbol exp (Symbol or scalar) – The exponent symbol The bases in x raised to the exponents in y. Symbol or scalar

Examples

>>> mx.sym.pow(2, 3)
8
>>> x = mx.sym.Variable('x')
>>> y = mx.sym.Variable('y')
>>> z = mx.sym.pow(x, 2)
>>> z.eval(x=mx.nd.array([1,2]))[0].asnumpy()
array([ 1.,  4.], dtype=float32)
>>> z = mx.sym.pow(3, y)
>>> z.eval(y=mx.nd.array([2,3]))[0].asnumpy()
array([  9.,  27.], dtype=float32)
>>> z = mx.sym.pow(x, y)
>>> z.eval(x=mx.nd.array([3,4]), y=mx.nd.array([2,3]))[0].asnumpy()
array([  9.,  64.], dtype=float32)

mxnet.symbol.maximum(left, right)

Returns element-wise maximum of the input elements.

Both inputs can be Symbol or scalar number. Broadcasting is not supported.

Parameters: left (Symbol or scalar) – First symbol to be compared. right (Symbol or scalar) – Second symbol to be compared. The element-wise maximum of the input symbols. Symbol or scalar

Examples

>>> mx.sym.maximum(2, 3.5)
3.5
>>> x = mx.sym.Variable('x')
>>> y = mx.sym.Variable('y')
>>> z = mx.sym.maximum(x, 4)
>>> z.eval(x=mx.nd.array([3,5,2,10]))[0].asnumpy()
array([  4.,   5.,   4.,  10.], dtype=float32)
>>> z = mx.sym.maximum(x, y)
>>> z.eval(x=mx.nd.array([3,4]), y=mx.nd.array([10,2]))[0].asnumpy()
array([ 10.,   4.], dtype=float32)

mxnet.symbol.minimum(left, right)

Returns element-wise minimum of the input elements.

Both inputs can be Symbol or scalar number. Broadcasting is not supported.

Parameters: left (Symbol or scalar) – First symbol to be compared. right (Symbol or scalar) – Second symbol to be compared. The element-wise minimum of the input symbols. Symbol or scalar

Examples

>>> mx.sym.minimum(2, 3.5)
2
>>> x = mx.sym.Variable('x')
>>> y = mx.sym.Variable('y')
>>> z = mx.sym.minimum(x, 4)
>>> z.eval(x=mx.nd.array([3,5,2,10]))[0].asnumpy()
array([ 3.,  4.,  2.,  4.], dtype=float32)
>>> z = mx.sym.minimum(x, y)
>>> z.eval(x=mx.nd.array([3,4]), y=mx.nd.array([10,2]))[0].asnumpy()
array([ 3.,  2.], dtype=float32)

mxnet.symbol.hypot(left, right)

Given the “legs” of a right triangle, returns its hypotenuse.

Equivalent to $$\sqrt(left^2 + right^2)$$, element-wise. Both inputs can be Symbol or scalar number. Broadcasting is not supported.

Parameters: left (Symbol or scalar) – First leg of the triangle(s). right (Symbol or scalar) – Second leg of the triangle(s). The hypotenuse of the triangle(s) Symbol or scalar

Examples

>>> mx.sym.hypot(3, 4)
5.0
>>> x = mx.sym.Variable('x')
>>> y = mx.sym.Variable('y')
>>> z = mx.sym.hypot(x, 4)
>>> z.eval(x=mx.nd.array([3,5,2]))[0].asnumpy()
array([ 5.,  6.40312433,  4.47213602], dtype=float32)
>>> z = mx.sym.hypot(x, y)
>>> z.eval(x=mx.nd.array([3,4]), y=mx.nd.array([10,2]))[0].asnumpy()
array([ 10.44030666,   4.47213602], dtype=float32)

mxnet.symbol.zeros(shape, dtype=None, **kwargs)

Returns a new symbol of given shape and type, filled with zeros.

Parameters: shape (int or sequence of ints) – Shape of the new array. dtype (str or numpy.dtype, optional) – The value type of the inner value, default to np.float32. out – The created Symbol. Symbol
mxnet.symbol.ones(shape, dtype=None, **kwargs)

Returns a new symbol of given shape and type, filled with ones.

Parameters: shape (int or sequence of ints) – Shape of the new array. dtype (str or numpy.dtype, optional) – The value type of the inner value, default to np.float32. out – The created Symbol Symbol
mxnet.symbol.full(shape, val, dtype=None, **kwargs)

Returns a new array of given shape and type, filled with the given value val.

Parameters: shape (int or sequence of ints) – Shape of the new array. val (scalar) – Fill value. dtype (str or numpy.dtype, optional) – The value type of the inner value, default to np.float32. out – The created Symbol Symbol
mxnet.symbol.arange(start, stop=None, step=1.0, repeat=1, name=None, dtype=None)

Returns evenly spaced values within a given interval.

Parameters: start (number) – Start of interval. The interval includes this value. The default start value is 0. stop (number, optional) – End of interval. The interval does not include this value. step (number, optional) – Spacing between values. repeat (int, optional) – “The repeating time of all elements. E.g repeat=3, the element a will be repeated three times –> a, a, a. dtype (str or numpy.dtype, optional) – The value type of the inner value, default to np.float32. out – The created Symbol Symbol
mxnet.symbol.Activation(data=None, act_type=_Null, name=None, attr=None, out=None, **kwargs)

Applies an activation function element-wise to the input.

The following activation functions are supported:

• relu: Rectified Linear Unit, $$y = max(x, 0)$$
• sigmoid: $$y = \frac{1}{1 + exp(-x)}$$
• tanh: Hyperbolic tangent, $$y = \frac{exp(x) - exp(-x)}{exp(x) + exp(-x)}$$
• softrelu: Soft ReLU, or SoftPlus, $$y = log(1 + exp(x))$$

Defined in src/operator/activation.cc:L91

Parameters: data (Symbol) – Input array to activation function. act_type ({'relu', 'sigmoid', 'softrelu', 'tanh'}, required) – Activation function to be applied. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol

Examples

A one-hidden-layer MLP with ReLU activation:

>>> data = Variable('data')
>>> mlp = FullyConnected(data=data, num_hidden=128, name='proj')
>>> mlp = Activation(data=mlp, act_type='relu', name='activation')
>>> mlp = FullyConnected(data=mlp, num_hidden=10, name='mlp')
>>> mlp
<Symbol mlp>


ReLU activation

>>> test_suites = [
... ('relu', lambda x: np.maximum(x, 0)),
... ('sigmoid', lambda x: 1 / (1 + np.exp(-x))),
... ('tanh', lambda x: np.tanh(x)),
... ('softrelu', lambda x: np.log(1 + np.exp(x)))
... ]
>>> x = test_utils.random_arrays((2, 3, 4))
>>> for act_type, numpy_impl in test_suites:
... op = Activation(act_type=act_type, name='act')
... y = test_utils.simple_forward(op, act_data=x)
... y_np = numpy_impl(x)
... print('%s: %s' % (act_type, test_utils.almost_equal(y, y_np)))
relu: True
sigmoid: True
tanh: True
softrelu: True

mxnet.symbol.BatchNorm(data=None, gamma=None, beta=None, moving_mean=None, moving_var=None, eps=_Null, momentum=_Null, fix_gamma=_Null, use_global_stats=_Null, output_mean_var=_Null, axis=_Null, cudnn_off=_Null, name=None, attr=None, out=None, **kwargs)

Batch normalization.

Normalizes a data batch by mean and variance, and applies a scale gamma as well as offset beta.

Assume the input has more than one dimension and we normalize along axis 1. We first compute the mean and variance along this axis:

$\begin{split}data\_mean[i] = mean(data[:,i,:,...]) \\ data\_var[i] = var(data[:,i,:,...])\end{split}$

Then compute the normalized output, which has the same shape as input, as following:

$out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]$

Both mean and var returns a scalar by treating the input as a vector.

Assume the input has size k on axis 1, then both gamma and beta have shape (k,). If output_mean_var is set to be true, then outputs both data_mean and data_var as well, which are needed for the backward pass.

Besides the inputs and the outputs, this operator accepts two auxiliary states, moving_mean and moving_var, which are k-length vectors. They are global statistics for the whole dataset, which are updated by:

moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
moving_var = moving_var * momentum + data_var * (1 - momentum)


If use_global_stats is set to be true, then moving_mean and moving_var are used instead of data_mean and data_var to compute the output. It is often used during inference.

The parameter axis specifies which axis of the input shape denotes the ‘channel’ (separately normalized groups). The default is 1. Specifying -1 sets the channel axis to be the last item in the input shape.

Both gamma and beta are learnable parameters. But if fix_gamma is true, then set gamma to 1 and its gradient to 0.

Defined in src/operator/batch_norm.cc:L399

Parameters: data (Symbol) – Input data to batch normalization gamma (Symbol) – gamma array beta (Symbol) – beta array moving_mean (Symbol) – running mean of input moving_var (Symbol) – running variance of input eps (double, optional, default=0.001) – Epsilon to prevent div 0. Must be no less than CUDNN_BN_MIN_EPSILON defined in cudnn.h when using cudnn (usually 1e-5) momentum (float, optional, default=0.9) – Momentum for moving average fix_gamma (boolean, optional, default=True) – Fix gamma while training use_global_stats (boolean, optional, default=False) – Whether use global moving statistics instead of local batch-norm. This will force change batch-norm into a scale shift operator. output_mean_var (boolean, optional, default=False) – Output All,normal mean and var axis (int, optional, default='1') – Specify which shape axis the channel is specified cudnn_off (boolean, optional, default=False) – Do not select CUDNN operator, if available name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.BatchNorm_v1(data=None, gamma=None, beta=None, eps=_Null, momentum=_Null, fix_gamma=_Null, use_global_stats=_Null, output_mean_var=_Null, name=None, attr=None, out=None, **kwargs)

Batch normalization.

Normalizes a data batch by mean and variance, and applies a scale gamma as well as offset beta.

Assume the input has more than one dimension and we normalize along axis 1. We first compute the mean and variance along this axis:

$\begin{split}data\_mean[i] = mean(data[:,i,:,...]) \\ data\_var[i] = var(data[:,i,:,...])\end{split}$

Then compute the normalized output, which has the same shape as input, as following:

$out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]$

Both mean and var returns a scalar by treating the input as a vector.

Assume the input has size k on axis 1, then both gamma and beta have shape (k,). If output_mean_var is set to be true, then outputs both data_mean and data_var as well, which are needed for the backward pass.

Besides the inputs and the outputs, this operator accepts two auxiliary states, moving_mean and moving_var, which are k-length vectors. They are global statistics for the whole dataset, which are updated by:

moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
moving_var = moving_var * momentum + data_var * (1 - momentum)


If use_global_stats is set to be true, then moving_mean and moving_var are used instead of data_mean and data_var to compute the output. It is often used during inference.

Both gamma and beta are learnable parameters. But if fix_gamma is true, then set gamma to 1 and its gradient to 0.

Defined in src/operator/batch_norm_v1.cc:L89

Parameters: data (Symbol) – Input data to batch normalization gamma (Symbol) – gamma array beta (Symbol) – beta array eps (float, optional, default=0.001) – Epsilon to prevent div 0 momentum (float, optional, default=0.9) – Momentum for moving average fix_gamma (boolean, optional, default=True) – Fix gamma while training use_global_stats (boolean, optional, default=False) – Whether use global moving statistics instead of local batch-norm. This will force change batch-norm into a scale shift operator. output_mean_var (boolean, optional, default=False) – Output All,normal mean and var name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.BilinearSampler(data=None, grid=None, name=None, attr=None, out=None, **kwargs)

Applies bilinear sampling to input feature map.

Bilinear Sampling is the key of [NIPS2015] “Spatial Transformer Networks”. The usage of the operator is very similar to remap function in OpenCV, except that the operator has the backward pass.

Given $$data$$ and $$grid$$, then the output is computed by

$\begin{split}x_{src} = grid[batch, 0, y_{dst}, x_{dst}] \\ y_{src} = grid[batch, 1, y_{dst}, x_{dst}] \\ output[batch, channel, y_{dst}, x_{dst}] = G(data[batch, channel, y_{src}, x_{src})\end{split}$

$$x_{dst}$$, $$y_{dst}$$ enumerate all spatial locations in $$output$$, and $$G()$$ denotes the bilinear interpolation kernel. The out-boundary points will be padded with zeros.The shape of the output will be (data.shape[0], data.shape[1], grid.shape[2], grid.shape[3]).

The operator assumes that $$data$$ has ‘NCHW’ layout and $$grid$$ has been normalized to [-1, 1].

BilinearSampler often cooperates with GridGenerator which generates sampling grids for BilinearSampler. GridGenerator supports two kinds of transformation: affine and warp. If users want to design a CustomOp to manipulate $$grid$$, please firstly refer to the code of GridGenerator.

Example 1:

## Zoom out data two times
data = array([[[[1, 4, 3, 6],
[1, 8, 8, 9],
[0, 4, 1, 5],
[1, 0, 1, 3]]]])

affine_matrix = array([[2, 0, 0],
[0, 2, 0]])

affine_matrix = reshape(affine_matrix, shape=(1, 6))

grid = GridGenerator(data=affine_matrix, transform_type='affine', target_shape=(4, 4))

out = BilinearSampler(data, grid)

out
[[[[ 0,   0,     0,   0],
[ 0,   3.5,   6.5, 0],
[ 0,   1.25,  2.5, 0],
[ 0,   0,     0,   0]]]


Example 2:

## shift data horizontally by -1 pixel

data = array([[[[1, 4, 3, 6],
[1, 8, 8, 9],
[0, 4, 1, 5],
[1, 0, 1, 3]]]])

warp_maxtrix = array([[[[1, 1, 1, 1],
[1, 1, 1, 1],
[1, 1, 1, 1],
[1, 1, 1, 1]],
[[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]]]])

grid = GridGenerator(data=warp_matrix, transform_type='warp')
out = BilinearSampler(data, grid)

out
[[[[ 4,  3,  6,  0],
[ 8,  8,  9,  0],
[ 4,  1,  5,  0],
[ 0,  1,  3,  0]]]


Defined in src/operator/bilinear_sampler.cc:L244

Parameters: data (Symbol) – Input data to the BilinearsamplerOp. grid (Symbol) – Input grid to the BilinearsamplerOp.grid has two channels: x_src, y_src name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.BlockGrad(data=None, name=None, attr=None, out=None, **kwargs)

Stops the accumulated gradient of the inputs from flowing through this operator in the backward direction. In other words, this operator prevents the contribution of its inputs to be taken into account for computing gradients.

Example:

v1 = [1, 2]
v2 = [0, 1]
a = Variable('a')
b = Variable('b')

executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2))
executor.forward(is_train=True, a=v1, b=v2)
executor.outputs
[ 1.  5.]

executor.backward()
[ 0.  0.]
[ 1.  1.]


Defined in src/operator/tensor/elemwise_unary_op.cc:L117

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.Cast(data=None, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Casts all elements of the input to a new type.

Note

Cast is deprecated. Use cast instead.

Example:

cast([0.9, 1.3], dtype='int32') = [0, 1]
cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]


Defined in src/operator/tensor/elemwise_unary_op.cc:L193

Parameters: data (Symbol) – The input. dtype ({'float16', 'float32', 'float64', 'int32', 'uint8'}, required) – Output data type. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.Concat(*data, **kwargs)

Joins input arrays along a given axis.

Note

Concat is deprecated. Use concat instead.

The dimensions of the input arrays should be the same except the axis along which they will be concatenated. The dimension of the output array along the concatenated axis will be equal to the sum of the corresponding dimensions of the input arrays.

Example:

x = [[1,1],[2,2]]
y = [[3,3],[4,4],[5,5]]
z = [[6,6], [7,7],[8,8]]

concat(x,y,z,dim=0) = [[ 1.,  1.],
[ 2.,  2.],
[ 3.,  3.],
[ 4.,  4.],
[ 5.,  5.],
[ 6.,  6.],
[ 7.,  7.],
[ 8.,  8.]]

Note that you cannot concat x,y,z along dimension 1 since dimension
0 is not the same for all the input arrays.

concat(y,z,dim=1) = [[ 3.,  3.,  6.,  6.],
[ 4.,  4.,  7.,  7.],
[ 5.,  5.,  8.,  8.]]


Defined in src/operator/concat.cc:L98 This function support variable length of positional input.

Parameters: data (Symbol[]) – List of arrays to concatenate dim (int, optional, default='1') – the dimension to be concated. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol

Examples

Concat two (or more) inputs along a specific dimension:

>>> a = Variable('a')
>>> b = Variable('b')
>>> c = Concat(a, b, dim=1, name='my-concat')
>>> c
<Symbol my-concat>
>>> SymbolDoc.get_output_shape(c, a=(128, 10, 3, 3), b=(128, 15, 3, 3))
{'my-concat_output': (128L, 25L, 3L, 3L)}


Note the shape should be the same except on the dimension that is being concatenated.

mxnet.symbol.Convolution(data=None, weight=None, bias=None, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, num_filter=_Null, num_group=_Null, workspace=_Null, no_bias=_Null, cudnn_tune=_Null, cudnn_off=_Null, layout=_Null, name=None, attr=None, out=None, **kwargs)

Compute N-D convolution on (N+2)-D input.

In the 2-D convolution, given input data with shape (batch_size, channel, height, width), the output is computed by

$out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star weight[i,j,:,:]$

where $$\star$$ is the 2-D cross-correlation operator.

For general 2-D convolution, the shapes are

• data: (batch_size, channel, height, width)
• weight: (num_filter, channel, kernel[0], kernel[1])
• bias: (num_filter,)
• out: (batch_size, num_filter, out_height, out_width).

Define:

f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1


then we have:

out_height=f(height, kernel[0], pad[0], stride[0], dilate[0])


If no_bias is set to be true, then the bias term is ignored.

The default data layout is NCHW, namely (batch_size, channel, height, width). We can choose other layouts such as NHWC.

If num_group is larger than 1, denoted by g, then split the input data evenly into g parts along the channel axis, and also evenly split weight along the first dimension. Next compute the convolution on the i-th part of the data with the i-th weight part. The output is obtained by concatenating all the g results.

1-D convolution does not have height dimension but only width in space.

• data: (batch_size, channel, width)
• weight: (num_filter, channel, kernel[0])
• bias: (num_filter,)
• out: (batch_size, num_filter, out_width).

3-D convolution adds an additional depth dimension besides height and width. The shapes are

• data: (batch_size, channel, depth, height, width)
• weight: (num_filter, channel, kernel[0], kernel[1], kernel[2])
• bias: (num_filter,)
• out: (batch_size, num_filter, out_depth, out_height, out_width).

Both weight and bias are learnable parameters.

There are other options to tune the performance.

• cudnn_tune: enable this option leads to higher startup time but may give faster speed. Options are
• off: no tuning
• limited_workspace:run test and pick the fastest algorithm that doesn’t exceed workspace limit.
• fastest: pick the fastest algorithm and ignore workspace limit.
• None (default): the behavior is determined by environment variable MXNET_CUDNN_AUTOTUNE_DEFAULT. 0 for off, 1 for limited workspace (default), 2 for fastest.
• workspace: A large number leads to more (GPU) memory usage but may improve the performance.

Defined in src/operator/convolution.cc:L169

Parameters: data (Symbol) – Input data to the ConvolutionOp. weight (Symbol) – Weight matrix. bias (Symbol) – Bias parameter. kernel (Shape(tuple), required) – convolution kernel size: (h, w) or (d, h, w) stride (Shape(tuple), optional, default=()) – convolution stride: (h, w) or (d, h, w) dilate (Shape(tuple), optional, default=()) – convolution dilate: (h, w) or (d, h, w) pad (Shape(tuple), optional, default=()) – pad for convolution: (h, w) or (d, h, w) num_filter (int (non-negative), required) – convolution filter(channel) number num_group (int (non-negative), optional, default=1) – Number of group partitions. workspace (long (non-negative), optional, default=1024) – Maximum temporary workspace allowed for convolution (MB). no_bias (boolean, optional, default=False) – Whether to disable bias parameter. cudnn_tune ({None, 'fastest', 'limited_workspace', 'off'},optional, default='None') – Whether to pick convolution algo by running performance test. cudnn_off (boolean, optional, default=False) – Turn off cudnn for this layer. layout ({None, 'NCDHW', 'NCHW', 'NCW', 'NDHWC', 'NHWC'},optional, default='None') – Set layout for input, output and weight. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.Convolution_v1(data=None, weight=None, bias=None, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, num_filter=_Null, num_group=_Null, workspace=_Null, no_bias=_Null, cudnn_tune=_Null, cudnn_off=_Null, layout=_Null, name=None, attr=None, out=None, **kwargs)

This operator is DEPRECATED. Apply convolution to input then add a bias.

Parameters: data (Symbol) – Input data to the ConvolutionV1Op. weight (Symbol) – Weight matrix. bias (Symbol) – Bias parameter. kernel (Shape(tuple), required) – convolution kernel size: (h, w) or (d, h, w) stride (Shape(tuple), optional, default=()) – convolution stride: (h, w) or (d, h, w) dilate (Shape(tuple), optional, default=()) – convolution dilate: (h, w) or (d, h, w) pad (Shape(tuple), optional, default=()) – pad for convolution: (h, w) or (d, h, w) num_filter (int (non-negative), required) – convolution filter(channel) number num_group (int (non-negative), optional, default=1) – Number of group partitions. Equivalent to slicing input into num_group partitions, apply convolution on each, then concatenate the results workspace (long (non-negative), optional, default=1024) – Maximum tmp workspace allowed for convolution (MB). no_bias (boolean, optional, default=False) – Whether to disable bias parameter. cudnn_tune ({None, 'fastest', 'limited_workspace', 'off'},optional, default='None') – Whether to pick convolution algo by running performance test. Leads to higher startup time but may give faster speed. Options are: ‘off’: no tuning ‘limited_workspace’: run test and pick the fastest algorithm that doesn’t exceed workspace limit. ‘fastest’: pick the fastest algorithm and ignore workspace limit. If set to None (default), behavior is determined by environment variable MXNET_CUDNN_AUTOTUNE_DEFAULT: 0 for off, 1 for limited workspace (default), 2 for fastest. cudnn_off (boolean, optional, default=False) – Turn off cudnn for this layer. layout ({None, 'NCDHW', 'NCHW', 'NDHWC', 'NHWC'},optional, default='None') – Set layout for input, output and weight. Empty for default layout: NCHW for 2d and NCDHW for 3d. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.Correlation(data1=None, data2=None, kernel_size=_Null, max_displacement=_Null, stride1=_Null, stride2=_Null, pad_size=_Null, is_multiply=_Null, name=None, attr=None, out=None, **kwargs)

Applies correlation to inputs.

The correlation layer performs multiplicative patch comparisons between two feature maps.

Given two multi-channel feature maps $$f_{1}, f_{2}$$, with $$w$$, $$h$$, and $$c$$ being their width, height, and number of channels, the correlation layer lets the network compare each patch from $$f_{1}$$ with each patch from $$f_{2}$$.

For now we consider only a single comparison of two patches. The ‘correlation’ of two patches centered at $$x_{1}$$ in the first map and $$x_{2}$$ in the second map is then defined as:

$\begin{split}c(x_{1}, x_{2}) = \sum_{o \in [-k,k] \times [-k,k]} <f_{1}(x_{1} + o), f_{2}(x_{2} + o)>\end{split}$

for a square patch of size $$K:=2k+1$$.

Note that the equation above is identical to one step of a convolution in neural networks, but instead of convolving data with a filter, it convolves data with other data. For this reason, it has no training weights.

Computing $$c(x_{1}, x_{2})$$ involves $$c * K^{2}$$ multiplications. Comparing all patch combinations involves $$w^{2}*h^{2}$$ such computations.

Given a maximum displacement $$d$$, for each location $$x_{1}$$ it computes correlations $$c(x_{1}, x_{2})$$ only in a neighborhood of size $$D:=2d+1$$, by limiting the range of $$x_{2}$$. We use strides $$s_{1}, s_{2}$$, to quantize $$x_{1}$$ globally and to quantize $$x_{2}$$ within the neighborhood centered around $$x_{1}$$.

The final output is defined by the following expression:

$out[n, q, i, j] = c(x_{i, j}, x_{q})$

where $$i$$ and $$j$$ enumerate spatial locations in $$f_{1}$$, and $$q$$ denotes the $$q^{th}$$ neighborhood of $$x_{i,j}$$.

Defined in src/operator/correlation.cc:L191

Parameters: data1 (Symbol) – Input data1 to the correlation. data2 (Symbol) – Input data2 to the correlation. kernel_size (int (non-negative), optional, default=1) – kernel size for Correlation must be an odd number max_displacement (int (non-negative), optional, default=1) – Max displacement of Correlation stride1 (int (non-negative), optional, default=1) – stride1 quantize data1 globally stride2 (int (non-negative), optional, default=1) – stride2 quantize data2 within the neighborhood centered around data1 pad_size (int (non-negative), optional, default=0) – pad for Correlation is_multiply (boolean, optional, default=True) – operation type is either multiplication or subduction name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.Crop(*data, **kwargs)

Note

Crop is deprecated. Use slice instead.

Crop the 2nd and 3rd dim of input data, with the corresponding size of h_w or with width and height of the second input symbol, i.e., with one input, we need h_w to specify the crop height and width, otherwise the second input symbol’s size will be used

Defined in src/operator/crop.cc:L49 This function support variable length of positional input.

Parameters: data (Symbol or Symbol[]) – Tensor or List of Tensors, the second input will be used as crop_like shape reference offset (Shape(tuple), optional, default=(0,0)) – crop offset coordinate: (y, x) h_w (Shape(tuple), optional, default=(0,0)) – crop height and width: (h, w) center_crop (boolean, optional, default=False) – If set to true, then it will use be the center_crop,or it will crop using the shape of crop_like name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.Custom(*data, **kwargs)

Apply a custom operator implemented in a frontend language (like Python).

Custom operators should override required methods like forward and backward. The custom operator must be registered before it can be used. Please check the tutorial here: http://mxnet.io/how_to/new_op.html.

Defined in src/operator/custom/custom.cc:L355

Parameters: data (Symbol[]) – Input data for the custom operator. op_type (string) – Name of the custom operator. This is the name that is passed to mx.operator.register to register the operator. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.Deconvolution(data=None, weight=None, bias=None, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, adj=_Null, target_shape=_Null, num_filter=_Null, num_group=_Null, workspace=_Null, no_bias=_Null, cudnn_tune=_Null, cudnn_off=_Null, layout=_Null, name=None, attr=None, out=None, **kwargs)

Computes 2D transposed convolution (aka fractionally strided convolution) of the input tensor. This operation can be seen as the gradient of Convolution operation with respect to its input. Convolution usually reduces the size of the input. Transposed convolution works the other way, going from a smaller input to a larger output while preserving the connectivity pattern.

Parameters: data (Symbol) – Input tensor to the deconvolution operation. weight (Symbol) – Weights representing the kernel. bias (Symbol) – Bias added to the result after the deconvolution operation. kernel (Shape(tuple), required) – Deconvolution kernel size: (h, w) or (d, h, w). This is same as the kernel size used for the corresponding convolution stride (Shape(tuple), optional, default=()) – The stride used for the corresponding convolution: (h, w) or (d, h, w). dilate (Shape(tuple), optional, default=()) – Dilation factor for each dimension of the input: (h, w) or (d, h, w). pad (Shape(tuple), optional, default=()) – The amount of implicit zero padding added during convolution for each dimension of the input: (h, w) or (d, h, w). (kernel-1)/2 is usually a good choice. If target_shape is set, pad will be ignored and a padding that will generate the target shape will be used. adj (Shape(tuple), optional, default=()) – Adjustment for output shape: (h, w) or (d, h, w). If target_shape is set, adj will be ignored and computed accordingly. target_shape (Shape(tuple), optional, default=()) – Shape of the output tensor: (h, w) or (d, h, w). num_filter (int (non-negative), required) – Number of output filters. num_group (int (non-negative), optional, default=1) – Number of groups partition. workspace (long (non-negative), optional, default=512) – Maximum temporal workspace allowed for deconvolution (MB). no_bias (boolean, optional, default=True) – Whether to disable bias parameter. cudnn_tune ({None, 'fastest', 'limited_workspace', 'off'},optional, default='None') – Whether to pick convolution algorithm by running performance test. cudnn_off (boolean, optional, default=False) – Turn off cudnn for this layer. layout ({None, 'NCDHW', 'NCHW', 'NCW', 'NDHWC', 'NHWC'},optional, default='None') – Set layout for input, output and weight. Empty for default layout, NCW for 1d, NCHW for 2d and NCDHW for 3d. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.Dropout(data=None, p=_Null, mode=_Null, name=None, attr=None, out=None, **kwargs)

Applies dropout operation to input array.

• During training, each element of the input is set to zero with probability p. The whole array is rescaled by $$1/(1-p)$$ to keep the expected sum of the input unchanged.
• During testing, this operator does not change the input if mode is ‘training’. If mode is ‘always’, the same computaion as during training will be applied.

Example:

random.seed(998)
input_array = array([[3., 0.5,  -0.5,  2., 7.],
[2., -0.4,   7.,  3., 0.2]])
a = symbol.Variable('a')
dropout = symbol.Dropout(a, p = 0.2)
executor = dropout.simple_bind(a = input_array.shape)

## If training
executor.forward(is_train = True, a = input_array)
executor.outputs
[[ 3.75   0.625 -0.     2.5    8.75 ]
[ 2.5   -0.5    8.75   3.75   0.   ]]

## If testing
executor.forward(is_train = False, a = input_array)
executor.outputs
[[ 3.     0.5   -0.5    2.     7.   ]
[ 2.    -0.4    7.     3.     0.2  ]]


Defined in src/operator/dropout.cc:L77

Parameters: data (Symbol) – Input array to which dropout will be applied. p (float, optional, default=0.5) – Fraction of the input that gets dropped out during training time. mode ({'always', 'training'},optional, default='training') – Whether to only turn on dropout during training or to also turn on for inference. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol

Examples

Apply dropout to corrupt input as zero with probability 0.2:

>>> data = Variable('data')
>>> data_dp = Dropout(data=data, p=0.2)

>>> shape = (100, 100)  # take larger shapes to be more statistical stable
>>> x = np.ones(shape)
>>> op = Dropout(p=0.5, name='dp')
>>> # dropout is identity during testing
>>> y = test_utils.simple_forward(op, dp_data=x, is_train=False)
>>> test_utils.almost_equal(x, y)
True
>>> y = test_utils.simple_forward(op, dp_data=x, is_train=True)
>>> # expectation is (approximately) unchanged
>>> np.abs(x.mean() - y.mean()) < 0.1
True
>>> set(np.unique(y)) == set([0, 2])
True

mxnet.symbol.ElementWiseSum(*args, **kwargs)

$add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n$

add_n is potentially more efficient than calling add by n times.

Defined in src/operator/tensor/elemwise_sum.cc:L65 This function support variable length of positional input.

Parameters: args (Symbol[]) – Positional input arguments name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.Embedding(data=None, weight=None, input_dim=_Null, output_dim=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Maps integer indices to vector representations (embeddings).

This operator maps words to real-valued vectors in a high-dimensional space, called word embeddings. These embeddings can capture semantic and syntactic properties of the words. For example, it has been noted that in the learned embedding spaces, similar words tend to be close to each other and dissimilar words far apart.

For an input array of shape (d1, ..., dK), the shape of an output array is (d1, ..., dK, output_dim). All the input values should be integers in the range [0, input_dim).

If the input_dim is ip0 and output_dim is op0, then shape of the embedding weight matrix must be (ip0, op0).

By default, if any index mentioned is too large, it is replaced by the index that addresses the last vector in an embedding matrix.

Examples:

input_dim = 4
output_dim = 5

// Each row in weight matrix y represents a word. So, y = (w0,w1,w2,w3)
y = [[  0.,   1.,   2.,   3.,   4.],
[  5.,   6.,   7.,   8.,   9.],
[ 10.,  11.,  12.,  13.,  14.],
[ 15.,  16.,  17.,  18.,  19.]]

// Input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)]
x = [[ 1.,  3.],
[ 0.,  2.]]

// Mapped input x to its vector representation y.
Embedding(x, y, 4, 5) = [[[  5.,   6.,   7.,   8.,   9.],
[ 15.,  16.,  17.,  18.,  19.]],

[[  0.,   1.,   2.,   3.,   4.],
[ 10.,  11.,  12.,  13.,  14.]]]


Defined in src/operator/tensor/indexing_op.cc:L73

Parameters: data (Symbol) – The input array to the embedding operator. weight (Symbol) – The embedding weight matrix. input_dim (int, required) – Vocabulary size of the input indices. output_dim (int, required) – Dimension of the embedding vectors. dtype ({'float16', 'float32', 'float64', 'int32', 'uint8'},optional, default='float32') – Data type of weight. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol

Examples

Assume we want to map the 26 English alphabet letters to 16-dimensional vectorial representations.

>>> vocabulary_size = 26
>>> embed_dim = 16
>>> seq_len, batch_size = (10, 64)
>>> input = Variable('letters')
>>> op = Embedding(data=input, input_dim=vocabulary_size, output_dim=embed_dim,
...name='embed')
>>> SymbolDoc.get_output_shape(op, letters=(seq_len, batch_size))
{'embed_output': (10L, 64L, 16L)}

>>> vocab_size, embed_dim = (26, 16)
>>> batch_size = 12
>>> word_vecs = test_utils.random_arrays((vocab_size, embed_dim))
>>> op = Embedding(name='embed', input_dim=vocab_size, output_dim=embed_dim)
>>> x = np.random.choice(vocab_size, batch_size)
>>> y = test_utils.simple_forward(op, embed_data=x, embed_weight=word_vecs)
>>> y_np = word_vecs[x]
>>> test_utils.almost_equal(y, y_np)
True

mxnet.symbol.Flatten(data=None, name=None, attr=None, out=None, **kwargs)

Flattens the input array into a 2-D array by collapsing the higher dimensions.

Note

Flatten is deprecated. Use flatten instead.

For an input array with shape (d1, d2, ..., dk), flatten operation reshapes the input array into an output array of shape (d1, d2*...*dk).

Example:

x = [[
[1,2,3],
[4,5,6],
[7,8,9]
],
[    [1,2,3],
[4,5,6],
[7,8,9]
]],

flatten(x) = [[ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.],
[ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.]]


Defined in src/operator/tensor/matrix_op.cc:L150

Parameters: data (Symbol) – Input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol

Examples

Flatten is usually applied before FullyConnected, to reshape the 4D tensor produced by convolutional layers to 2D matrix:

>>> data = Variable('data')  # say this is 4D from some conv/pool
>>> flatten = Flatten(data=data, name='flat')  # now this is 2D
>>> SymbolDoc.get_output_shape(flatten, data=(2, 3, 4, 5))
{'flat_output': (2L, 60L)}

>>> test_dims = [(2, 3, 4, 5), (2, 3), (2,)]
>>> op = Flatten(name='flat')
>>> for dims in test_dims:
... x = test_utils.random_arrays(dims)
... y = test_utils.simple_forward(op, flat_data=x)
... y_np = x.reshape((dims[0], np.prod(dims[1:]).astype('int32')))
... print('%s: %s' % (dims, test_utils.almost_equal(y, y_np)))
(2, 3, 4, 5): True
(2, 3): True
(2,): True

mxnet.symbol.FullyConnected(data=None, weight=None, bias=None, num_hidden=_Null, no_bias=_Null, name=None, attr=None, out=None, **kwargs)

Applies a linear transformation: $$Y = XW^T + b$$.

Shapes:

• data: (batch_size, input_dim)
• weight: (num_hidden, input_dim)
• bias: (num_hidden,)
• out: (batch_size, num_hidden)

The learnable parameters include both weight and bias.

If no_bias is set to be true, then the bias term is ignored.

Defined in src/operator/fully_connected.cc:L90

Parameters: data (Symbol) – Input data. weight (Symbol) – Weight matrix. bias (Symbol) – Bias parameter. num_hidden (int, required) – Number of hidden nodes of the output. no_bias (boolean, optional, default=False) – Whether to disable bias parameter. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol

Examples

Construct a fully connected operator with target dimension 512.

>>> data = Variable('data')  # or some constructed NN
>>> op = FullyConnected(data=data,
... num_hidden=512,
... name='FC1')
>>> op
<Symbol FC1>
>>> SymbolDoc.get_output_shape(op, data=(128, 100))
{'FC1_output': (128L, 512L)}


A simple 3-layer MLP with ReLU activation:

>>> net = Variable('data')
>>> for i, dim in enumerate([128, 64]):
... net = FullyConnected(data=net, num_hidden=dim, name='FC%d' % i)
... net = Activation(data=net, act_type='relu', name='ReLU%d' % i)
>>> # 10-class predictor (e.g. MNIST)
>>> net = FullyConnected(data=net, num_hidden=10, name='pred')
>>> net
<Symbol pred>

>>> dim_in, dim_out = (3, 4)
>>> x, w, b = test_utils.random_arrays((10, dim_in), (dim_out, dim_in), (dim_out,))
>>> op = FullyConnected(num_hidden=dim_out, name='FC')
>>> out = test_utils.simple_forward(op, FC_data=x, FC_weight=w, FC_bias=b)
>>> # numpy implementation of FullyConnected
>>> out_np = np.dot(x, w.T) + b
>>> test_utils.almost_equal(out, out_np)
True

mxnet.symbol.GridGenerator(data=None, transform_type=_Null, target_shape=_Null, name=None, attr=None, out=None, **kwargs)

Generates 2D sampling grid for bilinear sampling.

Parameters: data (Symbol) – Input data to the function. transform_type ({'affine', 'warp'}, required) – The type of transformation. For affine, input data should be an affine matrix of size (batch, 6). For warp, input data should be an optical flow of size (batch, 2, h, w). target_shape (Shape(tuple), optional, default=(0,0)) – Specifies the output shape (H, W). This is required if transformation type is affine. If transformation type is warp, this parameter is ignored. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.IdentityAttachKLSparseReg(data=None, sparseness_target=_Null, penalty=_Null, momentum=_Null, name=None, attr=None, out=None, **kwargs)

Apply a sparse regularization to the output a sigmoid activation function.

Parameters: data (Symbol) – Input data. sparseness_target (float, optional, default=0.1) – The sparseness target penalty (float, optional, default=0.001) – The tradeoff parameter for the sparseness penalty momentum (float, optional, default=0.9) – The momentum for running average name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.InstanceNorm(data=None, gamma=None, beta=None, eps=_Null, name=None, attr=None, out=None, **kwargs)

Applies instance normalization to the n-dimensional input array.

This operator takes an n-dimensional input array where (n>2) and normalizes the input using the following formula:

$out = \frac{x - mean[data]}{ \sqrt{Var[data]} + \epsilon} * gamma + beta$

This layer is similar to batch normalization layer (BatchNorm) with two differences: first, the normalization is carried out per example (instance), not over a batch. Second, the same normalization is applied both at test and train time. This operation is also known as contrast normalization.

If the input data is of shape [batch, channel, spacial_dim1, spacial_dim2, ...], gamma and beta parameters must be vectors of shape [channel].

This implementation is based on paper:

 [1] Instance Normalization: The Missing Ingredient for Fast Stylization, D. Ulyanov, A. Vedaldi, V. Lempitsky, 2016 (arXiv:1607.08022v2).

Examples:

// Input of shape (2,1,2)
x = [[[ 1.1,  2.2]],
[[ 3.3,  4.4]]]

// gamma parameter of length 1
gamma = [1.5]

// beta parameter of length 1
beta = [0.5]

// Instance normalization is calculated with the above formula
InstanceNorm(x,gamma,beta) = [[[-0.997527  ,  1.99752665]],
[[-0.99752653,  1.99752724]]]


Defined in src/operator/instance_norm.cc:L94

Parameters: data (Symbol) – An n-dimensional input array (n > 2) of the form [batch, channel, spatial_dim1, spatial_dim2, ...]. gamma (Symbol) – A vector of length ‘channel’, which multiplies the normalized input. beta (Symbol) – A vector of length ‘channel’, which is added to the product of the normalized input and the weight. eps (float, optional, default=0.001) – An epsilon parameter to prevent division by 0. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.L2Normalization(data=None, eps=_Null, mode=_Null, name=None, attr=None, out=None, **kwargs)

Normalize the input array using the L2 norm.

For 1-D NDArray, it computes:

out = data / sqrt(sum(data ** 2) + eps)


For N-D NDArray, if the input array has shape (N, N, ..., N),

with mode = instance, it normalizes each instance in the multidimensional array by its L2 norm.:

for i in 0...N
out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps)


with mode = channel, it normalizes each channel in the array by its L2 norm.:

for i in 0...N
out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps)


with mode = spatial, it normalizes the cross channel norm for each position in the array by its L2 norm.:

for dim in 2...N
for i in 0...N
out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, indices=i, axis=dim) ** 2) + eps)
-dim-


Example:

x = [[[1,2],
[3,4]],
[[2,2],
[5,6]]]

L2Normalization(x, mode='instance')
=[[[ 0.18257418  0.36514837]
[ 0.54772252  0.73029673]]
[[ 0.24077171  0.24077171]
[ 0.60192931  0.72231513]]]

L2Normalization(x, mode='channel')
=[[[ 0.31622776  0.44721359]
[ 0.94868326  0.89442718]]
[[ 0.37139067  0.31622776]
[ 0.92847669  0.94868326]]]

L2Normalization(x, mode='spatial')
=[[[ 0.44721359  0.89442718]
[ 0.60000002  0.80000001]]
[[ 0.70710677  0.70710677]
[ 0.6401844   0.76822126]]]


Defined in src/operator/l2_normalization.cc:L92

Parameters: data (Symbol) – Input array to normalize. eps (float, optional, default=1e-10) – A small constant for numerical stability. mode ({'channel', 'instance', 'spatial'},optional, default='instance') – Specify the dimension along which to compute L2 norm. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.LRN(data=None, alpha=_Null, beta=_Null, knorm=_Null, nsize=_Null, name=None, attr=None, out=None, **kwargs)

Applies local response normalization to the input.

The local response normalization layer performs “lateral inhibition” by normalizing over local input regions.

If $$a_{x,y}^{i}$$ is the activity of a neuron computed by applying kernel $$i$$ at position $$(x, y)$$ and then applying the ReLU nonlinearity, the response-normalized activity $$b_{x,y}^{i}$$ is given by the expression:

$b_{x,y}^{i} = \frac{a_{x,y}^{i}}{\Bigg({k + \alpha \sum_{j=max(0, i-\frac{n}{2})}^{min(N-1, i+\frac{n}{2})} (a_{x,y}^{j})^{2}}\Bigg)^{\beta}}$

where the sum runs over $$n$$ “adjacent” kernel maps at the same spatial position, and $$N$$ is the total number of kernels in the layer.

Defined in src/operator/lrn.cc:L72

Parameters: data (Symbol) – Input data. alpha (float, optional, default=0.0001) – The variance scaling parameter $$lpha$$ in the LRN expression. beta (float, optional, default=0.75) – The power parameter $$eta$$ in the LRN expression. knorm (float, optional, default=2) – The parameter $$k$$ in the LRN expression. nsize (int (non-negative), required) – normalization window width in elements. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.LeakyReLU(data=None, act_type=_Null, slope=_Null, lower_bound=_Null, upper_bound=_Null, name=None, attr=None, out=None, **kwargs)

Applies Leaky rectified linear unit activation element-wise to the input.

Leaky ReLUs attempt to fix the “dying ReLU” problem by allowing a small slope when the input is negative and has a slope of one when input is positive.

The following modified ReLU Activation functions are supported:

• elu: Exponential Linear Unit. y = x > 0 ? x : slope * (exp(x)-1)
• leaky: Leaky ReLU. y = x > 0 ? x : slope * x
• prelu: Parametric ReLU. This is same as leaky except that slope is learnt during training.
• rrelu: Randomized ReLU. same as leaky but the slope is uniformly and randomly chosen from [lower_bound, upper_bound) for training, while fixed to be (lower_bound+upper_bound)/2 for inference.

Defined in src/operator/leaky_relu.cc:L57

Parameters: data (Symbol) – Input data to activation function. act_type ({'elu', 'leaky', 'prelu', 'rrelu'},optional, default='leaky') – Activation function to be applied. slope (float, optional, default=0.25) – Init slope for the activation. (For leaky and elu only) lower_bound (float, optional, default=0.125) – Lower bound of random slope. (For rrelu only) upper_bound (float, optional, default=0.334) – Upper bound of random slope. (For rrelu only) name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.LinearRegressionOutput(data=None, label=None, grad_scale=_Null, name=None, attr=None, out=None, **kwargs)

Computes and optimizes for squared loss during backward propagation. Just outputs data during forward propagation.

If $$\hat{y}_i$$ is the predicted value of the i-th sample, and $$y_i$$ is the corresponding target value, then the squared loss estimated over $$n$$ samples is defined as

$$\text{SquaredLoss}(y, \hat{y} ) = \frac{1}{n} \sum_{i=0}^{n-1} \left( y_i - \hat{y}_i \right)^2$$

Note

Use the LinearRegressionOutput as the final output layer of a net.

By default, gradients of this loss function are scaled by factor 1/n, where n is the number of training examples. The parameter grad_scale can be used to change this scale to grad_scale/n.

Defined in src/operator/regression_output.cc:L69

Parameters: data (Symbol) – Input data to the function. label (Symbol) – Input label to the function. grad_scale (float, optional, default=1) – Scale the gradient by a float factor name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.LogisticRegressionOutput(data=None, label=None, grad_scale=_Null, name=None, attr=None, out=None, **kwargs)

Applies a logistic function to the input.

The logistic function, also known as the sigmoid function, is computed as $$\frac{1}{1+exp(-x)}$$.

Commonly, the sigmoid is used to squash the real-valued output of a linear model :math:wTx+b into the [0,1] range so that it can be interpreted as a probability. It is suitable for binary classification or probability prediction tasks.

Note

Use the LogisticRegressionOutput as the final output layer of a net.

By default, gradients of this loss function are scaled by factor 1/n, where n is the number of training examples. The parameter grad_scale can be used to change this scale to grad_scale/n.

Defined in src/operator/regression_output.cc:L111

Parameters: data (Symbol) – Input data to the function. label (Symbol) – Input label to the function. grad_scale (float, optional, default=1) – Scale the gradient by a float factor name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.MAERegressionOutput(data=None, label=None, grad_scale=_Null, name=None, attr=None, out=None, **kwargs)

Computes mean absolute error of the input.

MAE is a risk metric corresponding to the expected value of the absolute error.

If $$\hat{y}_i$$ is the predicted value of the i-th sample, and $$y_i$$ is the corresponding target value, then the mean absolute error (MAE) estimated over $$n$$ samples is defined as

$$\text{MAE}(y, \hat{y} ) = \frac{1}{n} \sum_{i=0}^{n-1} \left| y_i - \hat{y}_i \right|$$

Note

Use the MAERegressionOutput as the final output layer of a net.

By default, gradients of this loss function are scaled by factor 1/n, where n is the number of training examples. The parameter grad_scale can be used to change this scale to grad_scale/n.

Defined in src/operator/regression_output.cc:L90

Parameters: data (Symbol) – Input data to the function. label (Symbol) – Input label to the function. grad_scale (float, optional, default=1) – Scale the gradient by a float factor name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.MakeLoss(data=None, grad_scale=_Null, valid_thresh=_Null, normalization=_Null, name=None, attr=None, out=None, **kwargs)

Make your own loss function in network construction.

This operator accepts a customized loss function symbol as a terminal loss and the symbol should be an operator with no backward dependency. The output of this function is the gradient of loss with respect to the input data.

For example, if you are a making a cross entropy loss function. Assume out is the predicted output and label is the true label, then the cross entropy can be defined as:

cross_entropy = label * log(out) + (1 - label) * log(1 - out)
loss = MakeLoss(cross_entropy)


We will need to use MakeLoss when we are creating our own loss function or we want to combine multiple loss functions. Also we may want to stop some variables’ gradients from backpropagation. See more detail in BlockGrad or stop_gradient.

In addition, we can give a scale to the loss by setting grad_scale, so that the gradient of the loss will be rescaled in the backpropagation.

Note

This operator should be used as a Symbol instead of NDArray.

Defined in src/operator/make_loss.cc:L70

Parameters: data (Symbol) – Input array. grad_scale (float, optional, default=1) – Gradient scale as a supplement to unary and binary operators valid_thresh (float, optional, default=0) – clip each element in the array to 0 when it is less than valid_thresh. This is used when normalization is set to 'valid'. normalization ({'batch', 'null', 'valid'},optional, default='null') – If this is set to null, the output gradient will not be normalized. If this is set to batch, the output gradient will be divided by the batch size. If this is set to valid, the output gradient will be divided by the number of valid input elements. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.Pad(data=None, mode=_Null, pad_width=_Null, constant_value=_Null, name=None, attr=None, out=None, **kwargs)

Pads an input array with a constant or edge values of the array.

Note

Note

Current implementation only supports 4D and 5D input arrays with padding applied only on axes 1, 2 and 3. Expects axes 4 and 5 in pad_width to be zero.

This operation pads an input array with either a constant_value or edge values along each axis of the input array. The amount of padding is specified by pad_width.

pad_width is a tuple of integer padding widths for each axis of the format (before_1, after_1, ... , before_N, after_N). The pad_width should be of length 2*N where N is the number of dimensions of the array.

For dimension N of the input array, before_N and after_N indicates how many values to add before and after the elements of the array along dimension N. The widths of the higher two dimensions before_1, after_1, before_2, after_2 must be 0.

Example:

x = [[[[  1.   2.   3.]
[  4.   5.   6.]]

[[  7.   8.   9.]
[ 10.  11.  12.]]]

[[[ 11.  12.  13.]
[ 14.  15.  16.]]

[[ 17.  18.  19.]
[ 20.  21.  22.]]]]

[[[[  1.   1.   2.   3.   3.]
[  1.   1.   2.   3.   3.]
[  4.   4.   5.   6.   6.]
[  4.   4.   5.   6.   6.]]

[[  7.   7.   8.   9.   9.]
[  7.   7.   8.   9.   9.]
[ 10.  10.  11.  12.  12.]
[ 10.  10.  11.  12.  12.]]]

[[[ 11.  11.  12.  13.  13.]
[ 11.  11.  12.  13.  13.]
[ 14.  14.  15.  16.  16.]
[ 14.  14.  15.  16.  16.]]

[[ 17.  17.  18.  19.  19.]
[ 17.  17.  18.  19.  19.]
[ 20.  20.  21.  22.  22.]
[ 20.  20.  21.  22.  22.]]]]

[[[[  0.   0.   0.   0.   0.]
[  0.   1.   2.   3.   0.]
[  0.   4.   5.   6.   0.]
[  0.   0.   0.   0.   0.]]

[[  0.   0.   0.   0.   0.]
[  0.   7.   8.   9.   0.]
[  0.  10.  11.  12.   0.]
[  0.   0.   0.   0.   0.]]]

[[[  0.   0.   0.   0.   0.]
[  0.  11.  12.  13.   0.]
[  0.  14.  15.  16.   0.]
[  0.   0.   0.   0.   0.]]

[[  0.   0.   0.   0.   0.]
[  0.  17.  18.  19.   0.]
[  0.  20.  21.  22.   0.]
[  0.   0.   0.   0.   0.]]]]


Parameters: data (Symbol) – An n-dimensional input array. mode ({'constant', 'edge', 'reflect'}, required) – Padding type to use. “constant” pads with constant_value “edge” pads using the edge values of the input array “reflect” pads by reflecting values with respect to the edges. pad_width (Shape(tuple), required) – Widths of the padding regions applied to the edges of each axis. It is a tuple of integer padding widths for each axis of the format (before_1, after_1, ... , before_N, after_N). It should be of length 2*N where N is the number of dimensions of the array.This is equivalent to pad_width in numpy.pad, but flattened. constant_value (double, optional, default=0) – The value used for padding when mode is “constant”. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.Pooling(data=None, global_pool=_Null, cudnn_off=_Null, kernel=_Null, pool_type=_Null, pooling_convention=_Null, stride=_Null, pad=_Null, name=None, attr=None, out=None, **kwargs)

Performs pooling on the input.

The shapes for 1-D pooling are

• data: (batch_size, channel, width),
• out: (batch_size, num_filter, out_width).

The shapes for 2-D pooling are

• data: (batch_size, channel, height, width)

• out: (batch_size, num_filter, out_height, out_width), with:

out_height = f(height, kernel[0], pad[0], stride[0])
out_width = f(width, kernel[1], pad[1], stride[1])


The definition of f depends on pooling_convention, which has two options:

• valid (default):

f(x, k, p, s) = floor((x+2*p-k)/s)+1

• full, which is compatible with Caffe:

f(x, k, p, s) = ceil((x+2*p-k)/s)+1


But global_pool is set to be true, then do a global pooling, namely reset kernel=(height, width).

Three pooling options are supported by pool_type:

• avg: average pooling
• max: max pooling
• sum: sum pooling

For 3-D pooling, an additional depth dimension is added before height. Namely the input data will have shape (batch_size, channel, depth, height, width).

Defined in src/operator/pooling.cc:L134

Parameters: data (Symbol) – Input data to the pooling operator. global_pool (boolean, optional, default=False) – Ignore kernel size, do global pooling based on current input feature map. cudnn_off (boolean, optional, default=False) – Turn off cudnn pooling and use MXNet pooling operator. kernel (Shape(tuple), required) – pooling kernel size: (y, x) or (d, y, x) pool_type ({'avg', 'max', 'sum'}, required) – Pooling type to be applied. pooling_convention ({'full', 'valid'},optional, default='valid') – Pooling convention to be applied. stride (Shape(tuple), optional, default=()) – stride: for pooling (y, x) or (d, y, x) pad (Shape(tuple), optional, default=()) – pad for pooling: (y, x) or (d, y, x) name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.Pooling_v1(data=None, global_pool=_Null, kernel=_Null, pool_type=_Null, pooling_convention=_Null, stride=_Null, pad=_Null, name=None, attr=None, out=None, **kwargs)

This operator is DEPRECATED. Perform pooling on the input.

The shapes for 2-D pooling is

• data: (batch_size, channel, height, width)

• out: (batch_size, num_filter, out_height, out_width), with:

out_height = f(height, kernel[0], pad[0], stride[0])
out_width = f(width, kernel[1], pad[1], stride[1])


The definition of f depends on pooling_convention, which has two options:

• valid (default):

f(x, k, p, s) = floor((x+2*p-k)/s)+1

• full, which is compatible with Caffe:

f(x, k, p, s) = ceil((x+2*p-k)/s)+1


But global_pool is set to be true, then do a global pooling, namely reset kernel=(height, width).

Three pooling options are supported by pool_type:

• avg: average pooling
• max: max pooling
• sum: sum pooling

1-D pooling is special case of 2-D pooling with weight=1 and kernel[1]=1.

For 3-D pooling, an additional depth dimension is added before height. Namely the input data will have shape (batch_size, channel, depth, height, width).

Defined in src/operator/pooling_v1.cc:L103

Parameters: data (Symbol) – Input data to the pooling operator. global_pool (boolean, optional, default=False) – Ignore kernel size, do global pooling based on current input feature map. kernel (Shape(tuple), required) – pooling kernel size: (y, x) or (d, y, x) pool_type ({'avg', 'max', 'sum'}, required) – Pooling type to be applied. pooling_convention ({'full', 'valid'},optional, default='valid') – Pooling convention to be applied. stride (Shape(tuple), optional, default=()) – stride: for pooling (y, x) or (d, y, x) pad (Shape(tuple), optional, default=()) – pad for pooling: (y, x) or (d, y, x) name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.RNN(data=None, parameters=None, state=None, state_cell=None, state_size=_Null, num_layers=_Null, bidirectional=_Null, mode=_Null, p=_Null, state_outputs=_Null, name=None, attr=None, out=None, **kwargs)

Applies a recurrent layer to input.

Parameters: data (Symbol) – Input data to RNN parameters (Symbol) – Vector of all RNN trainable parameters concatenated state (Symbol) – initial hidden state of the RNN state_cell (Symbol) – initial cell state for LSTM networks (only for LSTM) state_size (int (non-negative), required) – size of the state for each layer num_layers (int (non-negative), required) – number of stacked layers bidirectional (boolean, optional, default=False) – whether to use bidirectional recurrent layers mode ({'gru', 'lstm', 'rnn_relu', 'rnn_tanh'}, required) – the type of RNN to compute p (float, optional, default=0) – Dropout probability, fraction of the input that gets dropped out at training time state_outputs (boolean, optional, default=False) – Whether to have the states as symbol outputs. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.ROIPooling(data=None, rois=None, pooled_size=_Null, spatial_scale=_Null, name=None, attr=None, out=None, **kwargs)

Performs region of interest(ROI) pooling on the input array.

ROI pooling is a variant of a max pooling layer, in which the output size is fixed and region of interest is a parameter. Its purpose is to perform max pooling on the inputs of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a neural-net layer mostly used in training a Fast R-CNN network for object detection.

This operator takes a 4D feature map as an input array and region proposals as rois, then it pools over sub-regions of input and produces a fixed-sized output array regardless of the ROI size.

To crop the feature map accordingly, you can resize the bounding box coordinates by changing the parameters rois and spatial_scale.

The cropped feature maps are pooled by standard max pooling operation to a fixed size output indicated by a pooled_size parameter. batch_size will change to the number of region bounding boxes after ROIPooling.

The size of each region of interest doesn’t have to be perfectly divisible by the number of pooling sections(pooled_size).

Example:

x = [[[[  0.,   1.,   2.,   3.,   4.,   5.],
[  6.,   7.,   8.,   9.,  10.,  11.],
[ 12.,  13.,  14.,  15.,  16.,  17.],
[ 18.,  19.,  20.,  21.,  22.,  23.],
[ 24.,  25.,  26.,  27.,  28.,  29.],
[ 30.,  31.,  32.,  33.,  34.,  35.],
[ 36.,  37.,  38.,  39.,  40.,  41.],
[ 42.,  43.,  44.,  45.,  46.,  47.]]]]

// region of interest i.e. bounding box coordinates.
y = [[0,0,0,4,4]]

// returns array of shape (2,2) according to the given roi with max pooling.
ROIPooling(x, y, (2,2), 1.0) = [[[[ 14.,  16.],
[ 26.,  28.]]]]

// region of interest is changed due to the change in spacial_scale parameter.
ROIPooling(x, y, (2,2), 0.7) = [[[[  7.,   9.],
[ 19.,  21.]]]]


Defined in src/operator/roi_pooling.cc:L287

Parameters: data (Symbol) – The input array to the pooling operator, a 4D Feature maps rois (Symbol) – Bounding box coordinates, a 2D array of [[batch_index, x1, y1, x2, y2]], where (x1, y1) and (x2, y2) are top left and bottom right corners of designated region of interest. batch_index indicates the index of corresponding image in the input array pooled_size (Shape(tuple), required) – ROI pooling output shape (h,w) spatial_scale (float, required) – Ratio of input feature map height (or w) to raw image height (or w). Equals the reciprocal of total stride in convolutional layers name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.Reshape(data=None, shape=_Null, reverse=_Null, target_shape=_Null, keep_highest=_Null, name=None, attr=None, out=None, **kwargs)

Reshapes the input array.

Note

Reshape is deprecated, use reshape

Given an array and a shape, this function returns a copy of the array in the new shape. The shape is a tuple of integers such as (2,3,4).The size of the new shape should be same as the size of the input array.

Example:

reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]


Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:

• 0 copy this dimension from the input to the output shape.

Example:

- input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
- input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)

• -1 infers the dimension of the output shape by using the remainder of the input dimensions keeping the size of the new array same as that of the input array. At most one dimension of shape can be -1.

Example:

- input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
- input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
- input shape = (2,3,4), shape=(-1,), output shape = (24,)

• -2 copy all/remainder of the input dimensions to the output shape.

Example:

- input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
- input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
- input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)

• -3 use the product of two consecutive dimensions of the input shape as the output dimension.

Example:

- input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
- input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
- input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
- input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)

• -4 split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).

Example:

- input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
- input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)


If the argument reverse is set to 1, then the special values are inferred from right to left.

Example:

- without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5)
- with reverse=1, output shape will be (50,4).


Defined in src/operator/tensor/matrix_op.cc:L106

Parameters: data (Symbol) – Input data to reshape. shape (Shape(tuple), optional, default=()) – The target shape reverse (boolean, optional, default=False) – If true then the special values are inferred from right to left target_shape (Shape(tuple), optional, default=()) – (Deprecated! Use shape instead.) Target new shape. One and only one dim can be 0, in which case it will be inferred from the rest of dims keep_highest (boolean, optional, default=False) – (Deprecated! Use shape instead.) Whether keep the highest dim unchanged.If set to true, then the first dim in target_shape is ignored,and always fixed as input name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.SVMOutput(data=None, label=None, margin=_Null, regularization_coefficient=_Null, use_linear=_Null, name=None, attr=None, out=None, **kwargs)

Computes support vector machine based transformation of the input.

This tutorial demonstrates using SVM as output layer for classification instead of softmax: https://github.com/dmlc/mxnet/tree/master/example/svm_mnist.

Parameters: data (Symbol) – Input data for SVM transformation. label (Symbol) – Class label for the input data. margin (float, optional, default=1) – The loss function penalizes outputs that lie outside this margin. Default margin is 1. regularization_coefficient (float, optional, default=1) – Regularization parameter for the SVM. This balances the tradeoff between coefficient size and error. use_linear (boolean, optional, default=False) – Whether to use L1-SVM objective. L2-SVM objective is used by default. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.SequenceLast(data=None, sequence_length=None, use_sequence_length=_Null, name=None, attr=None, out=None, **kwargs)

Takes the last element of a sequence.

This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns a (n-1)-dimensional array of the form [batch_size, other_feature_dims].

Parameter sequence_length is used to handle variable-length sequences. sequence_length should be an input array of positive ints of dimension [batch_size]. To use this parameter, set use_sequence_length to True, otherwise each example in the batch is assumed to have the max sequence length.

Note

Alternatively, you can also use take operator.

Example:

x = [[[  1.,   2.,   3.],
[  4.,   5.,   6.],
[  7.,   8.,   9.]],

[[ 10.,   11.,   12.],
[ 13.,   14.,   15.],
[ 16.,   17.,   18.]],

[[  19.,   20.,   21.],
[  22.,   23.,   24.],
[  25.,   26.,   27.]]]

// returns last sequence when sequence_length parameter is not used
SequenceLast(x) = [[  19.,   20.,   21.],
[  22.,   23.,   24.],
[  25.,   26.,   27.]]

// sequence_length y is used
SequenceLast(x, y=[1,1,1], use_sequence_length=True) =
[[  1.,   2.,   3.],
[  4.,   5.,   6.],
[  7.,   8.,   9.]]

// sequence_length y is used
SequenceLast(x, y=[1,2,3], use_sequence_length=True) =
[[  1.,    2.,   3.],
[  13.,  14.,  15.],
[  25.,  26.,  27.]]


Defined in src/operator/sequence_last.cc:L91

Parameters: data (Symbol) – n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] where n>2 sequence_length (Symbol) – vector of sequence lengths of the form [batch_size] use_sequence_length (boolean, optional, default=False) – If set to true, this layer takes in an extra input parameter sequence_length to specify variable length sequence name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.SequenceMask(data=None, sequence_length=None, use_sequence_length=_Null, value=_Null, name=None, attr=None, out=None, **kwargs)

Sets all elements outside the sequence to a constant value.

This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape.

Parameter sequence_length is used to handle variable-length sequences. sequence_length should be an input array of positive ints of dimension [batch_size]. To use this parameter, set use_sequence_length to True, otherwise each example in the batch is assumed to have the max sequence length and this operator works as the identity operator.

Example:

x = [[[  1.,   2.,   3.],
[  4.,   5.,   6.]],

[[  7.,   8.,   9.],
[ 10.,  11.,  12.]],

[[ 13.,  14.,   15.],
[ 16.,  17.,   18.]]]

// Batch 1
B1 = [[  1.,   2.,   3.],
[  7.,   8.,   9.],
[ 13.,  14.,  15.]]

// Batch 2
B2 = [[  4.,   5.,   6.],
[ 10.,  11.,  12.],
[ 16.,  17.,  18.]]

// works as identity operator when sequence_length parameter is not used
SequenceMask(x) = [[[  1.,   2.,   3.],
[  4.,   5.,   6.]],

[[  7.,   8.,   9.],
[ 10.,  11.,  12.]],

[[ 13.,  14.,   15.],
[ 16.,  17.,   18.]]]

// sequence_length [1,1] means 1 of each batch will be kept
// and other rows are masked with default mask value = 0
[[[  1.,   2.,   3.],
[  4.,   5.,   6.]],

[[  0.,   0.,   0.],
[  0.,   0.,   0.]],

[[  0.,   0.,   0.],
[  0.,   0.,   0.]]]

// sequence_length [2,3] means 2 of batch B1 and 3 of batch B2 will be kept
// and other rows are masked with value = 1
[[[  1.,   2.,   3.],
[  4.,   5.,   6.]],

[[  7.,   8.,   9.],
[  10.,  11.,  12.]],

[[   1.,   1.,   1.],
[  16.,  17.,  18.]]]


Parameters: data (Symbol) – n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] where n>2 sequence_length (Symbol) – vector of sequence lengths of the form [batch_size] use_sequence_length (boolean, optional, default=False) – If set to true, this layer takes in an extra input parameter sequence_length to specify variable length sequence value (float, optional, default=0) – The value to be used as a mask. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.SequenceReverse(data=None, sequence_length=None, use_sequence_length=_Null, name=None, attr=None, out=None, **kwargs)

Reverses the elements of each sequence.

This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape.

Parameter sequence_length is used to handle variable-length sequences. sequence_length should be an input array of positive ints of dimension [batch_size]. To use this parameter, set use_sequence_length to True, otherwise each example in the batch is assumed to have the max sequence length.

Example:

x = [[[  1.,   2.,   3.],
[  4.,   5.,   6.]],

[[  7.,   8.,   9.],
[ 10.,  11.,  12.]],

[[ 13.,  14.,   15.],
[ 16.,  17.,   18.]]]

// Batch 1
B1 = [[  1.,   2.,   3.],
[  7.,   8.,   9.],
[ 13.,  14.,  15.]]

// Batch 2
B2 = [[  4.,   5.,   6.],
[ 10.,  11.,  12.],
[ 16.,  17.,  18.]]

// returns reverse sequence when sequence_length parameter is not used
SequenceReverse(x) = [[[ 13.,  14.,   15.],
[ 16.,  17.,   18.]],

[[  7.,   8.,   9.],
[ 10.,  11.,  12.]],

[[  1.,   2.,   3.],
[  4.,   5.,   6.]]]

// sequence_length [2,2] means 2 rows of
// both batch B1 and B2 will be reversed.
SequenceReverse(x, y=[2,2], use_sequence_length=True) =
[[[  7.,   8.,   9.],
[ 10.,  11.,  12.]],

[[  1.,   2.,   3.],
[  4.,   5.,   6.]],

[[ 13.,  14.,   15.],
[ 16.,  17.,   18.]]]

// sequence_length [2,3] means 2 of batch B2 and 3 of batch B3
// will be reversed.
SequenceReverse(x, y=[2,3], use_sequence_length=True) =
[[[  7.,   8.,   9.],
[ 16.,  17.,  18.]],

[[  1.,   2.,   3.],
[ 10.,  11.,  12.]],

[[ 13.,  14,   15.],
[  4.,   5.,   6.]]]


Defined in src/operator/sequence_reverse.cc:L112

Parameters: data (Symbol) – n-dimensional input array of the form [max_sequence_length, batch_size, other dims] where n>2 sequence_length (Symbol) – vector of sequence lengths of the form [batch_size] use_sequence_length (boolean, optional, default=False) – If set to true, this layer takes in an extra input parameter sequence_length to specify variable length sequence name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.SliceChannel(data=None, num_outputs=_Null, axis=_Null, squeeze_axis=_Null, name=None, attr=None, out=None, **kwargs)

Splits an array along a particular axis into multiple sub-arrays.

Note

SliceChannel is deprecated. Use split instead.

Note that num_outputs should evenly divide the length of the axis along which to split the array.

Example:

x  = [[[ 1.]
[ 2.]]
[[ 3.]
[ 4.]]
[[ 5.]
[ 6.]]]
x.shape = (3, 2, 1)

y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1)
y = [[[ 1.]]
[[ 3.]]
[[ 5.]]]

[[[ 2.]]
[[ 4.]]
[[ 6.]]]

y[0].shape = (3, 1, 1)

z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1)
z = [[[ 1.]
[ 2.]]]

[[[ 3.]
[ 4.]]]

[[[ 5.]
[ 6.]]]

z[0].shape = (1, 2, 1)


squeeze_axis=1 removes the axis with length 1 from the shapes of the output arrays. Note that setting squeeze_axis to 1 removes axis with length 1 only along the axis which it is split. Also squeeze_axis can be set to true only if input.shape[axis] == num_outputs.

Example:

z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1)
z = [[ 1.]
[ 2.]]

[[ 3.]
[ 4.]]

[[ 5.]
[ 6.]]
z[0].shape = (2 ,1 )


Defined in src/operator/slice_channel.cc:L106

Parameters: data (Symbol) – The input num_outputs (int, required) – Number of splits. Note that this should evenly divide the length of the axis. axis (int, optional, default='1') – Axis along which to split. squeeze_axis (boolean, optional, default=False) – If true, Removes the axis with length 1 from the shapes of the output arrays. Note that setting squeeze_axis to true removes axis with length 1 only along the axis which it is split. Also squeeze_axis can be set to true only if input.shape[axis] == num_outputs. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.Softmax(data=None, grad_scale=_Null, ignore_label=_Null, multi_output=_Null, use_ignore=_Null, preserve_shape=_Null, normalization=_Null, out_grad=_Null, name=None, attr=None, out=None, **kwargs)

Note

This operator has been renamed to SoftmaxOutput, which computes the gradient of cross-entropy loss w.r.t softmax output. To just compute softmax output, use the softmax operator.

Defined in src/operator/softmax_output.cc:L137

Parameters: data (Symbol) – Input array. grad_scale (float, optional, default=1) – Scales the gradient by a float factor. ignore_label (float, optional, default=-1) – The instances whose labels == ignore_label will be ignored during backward, if use_ignore is set to true). multi_output (boolean, optional, default=False) – If set to true, the softmax function will be computed along axis 1. This is applied when the shape of input array differs from the shape of label array. use_ignore (boolean, optional, default=False) – If set to true, the ignore_label value will not contribute to the backward gradient. preserve_shape (boolean, optional, default=False) – If set to true, the softmax function will be computed along the last axis (-1). normalization ({'batch', 'null', 'valid'},optional, default='null') – Normalizes the gradient. out_grad (boolean, optional, default=False) – Multiplies gradient with output gradient element-wise. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.SoftmaxActivation(data=None, mode=_Null, name=None, attr=None, out=None, **kwargs)

Applies softmax activation to input. This is intended for internal layers.

Note

This operator has been deprecated, please use softmax.

If mode = instance, this operator will compute a softmax for each instance in the batch. This is the default mode.

If mode = channel, this operator will compute a k-class softmax at each position of each instance, where k = num_channel. This mode can only be used when the input array has at least 3 dimensions. This can be used for fully convolutional network, image segmentation, etc.

Example:

>>> input_array = mx.nd.array([[3., 0.5, -0.5, 2., 7.],
>>>                            [2., -.4, 7.,   3., 0.2]])
>>> softmax_act = mx.nd.SoftmaxActivation(input_array)
>>> print softmax_act.asnumpy()
[[  1.78322066e-02   1.46375655e-03   5.38485940e-04   6.56010211e-03   9.73605454e-01]
[  6.56221947e-03   5.95310994e-04   9.73919690e-01   1.78379621e-02   1.08472735e-03]]


Defined in src/operator/softmax_activation.cc:L66

Parameters: data (Symbol) – Input array to activation function. mode ({'channel', 'instance'},optional, default='instance') – Specifies how to compute the softmax. If set to instance, it computes softmax for each instance. If set to channel, It computes cross channel softmax for each position of each instance. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.SoftmaxOutput(data=None, label=None, grad_scale=_Null, ignore_label=_Null, multi_output=_Null, use_ignore=_Null, preserve_shape=_Null, normalization=_Null, out_grad=_Null, name=None, attr=None, out=None, **kwargs)

Computes the gradient of cross entropy loss with respect to softmax output.

• This operator computes the gradient in two steps. The cross entropy loss does not actually need to be computed.

• Applies softmax function on the input array.
• Computes and returns the gradient of cross entropy loss w.r.t. the softmax output.
• The softmax function, cross entropy loss and gradient is given by:

• Softmax Function:

$\text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}$
• Cross Entropy Function:

$\text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)$
• The gradient of cross entropy loss w.r.t softmax output:

$\text{gradient} = \text{output} - \text{label}$
• During forward propagation, the softmax function is computed for each instance in the input array.

For general N-D input arrays with shape $$(d_1, d_2, ..., d_n)$$. The size is $$s=d_1 \cdot d_2 \cdot \cdot \cdot d_n$$. We can use the parameters preserve_shape and multi_output to specify the way to compute softmax:

• By default, preserve_shape is false. This operator will reshape the input array into a 2-D array with shape $$(d_1, \frac{s}{d_1})$$ and then compute the softmax function for each row in the reshaped array, and afterwards reshape it back to the original shape $$(d_1, d_2, ..., d_n)$$.
• If preserve_shape is true, the softmax function will be computed along the last axis (axis = -1).
• If multi_output is true, the softmax function will be computed along the second axis (axis = 1).
• During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed. The provided label can be a one-hot label array or a probability label array.

• If the parameter use_ignore is true, ignore_label can specify input instances with a particular label to be ignored during backward propagation. This has no effect when softmax output has same shape as label.

Example:

data = [[1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4]]
label = [1,0,2,3]
ignore_label = 1
SoftmaxOutput(data=data, label = label,\
multi_output=true, use_ignore=true,\
ignore_label=ignore_label)
## forward softmax output
[[ 0.0320586   0.08714432  0.23688284  0.64391428]
[ 0.25        0.25        0.25        0.25      ]
[ 0.25        0.25        0.25        0.25      ]
[ 0.25        0.25        0.25        0.25      ]]
[[ 0.    0.    0.    0.  ]
[-0.75  0.25  0.25  0.25]
[ 0.25  0.25 -0.75  0.25]
[ 0.25  0.25  0.25 -0.75]]
## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label.

• The parameter grad_scale can be used to rescale the gradient, which is often used to give each loss function different weights.

• This operator also supports various ways to normalize the gradient by normalization, The normalization is applied if softmax output has different shape than the labels. The normalization mode can be set to the followings:

• 'null': do nothing.
• 'batch': divide the gradient by the batch size.
• 'valid': divide the gradient by the number of instances which are not ignored.

Defined in src/operator/softmax_output.cc:L122

Parameters: data (Symbol) – Input array. label (Symbol) – Ground truth label. grad_scale (float, optional, default=1) – Scales the gradient by a float factor. ignore_label (float, optional, default=-1) – The instances whose labels == ignore_label will be ignored during backward, if use_ignore is set to true). multi_output (boolean, optional, default=False) – If set to true, the softmax function will be computed along axis 1. This is applied when the shape of input array differs from the shape of label array. use_ignore (boolean, optional, default=False) – If set to true, the ignore_label value will not contribute to the backward gradient. preserve_shape (boolean, optional, default=False) – If set to true, the softmax function will be computed along the last axis (-1). normalization ({'batch', 'null', 'valid'},optional, default='null') – Normalizes the gradient. out_grad (boolean, optional, default=False) – Multiplies gradient with output gradient element-wise. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.SpatialTransformer(data=None, loc=None, target_shape=_Null, transform_type=_Null, sampler_type=_Null, name=None, attr=None, out=None, **kwargs)

Applies a spatial transformer to input feature map.

Parameters: data (Symbol) – Input data to the SpatialTransformerOp. loc (Symbol) – localisation net, the output dim should be 6 when transform_type is affine. You shold initialize the weight and bias with identity tranform. target_shape (Shape(tuple), optional, default=(0,0)) – output shape(h, w) of spatial transformer: (y, x) transform_type ({'affine'}, required) – transformation type sampler_type ({'bilinear'}, required) – sampling type name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.SwapAxis(data=None, dim1=_Null, dim2=_Null, name=None, attr=None, out=None, **kwargs)

Interchanges two axes of an array.

Examples:

 x = [[1, 2, 3]])
swapaxes(x, 0, 1) = [[ 1],
[ 2],
[ 3]]

x = [[[ 0, 1],
[ 2, 3]],
[[ 4, 5],
[ 6, 7]]]  // (2,2,2) array

swapaxes(x, 0, 2) = [[[ 0, 4],
[ 2, 6]],
[[ 1, 5],
[ 3, 7]]]


Defined in src/operator/swapaxis.cc:L69

Parameters: data (Symbol) – Input array. dim1 (int (non-negative), optional, default=0) – the first axis to be swapped. dim2 (int (non-negative), optional, default=0) – the second axis to be swapped. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.UpSampling(*data, **kwargs)

Performs nearest neighbor/bilinear up sampling to inputs. This function support variable length of positional input.

Parameters: data (Symbol[]) – Array of tensors to upsample scale (int (non-negative), required) – Up sampling scale num_filter (int (non-negative), optional, default=0) – Input filter. Only used by bilinear sample_type. sample_type ({'bilinear', 'nearest'}, required) – upsampling method multi_input_mode ({'concat', 'sum'},optional, default='concat') – How to handle multiple input. concat means concatenate upsampled images along the channel dimension. sum means add all images together, only available for nearest neighbor upsampling. workspace (long (non-negative), optional, default=512) – Tmp workspace for deconvolution (MB) name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.abs(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise absolute value of the input.

Example:

abs([-2, 0, 3]) = [2, 0, 3]


Defined in src/operator/tensor/elemwise_unary_op.cc:L254

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.adam_update(weight=None, grad=None, mean=None, var=None, lr=_Null, beta1=_Null, beta2=_Null, epsilon=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, name=None, attr=None, out=None, **kwargs)

Adam update consists of the following steps, where g represents gradient and m, v are 1st and 2nd order moment estimates (mean and variance).

$\begin{split}g_t = \nabla J(W_{t-1})\\ m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t\\ v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\ W_t = W_{t-1} - \alpha \frac{ m_t }{ \sqrt{ v_t } + \epsilon }\end{split}$

m = beta1*m + (1-beta1)*grad
w += - learning_rate * m / (sqrt(v) + epsilon)


Defined in src/operator/optimizer_op.cc:L144

mxnet.symbol.add_n(*args, **kwargs)

$add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n$

add_n is potentially more efficient than calling add by n times.

Defined in src/operator/tensor/elemwise_sum.cc:L65 This function support variable length of positional input.

Parameters: args (Symbol[]) – Positional input arguments name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.arccos(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise inverse cosine of the input array.

The input should be in range [-1, 1]. The output is in the closed interval $$[0, \pi]$$

$arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0]$

Defined in src/operator/tensor/elemwise_unary_op.cc:L559

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.arccosh(data=None, name=None, attr=None, out=None, **kwargs)

Returns the element-wise inverse hyperbolic cosine of the input array, computed element-wise.

Defined in src/operator/tensor/elemwise_unary_op.cc:L665

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.arcsin(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise inverse sine of the input array.

The input should be in the range [-1, 1]. The output is in the closed interval of [$$-\pi/2$$, $$\pi/2$$].

$arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2]$

Defined in src/operator/tensor/elemwise_unary_op.cc:L542

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.arcsinh(data=None, name=None, attr=None, out=None, **kwargs)

Returns the element-wise inverse hyperbolic sine of the input array, computed element-wise.

Defined in src/operator/tensor/elemwise_unary_op.cc:L655

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.arctan(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise inverse tangent of the input array.

The output is in the closed interval $$[-\pi/2, \pi/2]$$

$arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4]$

Defined in src/operator/tensor/elemwise_unary_op.cc:L575

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.arctanh(data=None, name=None, attr=None, out=None, **kwargs)

Returns the element-wise inverse hyperbolic tangent of the input array, computed element-wise.

Defined in src/operator/tensor/elemwise_unary_op.cc:L675

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.argmax(data=None, axis=_Null, keepdims=_Null, name=None, attr=None, out=None, **kwargs)

Returns indices of the maximum values along an axis.

In the case of multiple occurrences of maximum values, the indices corresponding to the first occurrence are returned.

Examples:

x = [[ 0.,  1.,  2.],
[ 3.,  4.,  5.]]

// argmax along axis 0
argmax(x, axis=0) = [ 1.,  1.,  1.]

// argmax along axis 1
argmax(x, axis=1) = [ 2.,  2.]

// argmax along axis 1 keeping same dims as an input array
argmax(x, axis=1, keepdims=True) = [[ 2.],
[ 2.]]


Parameters: data (Symbol) – The input axis (int or None, optional, default='None') – The axis along which to perform the reduction. Negative values means indexing from right to left. Requires axis to be set as int, because global reduction is not supported yet. keepdims (boolean, optional, default=False) – If this is set to True, the reduced axis is left in the result as dimension with size one. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.argmax_channel(data=None, name=None, attr=None, out=None, **kwargs)

Returns argmax indices of each channel from the input array.

The result will be an NDArray of shape (num_channel,).

In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence are returned.

Examples:

x = [[ 0.,  1.,  2.],
[ 3.,  4.,  5.]]

argmax_channel(x) = [ 2.,  2.]


Parameters: data (Symbol) – The input array name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.argmin(data=None, axis=_Null, keepdims=_Null, name=None, attr=None, out=None, **kwargs)

Returns indices of the minimum values along an axis.

In the case of multiple occurrences of minimum values, the indices corresponding to the first occurrence are returned.

Examples:

x = [[ 0.,  1.,  2.],
[ 3.,  4.,  5.]]

// argmin along axis 0
argmin(x, axis=0) = [ 0.,  0.,  0.]

// argmin along axis 1
argmin(x, axis=1) = [ 0.,  0.]

// argmin along axis 1 keeping same dims as an input array
argmin(x, axis=1, keepdims=True) = [[ 0.],
[ 0.]]


Parameters: data (Symbol) – The input axis (int or None, optional, default='None') – The axis along which to perform the reduction. Negative values means indexing from right to left. Requires axis to be set as int, because global reduction is not supported yet. keepdims (boolean, optional, default=False) – If this is set to True, the reduced axis is left in the result as dimension with size one. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.argsort(data=None, axis=_Null, is_ascend=_Null, name=None, attr=None, out=None, **kwargs)

Returns the indices that would sort an input array along the given axis.

This function performs sorting along the given axis and returns an array of indices having same shape as an input array that index data in sorted order.

Examples:

x = [[ 0.3,  0.2,  0.4],
[ 0.1,  0.3,  0.2]]

// sort along axis -1
argsort(x) = [[ 1.,  0.,  2.],
[ 0.,  2.,  1.]]

// sort along axis 0
argsort(x, axis=0) = [[ 1.,  0.,  1.]
[ 0.,  1.,  0.]]

// flatten and then sort
argsort(x) = [ 3.,  1.,  5.,  0.,  4.,  2.]


Defined in src/operator/tensor/ordering_op.cc:L175

Parameters: data (Symbol) – The input array axis (int or None, optional, default='-1') – Axis along which to sort the input tensor. If not given, the flattened array is used. Default is -1. is_ascend (boolean, optional, default=True) – Whether to sort in ascending or descending order. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.batch_dot(lhs=None, rhs=None, transpose_a=_Null, transpose_b=_Null, name=None, attr=None, out=None, **kwargs)

Batchwise dot product.

batch_dot is used to compute dot product of x and y when x and y are data in batch, namely 3D arrays in shape of (batch_size, :, :).

For example, given x with shape (batch_size, n, m) and y with shape (batch_size, m, k), the result array will have shape (batch_size, n, k), which is computed by:

batch_dot(x,y)[i,:,:] = dot(x[i,:,:], y[i,:,:])


Defined in src/operator/tensor/matrix_op.cc:L430

Parameters: lhs (Symbol) – The first input rhs (Symbol) – The second input transpose_a (boolean, optional, default=False) – If true then transpose the first input before dot. transpose_b (boolean, optional, default=False) – If true then transpose the second input before dot. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.batch_take(a=None, indices=None, name=None, attr=None, out=None, **kwargs)

Takes elements from a data batch.

Note

batch_take is deprecated. Use pick instead.

Given an input array of shape (d0, d1) and indices of shape (i0,), the result will be an output array of shape (i0,) with:

output[i] = input[i, indices[i]]


Examples:

x = [[ 1.,  2.],
[ 3.,  4.],
[ 5.,  6.]]

// takes elements with specified indices
batch_take(x, [0,1,0]) = [ 1.  4.  5.]


Defined in src/operator/tensor/indexing_op.cc:L190

Parameters: a (Symbol) – The input array indices (Symbol) – The index array name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_add(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise sum of the input arrays with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

[ 2.,  2.,  2.]]

broadcast_plus(x, y) = [[ 1.,  1.,  1.],
[ 2.,  2.,  2.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_axes(data=None, axis=_Null, size=_Null, name=None, attr=None, out=None, **kwargs)

Broadcasts the input array over particular axes.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to (2,8,3,9). Elements will be duplicated on the broadcasted axes.

Example:

// given x of shape (1,2,1)
x = [[[ 1.],
[ 2.]]]

// broadcast x on on axis 2
broadcast_axis(x, axis=2, size=3) = [[[ 1.,  1.,  1.],
[ 2.,  2.,  2.]]]
// broadcast x on on axes 0 and 2
broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1.,  1.,  1.],
[ 2.,  2.,  2.]],
[[ 1.,  1.,  1.],
[ 2.,  2.,  2.]]]


Parameters: data (Symbol) – The input axis (Shape(tuple), optional, default=()) – The axes to perform the broadcasting. size (Shape(tuple), optional, default=()) – Target sizes of the broadcasting axes. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_axis(data=None, axis=_Null, size=_Null, name=None, attr=None, out=None, **kwargs)

Broadcasts the input array over particular axes.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to (2,8,3,9). Elements will be duplicated on the broadcasted axes.

Example:

// given x of shape (1,2,1)
x = [[[ 1.],
[ 2.]]]

// broadcast x on on axis 2
broadcast_axis(x, axis=2, size=3) = [[[ 1.,  1.,  1.],
[ 2.,  2.,  2.]]]
// broadcast x on on axes 0 and 2
broadcast_axis(x, axis=(0,2), size=(2,3)) = [[[ 1.,  1.,  1.],
[ 2.,  2.,  2.]],
[[ 1.,  1.,  1.],
[ 2.,  2.,  2.]]]


Parameters: data (Symbol) – The input axis (Shape(tuple), optional, default=()) – The axes to perform the broadcasting. size (Shape(tuple), optional, default=()) – Target sizes of the broadcasting axes. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_div(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise division of the input arrays with broadcasting.

Example:

x = [[ 6.,  6.,  6.],
[ 6.,  6.,  6.]]

y = [[ 2.],
[ 3.]]

broadcast_div(x, y) = [[ 3.,  3.,  3.],
[ 2.,  2.,  2.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_equal(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns the result of element-wise equal to (==) comparison operation with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_equal(x, y) = [[ 0.,  0.,  0.],
[ 1.,  1.,  1.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_greater(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns the result of element-wise greater than (>) comparison operation with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_greater(x, y) = [[ 1.,  1.,  1.],
[ 0.,  0.,  0.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_greater_equal(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns the result of element-wise greater than or equal to (>=) comparison operation with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_greater_equal(x, y) = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_hypot(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns the hypotenuse of a right angled triangle, given its “legs” with broadcasting.

It is equivalent to doing $$sqrt(x_1^2 + x_2^2)$$.

Example:

x = [[ 3.,  3.,  3.]]

y = [[ 4.],
[ 4.]]

broadcast_hypot(x, y) = [[ 5.,  5.,  5.],
[ 5.,  5.,  5.]]

z = [[ 0.],
[ 4.]]

broadcast_hypot(x, z) = [[ 3.,  3.,  3.],
[ 5.,  5.,  5.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_lesser(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns the result of element-wise lesser than (<) comparison operation with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_lesser(x, y) = [[ 0.,  0.,  0.],
[ 0.,  0.,  0.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_lesser_equal(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns the result of element-wise lesser than or equal to (<=) comparison operation with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_lesser_equal(x, y) = [[ 0.,  0.,  0.],
[ 1.,  1.,  1.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_maximum(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise maximum of the input arrays with broadcasting.

This function compares two input arrays and returns a new array having the element-wise maxima.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_maximum(x, y) = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_minimum(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise minimum of the input arrays with broadcasting.

This function compares two input arrays and returns a new array having the element-wise minima.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_maximum(x, y) = [[ 0.,  0.,  0.],
[ 1.,  1.,  1.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_minus(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise difference of the input arrays with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_sub(x, y) = [[ 1.,  1.,  1.],
[ 0.,  0.,  0.]]

broadcast_minus(x, y) = [[ 1.,  1.,  1.],
[ 0.,  0.,  0.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_mod(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise modulo of the input arrays with broadcasting.

Example:

x = [[ 8.,  8.,  8.],
[ 8.,  8.,  8.]]

y = [[ 2.],
[ 3.]]

broadcast_mod(x, y) = [[ 0.,  0.,  0.],
[ 2.,  2.,  2.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_mul(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise product of the input arrays with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_mul(x, y) = [[ 0.,  0.,  0.],
[ 1.,  1.,  1.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_not_equal(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns the result of element-wise not equal to (!=) comparison operation with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_not_equal(x, y) = [[ 1.,  1.,  1.],
[ 0.,  0.,  0.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_plus(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise sum of the input arrays with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

[ 2.,  2.,  2.]]

broadcast_plus(x, y) = [[ 1.,  1.,  1.],
[ 2.,  2.,  2.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_power(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns result of first array elements raised to powers from second array, element-wise with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_power(x, y) = [[ 2.,  2.,  2.],
[ 4.,  4.,  4.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_sub(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise difference of the input arrays with broadcasting.

Example:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

y = [[ 0.],
[ 1.]]

broadcast_sub(x, y) = [[ 1.,  1.,  1.],
[ 0.,  0.,  0.]]

broadcast_minus(x, y) = [[ 1.,  1.,  1.],
[ 0.,  0.,  0.]]


Parameters: lhs (Symbol) – First input to the function rhs (Symbol) – Second input to the function name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.broadcast_to(data=None, shape=_Null, name=None, attr=None, out=None, **kwargs)

Broadcasts the input array to a new shape.

Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations with arrays of different shapes efficiently without creating multiple copies of arrays. Also see, Broadcasting for more explanation.

Broadcasting is allowed on axes with size 1, such as from (2,1,3,1) to (2,8,3,9). Elements will be duplicated on the broadcasted axes.

For example:

broadcast_to([[1,2,3]], shape=(2,3)) = [[ 1.,  2.,  3.],
[ 1.,  2.,  3.]])


The dimension which you do not want to change can also be kept as 0 which means copy the original value. So with shape=(2,0), we will obtain the same result as in the above example.

Parameters: data (Symbol) – The input shape (Shape(tuple), optional, default=()) – The shape of the desired array. We can set the dim to zero if it’s same as the original. E.g A = broadcast_to(B, shape=(10, 0, 0)) has the same meaning as A = broadcast_axis(B, axis=0, size=10). name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.cast(data=None, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Casts all elements of the input to a new type.

Note

Cast is deprecated. Use cast instead.

Example:

cast([0.9, 1.3], dtype='int32') = [0, 1]
cast([1e20, 11.1], dtype='float16') = [inf, 11.09375]
cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253]


Defined in src/operator/tensor/elemwise_unary_op.cc:L193

Parameters: data (Symbol) – The input. dtype ({'float16', 'float32', 'float64', 'int32', 'uint8'}, required) – Output data type. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.ceil(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise ceiling of the input.

The ceil of the scalar x is the smallest integer i, such that i >= x.

Example:

ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  2.,  2.,  3.]


Defined in src/operator/tensor/elemwise_unary_op.cc:L313

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.choose_element_0index(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Choose one element from each line(row for python, column for R/Julia) in lhs according to index indicated by rhs. This function assume rhs uses 0-based index.

Parameters: lhs (NDArray) – Left operand to the function. rhs (NDArray) – Right operand to the function. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.clip(data=None, a_min=_Null, a_max=_Null, name=None, attr=None, out=None, **kwargs)

Clips (limits) the values in an array.

Given an interval, values outside the interval are clipped to the interval edges. Clipping x between a_min and a_x would be:

clip(x, a_min, a_max) = max(min(x, a_max), a_min))


Example:

x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

clip(x,1,8) = [ 1.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  8.]


Defined in src/operator/tensor/matrix_op.cc:L475

Parameters: data (Symbol) – Input array. a_min (float, required) – Minimum value a_max (float, required) – Maximum value name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.concat(*data, **kwargs)

Joins input arrays along a given axis.

Note

Concat is deprecated. Use concat instead.

The dimensions of the input arrays should be the same except the axis along which they will be concatenated. The dimension of the output array along the concatenated axis will be equal to the sum of the corresponding dimensions of the input arrays.

Example:

x = [[1,1],[2,2]]
y = [[3,3],[4,4],[5,5]]
z = [[6,6], [7,7],[8,8]]

concat(x,y,z,dim=0) = [[ 1.,  1.],
[ 2.,  2.],
[ 3.,  3.],
[ 4.,  4.],
[ 5.,  5.],
[ 6.,  6.],
[ 7.,  7.],
[ 8.,  8.]]

Note that you cannot concat x,y,z along dimension 1 since dimension
0 is not the same for all the input arrays.

concat(y,z,dim=1) = [[ 3.,  3.,  6.,  6.],
[ 4.,  4.,  7.,  7.],
[ 5.,  5.,  8.,  8.]]


Defined in src/operator/concat.cc:L98 This function support variable length of positional input.

Parameters: data (Symbol[]) – List of arrays to concatenate dim (int, optional, default='1') – the dimension to be concated. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.cos(data=None, name=None, attr=None, out=None, **kwargs)

Computes the element-wise cosine of the input array.

The input should be in radians ($$2\pi$$ rad equals 360 degrees).

$cos([0, \pi/4, \pi/2]) = [1, 0.707, 0]$

Defined in src/operator/tensor/elemwise_unary_op.cc:L509

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.cosh(data=None, name=None, attr=None, out=None, **kwargs)

Returns the hyperbolic cosine of the input array, computed element-wise.

$cosh(x) = 0.5\times(exp(x) + exp(-x))$

Defined in src/operator/tensor/elemwise_unary_op.cc:L631

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.crop(data=None, begin=_Null, end=_Null, name=None, attr=None, out=None, **kwargs)

Slices a contiguous region of the array.

Note

crop is deprecated. Use slice instead.

This function returns a sliced continuous region of the array between the indices given by begin and end.

For an input array of n dimensions, slice operation with begin=(b_0, b_1...b_n-1) indices and end=(e_1, e_2, ... e_n) indices will result in an array with the shape (e_1-b_0, ..., e_n-b_n-1).

The resulting array’s k-th dimension contains elements from the k-th dimension of the input array with the open range [b_k, e_k).

Example:

x = [[  1.,   2.,   3.,   4.],
[  5.,   6.,   7.,   8.],
[  9.,  10.,  11.,  12.]]

slice(x, begin=(0,1), end=(2,4)) = [[ 2.,  3.,  4.],
[ 6.,  7.,  8.]]


Defined in src/operator/tensor/matrix_op.cc:L275

Parameters: data (Symbol) – Source input begin (Shape(tuple), required) – starting indices for the slice operation, supports negative indices. end (Shape(tuple), required) – ending indices for the slice operation, supports negative indices. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.degrees(data=None, name=None, attr=None, out=None, **kwargs)

Converts each element of the input array from radians to degrees.

$degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360]$

Defined in src/operator/tensor/elemwise_unary_op.cc:L589

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.dot(lhs=None, rhs=None, transpose_a=_Null, transpose_b=_Null, name=None, attr=None, out=None, **kwargs)

Dot product of two arrays.

dot‘s behavior depends on the input array dimensions:

• 1-D arrays: inner product of vectors

• 2-D arrays: matrix multiplication

• N-D arrays: a sum product over the last axis of the first input and the first axis of the second input

For example, given 3-D x with shape (n,m,k) and y with shape (k,r,s), the result array will have shape (n,m,r,s). It is computed by:

dot(x,y)[i,j,a,b] = sum(x[i,j,:]*y[:,a,b])


Example:

x = reshape([0,1,2,3,4,5,6,7], shape=(2,2,2))
y = reshape([7,6,5,4,3,2,1,0], shape=(2,2,2))
dot(x,y)[0,0,1,1] = 0
sum(x[0,0,:]*y[:,1,1]) = 0


Defined in src/operator/tensor/matrix_op.cc:L394

Parameters: lhs (Symbol) – The first input rhs (Symbol) – The second input transpose_a (boolean, optional, default=False) – If true then transpose the first input before dot. transpose_b (boolean, optional, default=False) – If true then transpose the second input before dot. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.elemwise_add(lhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Parameters: lhs (Symbol) – first input rhs (Symbol) – second input name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.exp(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise exponential value of the input.

$exp(x) = e^x \approx 2.718^x$

Example:

exp([0, 1, 2]) = [inf, 1, 0.707]


Defined in src/operator/tensor/elemwise_unary_op.cc:L420

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.expand_dims(data=None, axis=_Null, name=None, attr=None, out=None, **kwargs)

Inserts a new axis of size 1 into the array shape

For example, given x with shape (2,3,4), then expand_dims(x, axis=1) will return a new array with shape (2,1,3,4).

Defined in src/operator/tensor/matrix_op.cc:L231

Parameters: data (Symbol) – Source input axis (int, required) – Position where new axis is to be inserted. Suppose that the input NDArray‘s dimension is ndim, the range of the inserted axis is [-ndim, ndim] name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.expm1(data=None, name=None, attr=None, out=None, **kwargs)

Returns exp(x) - 1 computed element-wise on the input.

This function provides greater precision than exp(x) - 1 for small values of x.

Defined in src/operator/tensor/elemwise_unary_op.cc:L493

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.fill_element_0index(lhs=None, mhs=None, rhs=None, name=None, attr=None, out=None, **kwargs)

Fill one element of each line(row for python, column for R/Julia) in lhs according to index indicated by rhs and values indicated by mhs. This function assume rhs uses 0-based index.

Parameters: lhs (NDArray) – Left operand to the function. mhs (NDArray) – Middle operand to the function. rhs (NDArray) – Right operand to the function. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.fix(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise rounded value to the nearest integer towards zero of the input.

Example:

fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1.,  1., 2.]


Defined in src/operator/tensor/elemwise_unary_op.cc:L351

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.flatten(data=None, name=None, attr=None, out=None, **kwargs)

Flattens the input array into a 2-D array by collapsing the higher dimensions.

Note

Flatten is deprecated. Use flatten instead.

For an input array with shape (d1, d2, ..., dk), flatten operation reshapes the input array into an output array of shape (d1, d2*...*dk).

Example:

x = [[
[1,2,3],
[4,5,6],
[7,8,9]
],
[    [1,2,3],
[4,5,6],
[7,8,9]
]],

flatten(x) = [[ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.],
[ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.]]


Defined in src/operator/tensor/matrix_op.cc:L150

Parameters: data (Symbol) – Input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.flip(data=None, axis=_Null, name=None, attr=None, out=None, **kwargs)

Reverses the order of elements along given axis while preserving array shape.

Note: reverse and flip are equivalent. We use reverse in the following examples.

Examples:

x = [[ 0.,  1.,  2.,  3.,  4.],
[ 5.,  6.,  7.,  8.,  9.]]

reverse(x, axis=0) = [[ 5.,  6.,  7.,  8.,  9.],
[ 0.,  1.,  2.,  3.,  4.]]

reverse(x, axis=1) = [[ 4.,  3.,  2.,  1.,  0.],
[ 9.,  8.,  7.,  6.,  5.]]


Defined in src/operator/tensor/matrix_op.cc:L619

Parameters: data (Symbol) – Input data array axis (Shape(tuple), required) – The axis which to reverse elements. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.floor(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise floor of the input.

The floor of the scalar x is the largest integer i, such that i <= x.

Example:

floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2.,  1.,  1.,  2.]


Defined in src/operator/tensor/elemwise_unary_op.cc:L326

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.gamma(data=None, name=None, attr=None, out=None, **kwargs)

Returns the gamma function (extension of the factorial function to the reals) , computed element-wise on the input array.

From:src/operator/tensor/elemwise_unary_op.cc:685

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.gammaln(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise log of the absolute value of the gamma function of the input.

From:src/operator/tensor/elemwise_unary_op.cc:695

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.identity(data=None, name=None, attr=None, out=None, **kwargs)

Returns a copy of the input.

From:src/operator/tensor/elemwise_unary_op.cc:67

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg_gemm(A=None, B=None, C=None, transpose_a=_Null, transpose_b=_Null, alpha=_Null, beta=_Null, name=None, attr=None, out=None, **kwargs)

Performs general matrix multiplication and accumulation. Input are three tensors A, B, C each of dimension n >= 2 and each having the same shape on the leading n-2 dimensions. For every n-2 dimensional index i let Ai, Bi, Ci be the matrices given by the last 2 dimensions. The operator performs the BLAS3 function gemm

outi = alpha * op(Ai) * op(Bi) + beta * Ci

on all such triples of matrices. Here alpha and beta are scalar operator parameters and op() is either the identity or the matrix transposition.

In case of n=2, a single gemm function is performed on the matrices A, B, C.

Note

The operator does only support float32 and float64 data types and provides proper backward gradients.

Examples:

// Single matrix multiply-add
A = [[1.0, 1.0], [1.0, 1.0]]
B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
C = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
linalg_gemm(A, B, C, transpose_b = 1, alpha = 2.0 , beta = 10.0)
= [[14.0, 14.0, 14.0], [14.0, 14.0, 14.0]]

A = [[[1.0, 1.0]], [[0.1, 0.1]]]
B = [[[1.0, 1.0]], [[0.1, 0.1]]]
C = [[[10.0]], [[0.01]]]
linalg_gemm(A, B, C, transpose_b = 1, alpha = 2.0 , beta = 10.0)
= [[[104.0]], [[0.14]]]


Defined in src/operator/tensor/la_op.cc:L66

Parameters: A (Symbol) – Tensor of input matrices B (Symbol) – Tensor of input matrices C (Symbol) – Tensor of input matrices transpose_a (boolean, optional, default=False) – Multiply with transposed of first input (A). transpose_b (boolean, optional, default=False) – Multiply with transposed of second input (B). alpha (double, optional, default=1) – Scalar factor multiplied with A*B. beta (double, optional, default=1) – Scalar factor multiplied with C. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg_gemm2(A=None, B=None, transpose_a=_Null, transpose_b=_Null, alpha=_Null, name=None, attr=None, out=None, **kwargs)

Performs general matrix multiplication. Input are two tensors A, B each of dimension n >= 2 and each having the same shape on the leading n-2 dimensions. For every n-2 dimensional index i let Ai, Bi be the matrices given by the last 2 dimensions. The operator performs the BLAS3 function gemm (restricted to two arguments)

outi = alpha * op(Ai) * op(Bi)

on all such pairs of matrices. Here alpha is a scalar operator parameter and op() is either the identity or the matrix transposition.

In case of n=2, a single gemm function is performed on the matrices A, B.

Note

The operator does only support float32 and float64 data types and provides proper backward gradients.

Examples:

// Single matrix multiply
A = [[1.0, 1.0], [1.0, 1.0]]
B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
linalg_gemm2(A, B, transpose_b = 1, alpha = 2.0)
= [[4.0, 4.0, 4.0], [4.0, 4.0, 4.0]]

// Batch matrix multiply
A = [[[1.0, 1.0]], [[0.1, 0.1]]]
B = [[[1.0, 1.0]], [[0.1, 0.1]]]
linalg_gemm2(A, B, transpose_b = 1, alpha = 2.0 )
= [[[4.0]], [[0.04 ]]]


Defined in src/operator/tensor/la_op.cc:L124

Parameters: A (Symbol) – Tensor of input matrices B (Symbol) – Tensor of input matrices transpose_a (boolean, optional, default=False) – Multiply with transposed of first input (A). transpose_b (boolean, optional, default=False) – Multiply with transposed of second input (B). alpha (double, optional, default=1) – Scalar factor multiplied with A*B. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg_potrf(A=None, name=None, attr=None, out=None, **kwargs)

Performs Cholesky factorization of a symmetric positive-definite matrix. Input is a tensor A of dimension n >= 2. For every n-2 dimensional index i let Ai be the matrix given by the last 2 dimensions. The operator performs the Cholesky factorization (LAPACK function potrf) on each Ai, i.e. it computes a lower triangular matrix Ui such that

Ai = Ui * UiT

for all such matrices. The matrices Ai must be all symmetric and positive-definite. The resulting matrices Ui will contain zeros in the upper triangle apart from the diagonal.

In case of n=2, a single Cholesky factorization is performed on the matrix A.

Note

The operator does only support float32 and float64 data types and provides proper backward gradients.

Examples:

// Single matrix factorization
A = [[4.0, 1.0], [1.0, 4.25]]
linalg_potrf(A) = [[2.0, 0], [0.5, 2.0]]

// Batch matrix factorization
A = [[[4.0, 1.0], [1.0, 4.25]], [[16.0, 4.0], [4.0, 17.0]]]
linalg_potrf(A) = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]


Defined in src/operator/tensor/la_op.cc:L177

Parameters: A (Symbol) – Tensor of input matrices to be decomposed name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg_potri(A=None, name=None, attr=None, out=None, **kwargs)

Performs matrix inversion from a Cholesky factorization. Input is a tensor A of dimension n >= 2. For every n-2 dimensional index i let Ai be the matrix given by the last 2 dimensions. The operator assumes that each Ai is the Cholesky factorization of some symmetric positive-definite matrix Bi given as a lower triangular matrix (so A is the output of a prior call to operator linalg_potrf). The operator computes the inverse of each Bi from this decomposition, i.e

outi = Bi-1

for all such matrices.

In case of n=2, the operation is performed on the matrix A itself.

Note

The operator does only support float32 and float64 data types and provides proper backward gradients.

Examples:

// Single matrix inverse
A = [[2.0, 0], [0.5, 2.0]]
linalg_potri(A) = [[0.26563, -0.0625], [-0.0625, 0.25]]

// Batch matrix inverse
A = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
linalg_potri(A) = [[[0.26563, -0.0625], [-0.0625, 0.25]],
[[0.06641, -0.01562], [-0.01562, 0,0625]]]


Defined in src/operator/tensor/la_op.cc:L229

Parameters: A (Symbol) – Tensor of lower triangular matrices name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg_sumlogdiag(A=None, name=None, attr=None, out=None, **kwargs)

Computes the sum of the logarithms of all diagonal elements in a matrix. Input is a tensor A of dimension n >= 2. For every n-2 dimensional index i let Ai be the matrix given by the last 2 dimensions. The operator performs a reduction of each such matrix to a scalar by summing up the logarithms of all diagonal elements. All matrices must be square and all diagonal elements must be positive.

In case of n=2, A represents a single matrix on which the reduction will be performed.

Note

The operator does only support float32 and float64 data types and provides proper backward gradients.

Examples:

// Single matrix reduction
A = [[1.0, 1.0], [1.0, 7.0]]
linalg_sumlogdiag(A) = [1.9459]

// Batch matrix reduction
A = [[[1.0, 1.0], [1.0, 7.0]], [[3.0, 0], [0, 17.0]]]
linalg_sumlogdiag(A) = [1.9459, 3.9318]


Defined in src/operator/tensor/la_op.cc:L397

Parameters: A (Symbol) – Tensor of square matrices name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg_trmm(A=None, B=None, transpose=_Null, rightside=_Null, alpha=_Null, name=None, attr=None, out=None, **kwargs)

Performs multiplication with a triangular matrix. Input are two tensors A, B each of dimension n >= 2 and each having the same shape on the leading n-2 dimensions. For every n-2 dimensional index i let Ai, Bi be the matrices given by the last 2 dimensions. The operator performs the BLAS3 function trmm

outi = alpha * op(Ai) * Bi

or

outi = alpha * Bi * op(Ai)

on all such pairs of matrices. Here alpha is a scalar operator parameter, op() is either the identity or the matrix transposition (depending on the parameter transpose) and the order of matrix multiplication depends on the parameter rightside. All matrices Ai must be lower triangular.

In case of n=2, a single trmm function is performed on the matrices A, B.

Note

The operator does only support float32 and float64 data types and provides proper backward gradients.

Examples:

// Single matrix multiply
A = [[1.0, 0], [1.0, 1.0]]
B = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
linalg_trmm(A, B, alpha = 2.0) = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]

// Batch matrix multiply
A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
B = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], [[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]]]
linalg_trmm(A, B, alpha = 2.0 ) = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
[[1.0, 1.0, 1.0], [2.0, 2.0, 2.0]]]


Defined in src/operator/tensor/la_op.cc:L286

Parameters: A (Symbol) – Tensor of lower triangular matrices B (Symbol) – Tensor of matrices transpose (boolean, optional, default=False) – Use transposed of the triangular matrix rightside (boolean, optional, default=False) – Multiply triangular matrix from the right to non-triangular one. alpha (double, optional, default=1) – Scalar factor to be applied to the result. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.linalg_trsm(A=None, B=None, transpose=_Null, rightside=_Null, alpha=_Null, name=None, attr=None, out=None, **kwargs)

Solves matrix equations involving a triangular matrix. Input are two tensors A, B each of dimension n >= 2 and each having the same shape on the leading n-2 dimensions. For every n-2 dimensional index i let Ai, Bi be the matrices given by the last 2 dimensions. The operator performs the BLAS3 function trsm, i.e. it solves the equation

op(Ai) * Xi = alpha * Bi

or

Xi * op(Ai) = alpha * Bi

on all such pairs of matrices. Here alpha is a scalar operator parameter, op() is either the identity or the matrix transposition (depending on the parameter transpose) and the order of multiplication on the left depends on the parameter rightside. All matrices Ai must be lower triangular.

In case of n=2, a single trsm function is performed on the matrices A, B.

Note

The operator does only support float32 and float64 data types and provides proper backward gradients.

Examples:

// Single matrix solve
A = [[1.0, 0], [1.0, 1.0]]
B = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]
linalg_trsm(A, B, alpha = 0.5) = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]

// Batch matrix solve
A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
B = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
[[4.0, 4.0, 4.0], [8.0, 8.0, 8.0]]]
linalg_trsm(A, B, alpha = 0.5 ) = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]],
[[2.0, 2.0, 2.0 ], [2.0, 2.0, 2.0]]]


Defined in src/operator/tensor/la_op.cc:L349

Parameters: A (Symbol) – Tensor of lower triangular matrices B (Symbol) – Tensor of matrices transpose (boolean, optional, default=False) – Use transposed of the triangular matrix rightside (boolean, optional, default=False) – Multiply triangular matrix from the right to non-triangular one. alpha (double, optional, default=1) – Scalar factor to be applied to the result. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.log(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise Natural logarithmic value of the input.

The natural logarithm is logarithm in base e, so that log(exp(x)) = x

Defined in src/operator/tensor/elemwise_unary_op.cc:L430

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.log10(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise Base-10 logarithmic value of the input.

10**log10(x) = x

Defined in src/operator/tensor/elemwise_unary_op.cc:L440

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.log1p(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise log(1 + x) value of the input.

This function is more accurate than log(1 + x) for small x so that $$1+x\approx 1$$

Defined in src/operator/tensor/elemwise_unary_op.cc:L480

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.log2(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise Base-2 logarithmic value of the input.

2**log2(x) = x

Defined in src/operator/tensor/elemwise_unary_op.cc:L450

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.log_softmax(data=None, axis=_Null, name=None, attr=None, out=None, **kwargs)

Computes the log softmax of the input. This is equivalent to computing softmax followed by log.

Examples:

>>> x = mx.nd.array([1, 2, .1])
>>> mx.nd.log_softmax(x).asnumpy()
array([-1.41702998, -0.41702995, -2.31702995], dtype=float32)

>>> x = mx.nd.array( [[1, 2, .1],[.1, 2, 1]] )
>>> mx.nd.log_softmax(x, axis=0).asnumpy()
array([[-0.34115392, -0.69314718, -1.24115396],
[-1.24115396, -0.69314718, -0.34115392]], dtype=float32)

Parameters: data (Symbol) – The input array. axis (int, optional, default='-1') – The axis along which to compute softmax. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.make_loss(data=None, name=None, attr=None, out=None, **kwargs)

Stops gradient computation. .. note:: make_loss is deprecated, use MakeLoss.

Defined in src/operator/tensor/elemwise_unary_op.cc:L128

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.max(data=None, axis=_Null, keepdims=_Null, exclude=_Null, name=None, attr=None, out=None, **kwargs)

Computes the max of array elements over given axes.

Parameters: data (Symbol) – The input axis (Shape(tuple), optional, default=()) – The axis or axes along which to perform the reduction. The default, axis=(), will compute over all elements into a scalar array with shape (1,). If axis is int, a reduction is performed on a particular axis. If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If exclude is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims (boolean, optional, default=False) – If this is set to True, the reduced axes are left in the result as dimension with size one. exclude (boolean, optional, default=False) – Whether to perform reduction on axis that are NOT in axis instead. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.max_axis(data=None, axis=_Null, keepdims=_Null, exclude=_Null, name=None, attr=None, out=None, **kwargs)

Computes the max of array elements over given axes.

Parameters: data (Symbol) – The input axis (Shape(tuple), optional, default=()) – The axis or axes along which to perform the reduction. The default, axis=(), will compute over all elements into a scalar array with shape (1,). If axis is int, a reduction is performed on a particular axis. If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If exclude is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims (boolean, optional, default=False) – If this is set to True, the reduced axes are left in the result as dimension with size one. exclude (boolean, optional, default=False) – Whether to perform reduction on axis that are NOT in axis instead. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.mean(data=None, axis=_Null, keepdims=_Null, exclude=_Null, name=None, attr=None, out=None, **kwargs)

Computes the mean of array elements over given axes.

Parameters: data (Symbol) – The input axis (Shape(tuple), optional, default=()) – The axis or axes along which to perform the reduction. The default, axis=(), will compute over all elements into a scalar array with shape (1,). If axis is int, a reduction is performed on a particular axis. If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If exclude is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims (boolean, optional, default=False) – If this is set to True, the reduced axes are left in the result as dimension with size one. exclude (boolean, optional, default=False) – Whether to perform reduction on axis that are NOT in axis instead. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.min(data=None, axis=_Null, keepdims=_Null, exclude=_Null, name=None, attr=None, out=None, **kwargs)

Computes the min of array elements over given axes.

Parameters: data (Symbol) – The input axis (Shape(tuple), optional, default=()) – The axis or axes along which to perform the reduction. The default, axis=(), will compute over all elements into a scalar array with shape (1,). If axis is int, a reduction is performed on a particular axis. If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If exclude is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims (boolean, optional, default=False) – If this is set to True, the reduced axes are left in the result as dimension with size one. exclude (boolean, optional, default=False) – Whether to perform reduction on axis that are NOT in axis instead. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.min_axis(data=None, axis=_Null, keepdims=_Null, exclude=_Null, name=None, attr=None, out=None, **kwargs)

Computes the min of array elements over given axes.

Parameters: data (Symbol) – The input axis (Shape(tuple), optional, default=()) – The axis or axes along which to perform the reduction. The default, axis=(), will compute over all elements into a scalar array with shape (1,). If axis is int, a reduction is performed on a particular axis. If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If exclude is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims (boolean, optional, default=False) – If this is set to True, the reduced axes are left in the result as dimension with size one. exclude (boolean, optional, default=False) – Whether to perform reduction on axis that are NOT in axis instead. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.mp_sgd_mom_update(weight=None, grad=None, mom=None, weight32=None, lr=_Null, momentum=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, name=None, attr=None, out=None, **kwargs)

Updater function for multi-precision sgd optimizer

mxnet.symbol.mp_sgd_update(weight=None, grad=None, weight32=None, lr=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, name=None, attr=None, out=None, **kwargs)

Updater function for multi-precision sgd optimizer

mxnet.symbol.nanprod(data=None, axis=_Null, keepdims=_Null, exclude=_Null, name=None, attr=None, out=None, **kwargs)

Computes the product of array elements over given axes treating Not a Numbers (NaN) as one.

Parameters: data (Symbol) – The input axis (Shape(tuple), optional, default=()) – The axis or axes along which to perform the reduction. The default, axis=(), will compute over all elements into a scalar array with shape (1,). If axis is int, a reduction is performed on a particular axis. If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If exclude is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims (boolean, optional, default=False) – If this is set to True, the reduced axes are left in the result as dimension with size one. exclude (boolean, optional, default=False) – Whether to perform reduction on axis that are NOT in axis instead. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.nansum(data=None, axis=_Null, keepdims=_Null, exclude=_Null, name=None, attr=None, out=None, **kwargs)

Computes the sum of array elements over given axes treating Not a Numbers (NaN) as zero.

Parameters: data (Symbol) – The input axis (Shape(tuple), optional, default=()) – The axis or axes along which to perform the reduction. The default, axis=(), will compute over all elements into a scalar array with shape (1,). If axis is int, a reduction is performed on a particular axis. If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If exclude is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims (boolean, optional, default=False) – If this is set to True, the reduced axes are left in the result as dimension with size one. exclude (boolean, optional, default=False) – Whether to perform reduction on axis that are NOT in axis instead. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.negative(data=None, name=None, attr=None, out=None, **kwargs)

Numerical negative of the argument, element-wise.

From:src/operator/tensor/elemwise_unary_op.cc:224

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.norm(data=None, name=None, attr=None, out=None, **kwargs)

Flattens the input array and then computes the l2 norm.

Examples:

x = [[1, 2],
[3, 4]]

norm(x) = [5.47722578]


Parameters: data (Symbol) – Source input name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.normal(loc=_Null, scale=_Null, shape=_Null, ctx=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Draw random samples from a normal (Gaussian) distribution.

Note

The existing alias normal is deprecated.

Samples are distributed according to a normal distribution parametrized by loc (mean) and scale (standard deviation).

Example:

random_normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478],
[-1.23474145,  1.55807114]]


Defined in src/operator/random/sample_op.cc:L80

Parameters: loc (float, optional, default=0) – Mean of the distribution. scale (float, optional, default=1) – Standard deviation of the distribution. shape (Shape(tuple), optional, default=()) – Shape of the output. ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.one_hot(indices=None, depth=_Null, on_value=_Null, off_value=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Returns a one-hot array.

The locations represented by indices take value on_value, while all other locations take value off_value.

one_hot operation with indices of shape (i0, i1) and depth of d would result in an output array of shape (i0, i1, d) with:

output[i,j,:] = off_value
output[i,j,indices[i,j]] = on_value


Examples:

one_hot([1,0,2,0], 3) = [[ 0.  1.  0.]
[ 1.  0.  0.]
[ 0.  0.  1.]
[ 1.  0.  0.]]

one_hot([1,0,2,0], 3, on_value=8, off_value=1,
dtype='int32') = [[1 8 1]
[8 1 1]
[1 1 8]
[8 1 1]]

one_hot([[1,0],[1,0],[2,0]], 3) = [[[ 0.  1.  0.]
[ 1.  0.  0.]]

[[ 0.  1.  0.]
[ 1.  0.  0.]]

[[ 0.  0.  1.]
[ 1.  0.  0.]]]


Defined in src/operator/tensor/indexing_op.cc:L236

Parameters: indices (Symbol) – array of locations where to set on_value depth (int, required) – Depth of the one hot dimension. on_value (double, optional, default=1) – The value assigned to the locations represented by indices. off_value (double, optional, default=0) – The value assigned to the locations not represented by indices. dtype ({'float16', 'float32', 'float64', 'int32', 'uint8'},optional, default='float32') – DType of the output name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.ones_like(data=None, name=None, attr=None, out=None, **kwargs)

Return an array of ones with the same shape and type as the input array.

Examples:

x = [[ 0.,  0.,  0.],
[ 0.,  0.,  0.]]

ones_like(x) = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

Parameters: data (Symbol) – The input name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.pad(data=None, mode=_Null, pad_width=_Null, constant_value=_Null, name=None, attr=None, out=None, **kwargs)

Pads an input array with a constant or edge values of the array.

Note

Note

Current implementation only supports 4D and 5D input arrays with padding applied only on axes 1, 2 and 3. Expects axes 4 and 5 in pad_width to be zero.

This operation pads an input array with either a constant_value or edge values along each axis of the input array. The amount of padding is specified by pad_width.

pad_width is a tuple of integer padding widths for each axis of the format (before_1, after_1, ... , before_N, after_N). The pad_width should be of length 2*N where N is the number of dimensions of the array.

For dimension N of the input array, before_N and after_N indicates how many values to add before and after the elements of the array along dimension N. The widths of the higher two dimensions before_1, after_1, before_2, after_2 must be 0.

Example:

x = [[[[  1.   2.   3.]
[  4.   5.   6.]]

[[  7.   8.   9.]
[ 10.  11.  12.]]]

[[[ 11.  12.  13.]
[ 14.  15.  16.]]

[[ 17.  18.  19.]
[ 20.  21.  22.]]]]

[[[[  1.   1.   2.   3.   3.]
[  1.   1.   2.   3.   3.]
[  4.   4.   5.   6.   6.]
[  4.   4.   5.   6.   6.]]

[[  7.   7.   8.   9.   9.]
[  7.   7.   8.   9.   9.]
[ 10.  10.  11.  12.  12.]
[ 10.  10.  11.  12.  12.]]]

[[[ 11.  11.  12.  13.  13.]
[ 11.  11.  12.  13.  13.]
[ 14.  14.  15.  16.  16.]
[ 14.  14.  15.  16.  16.]]

[[ 17.  17.  18.  19.  19.]
[ 17.  17.  18.  19.  19.]
[ 20.  20.  21.  22.  22.]
[ 20.  20.  21.  22.  22.]]]]

[[[[  0.   0.   0.   0.   0.]
[  0.   1.   2.   3.   0.]
[  0.   4.   5.   6.   0.]
[  0.   0.   0.   0.   0.]]

[[  0.   0.   0.   0.   0.]
[  0.   7.   8.   9.   0.]
[  0.  10.  11.  12.   0.]
[  0.   0.   0.   0.   0.]]]

[[[  0.   0.   0.   0.   0.]
[  0.  11.  12.  13.   0.]
[  0.  14.  15.  16.   0.]
[  0.   0.   0.   0.   0.]]

[[  0.   0.   0.   0.   0.]
[  0.  17.  18.  19.   0.]
[  0.  20.  21.  22.   0.]
[  0.   0.   0.   0.   0.]]]]


Parameters: data (Symbol) – An n-dimensional input array. mode ({'constant', 'edge', 'reflect'}, required) – Padding type to use. “constant” pads with constant_value “edge” pads using the edge values of the input array “reflect” pads by reflecting values with respect to the edges. pad_width (Shape(tuple), required) – Widths of the padding regions applied to the edges of each axis. It is a tuple of integer padding widths for each axis of the format (before_1, after_1, ... , before_N, after_N). It should be of length 2*N where N is the number of dimensions of the array.This is equivalent to pad_width in numpy.pad, but flattened. constant_value (double, optional, default=0) – The value used for padding when mode is “constant”. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.pick(data=None, index=None, axis=_Null, keepdims=_Null, name=None, attr=None, out=None, **kwargs)

Picks elements from an input array according to the input indices along the given axis.

Given an input array of shape (d0, d1) and indices of shape (i0,), the result will be an output array of shape (i0,) with:

output[i] = input[i, indices[i]]


By default, if any index mentioned is too large, it is replaced by the index that addresses the last element along an axis (the clip mode).

This function supports n-dimensional input and (n-1)-dimensional indices arrays.

Examples:

x = [[ 1.,  2.],
[ 3.,  4.],
[ 5.,  6.]]

// picks elements with specified indices along axis 0
pick(x, y=[0,1], 0) = [ 1.,  4.]

// picks elements with specified indices along axis 1
pick(x, y=[0,1,0], 1) = [ 1.,  4.,  5.]

y = [[ 1.],
[ 0.],
[ 2.]]

// picks elements with specified indices along axis 1 and dims are maintained
pick(x,y, 1, keepdims=True) = [[ 2.],
[ 3.],
[ 6.]]


Parameters: data (Symbol) – The input array index (Symbol) – The index array axis (int or None, optional, default='None') – The axis along which to perform the reduction. Negative values means indexing from right to left. Requires axis to be set as int, because global reduction is not supported yet. keepdims (boolean, optional, default=False) – If this is set to True, the reduced axis is left in the result as dimension with size one. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.prod(data=None, axis=_Null, keepdims=_Null, exclude=_Null, name=None, attr=None, out=None, **kwargs)

Computes the product of array elements over given axes.

Parameters: data (Symbol) – The input axis (Shape(tuple), optional, default=()) – The axis or axes along which to perform the reduction. The default, axis=(), will compute over all elements into a scalar array with shape (1,). If axis is int, a reduction is performed on a particular axis. If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If exclude is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims (boolean, optional, default=False) – If this is set to True, the reduced axes are left in the result as dimension with size one. exclude (boolean, optional, default=False) – Whether to perform reduction on axis that are NOT in axis instead. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.radians(data=None, name=None, attr=None, out=None, **kwargs)

Converts each element of the input array from degrees to radians.

$radians([0, 90, 180, 270, 360]) = [0, \pi/2, \pi, 3\pi/2, 2\pi]$

Defined in src/operator/tensor/elemwise_unary_op.cc:L603

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.random_exponential(lam=_Null, shape=_Null, ctx=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Draw random samples from an exponential distribution.

Samples are distributed according to an exponential distribution parametrized by lambda (rate).

Example:

random_exponential(lam=4, shape=(2,2)) = [[ 0.0097189 ,  0.08999364],
[ 0.04146638,  0.31715935]]


Defined in src/operator/random/sample_op.cc:L106

Parameters: lam (float, optional, default=1) – Lambda parameter (rate) of the exponential distribution. shape (Shape(tuple), optional, default=()) – Shape of the output. ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.random_gamma(alpha=_Null, beta=_Null, shape=_Null, ctx=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Draw random samples from a gamma distribution.

Samples are distributed according to a gamma distribution parametrized by alpha (shape) and beta (scale).

Example:

random_gamma(alpha=9, beta=0.5, shape=(2,2)) = [[ 7.10486984,  3.37695289],
[ 3.91697288,  3.65933681]]


Defined in src/operator/random/sample_op.cc:L93

Parameters: alpha (float, optional, default=1) – Alpha parameter (shape) of the gamma distribution. beta (float, optional, default=1) – Beta parameter (scale) of the gamma distribution. shape (Shape(tuple), optional, default=()) – Shape of the output. ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.random_generalized_negative_binomial(mu=_Null, alpha=_Null, shape=_Null, ctx=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Draw random samples from a generalized negative binomial distribution.

Samples are distributed according to a generalized negative binomial distribution parametrized by mu (mean) and alpha (dispersion). alpha is defined as 1/k where k is the failure limit of the number of unsuccessful experiments (generalized to real numbers). Samples will always be returned as a floating point data type.

Example:

random_generalized_negative_binomial(mu=2.0, alpha=0.3, shape=(2,2)) = [[ 2.,  1.],
[ 6.,  4.]]


Defined in src/operator/random/sample_op.cc:L151

Parameters: mu (float, optional, default=1) – Mean of the negative binomial distribution. alpha (float, optional, default=1) – Alpha (dispersion) parameter of the negative binomial distribution. shape (Shape(tuple), optional, default=()) – Shape of the output. ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.random_negative_binomial(k=_Null, p=_Null, shape=_Null, ctx=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Draw random samples from a negative binomial distribution.

Samples are distributed according to a negative binomial distribution parametrized by k (limit of unsuccessful experiments) and p (failure probability in each experiment). Samples will always be returned as a floating point data type.

Example:

random_negative_binomial(k=3, p=0.4, shape=(2,2)) = [[ 4.,  7.],
[ 2.,  5.]]


Defined in src/operator/random/sample_op.cc:L135

Parameters: k (int, optional, default='1') – Limit of unsuccessful experiments. p (float, optional, default=1) – Failure probability in each experiment. shape (Shape(tuple), optional, default=()) – Shape of the output. ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.random_normal(loc=_Null, scale=_Null, shape=_Null, ctx=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Draw random samples from a normal (Gaussian) distribution.

Note

The existing alias normal is deprecated.

Samples are distributed according to a normal distribution parametrized by loc (mean) and scale (standard deviation).

Example:

random_normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478],
[-1.23474145,  1.55807114]]


Defined in src/operator/random/sample_op.cc:L80

Parameters: loc (float, optional, default=0) – Mean of the distribution. scale (float, optional, default=1) – Standard deviation of the distribution. shape (Shape(tuple), optional, default=()) – Shape of the output. ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.random_poisson(lam=_Null, shape=_Null, ctx=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Draw random samples from a Poisson distribution.

Samples are distributed according to a Poisson distribution parametrized by lambda (rate). Samples will always be returned as a floating point data type.

Example:

random_poisson(lam=4, shape=(2,2)) = [[ 5.,  2.],
[ 4.,  6.]]


Defined in src/operator/random/sample_op.cc:L120

Parameters: lam (float, optional, default=1) – Lambda parameter (rate) of the Poisson distribution. shape (Shape(tuple), optional, default=()) – Shape of the output. ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.random_uniform(low=_Null, high=_Null, shape=_Null, ctx=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Draw random samples from a uniform distribution.

Note

The existing alias uniform is deprecated.

Samples are uniformly distributed over the half-open interval [low, high) (includes low, but excludes high).

Example:

random_uniform(low=0, high=1, shape=(2,2)) = [[ 0.60276335,  0.85794562],
[ 0.54488319,  0.84725171]]


Defined in src/operator/random/sample_op.cc:L63

Parameters: low (float, optional, default=0) – Lower bound of the distribution. high (float, optional, default=1) – Upper bound of the distribution. shape (Shape(tuple), optional, default=()) – Shape of the output. ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.reciprocal(data=None, name=None, attr=None, out=None, **kwargs)

Returns the reciprocal of the argument, element-wise.

Calculates 1/x.

Example:

reciprocal([-2, 1, 3, 1.6, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0]


Defined in src/operator/tensor/elemwise_unary_op.cc:L238

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.relu(data=None, name=None, attr=None, out=None, **kwargs)

Computes rectified linear.

$max(features, 0)$

Defined in src/operator/tensor/elemwise_unary_op.cc:L36

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.repeat(data=None, repeats=_Null, axis=_Null, name=None, attr=None, out=None, **kwargs)

Repeats elements of an array.

By default, repeat flattens the input array into 1-D and then repeats the elements:

x = [[ 1, 2],
[ 3, 4]]

repeat(x, repeats=2) = [ 1.,  1.,  2.,  2.,  3.,  3.,  4.,  4.]


The parameter axis specifies the axis along which to perform repeat:

repeat(x, repeats=2, axis=1) = [[ 1.,  1.,  2.,  2.],
[ 3.,  3.,  4.,  4.]]

repeat(x, repeats=2, axis=0) = [[ 1.,  2.],
[ 1.,  2.],
[ 3.,  4.],
[ 3.,  4.]]

repeat(x, repeats=2, axis=-1) = [[ 1.,  1.,  2.,  2.],
[ 3.,  3.,  4.,  4.]]


Defined in src/operator/tensor/matrix_op.cc:L517

Parameters: data (Symbol) – Input data array repeats (int, required) – The number of repetitions for each element. axis (int or None, optional, default='None') – The axis along which to repeat values. The negative numbers are interpreted counting from the backward. By default, use the flattened input array, and return a flat output array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.reshape(data=None, shape=_Null, reverse=_Null, target_shape=_Null, keep_highest=_Null, name=None, attr=None, out=None, **kwargs)

Reshapes the input array.

Note

Reshape is deprecated, use reshape

Given an array and a shape, this function returns a copy of the array in the new shape. The shape is a tuple of integers such as (2,3,4).The size of the new shape should be same as the size of the input array.

Example:

reshape([1,2,3,4], shape=(2,2)) = [[1,2], [3,4]]


Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below:

• 0 copy this dimension from the input to the output shape.

Example:

- input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2)
- input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4)

• -1 infers the dimension of the output shape by using the remainder of the input dimensions keeping the size of the new array same as that of the input array. At most one dimension of shape can be -1.

Example:

- input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4)
- input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8)
- input shape = (2,3,4), shape=(-1,), output shape = (24,)

• -2 copy all/remainder of the input dimensions to the output shape.

Example:

- input shape = (2,3,4), shape = (-2,), output shape = (2,3,4)
- input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4)
- input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1)

• -3 use the product of two consecutive dimensions of the input shape as the output dimension.

Example:

- input shape = (2,3,4), shape = (-3,4), output shape = (6,4)
- input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20)
- input shape = (2,3,4), shape = (0,-3), output shape = (2,12)
- input shape = (2,3,4), shape = (-3,-2), output shape = (6,4)

• -4 split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1).

Example:

- input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4)
- input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4)


If the argument reverse is set to 1, then the special values are inferred from right to left.

Example:

- without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5)
- with reverse=1, output shape will be (50,4).


Defined in src/operator/tensor/matrix_op.cc:L106

Parameters: data (Symbol) – Input data to reshape. shape (Shape(tuple), optional, default=()) – The target shape reverse (boolean, optional, default=False) – If true then the special values are inferred from right to left target_shape (Shape(tuple), optional, default=()) – (Deprecated! Use shape instead.) Target new shape. One and only one dim can be 0, in which case it will be inferred from the rest of dims keep_highest (boolean, optional, default=False) – (Deprecated! Use shape instead.) Whether keep the highest dim unchanged.If set to true, then the first dim in target_shape is ignored,and always fixed as input name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.reverse(data=None, axis=_Null, name=None, attr=None, out=None, **kwargs)

Reverses the order of elements along given axis while preserving array shape.

Note: reverse and flip are equivalent. We use reverse in the following examples.

Examples:

x = [[ 0.,  1.,  2.,  3.,  4.],
[ 5.,  6.,  7.,  8.,  9.]]

reverse(x, axis=0) = [[ 5.,  6.,  7.,  8.,  9.],
[ 0.,  1.,  2.,  3.,  4.]]

reverse(x, axis=1) = [[ 4.,  3.,  2.,  1.,  0.],
[ 9.,  8.,  7.,  6.,  5.]]


Defined in src/operator/tensor/matrix_op.cc:L619

Parameters: data (Symbol) – Input data array axis (Shape(tuple), required) – The axis which to reverse elements. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.rint(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise rounded value to the nearest integer of the input.

Note

• For input n.5 rint returns n while round returns n+1.
• For input -n.5 both rint and round returns -n-1.

Example:

rint([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  1., -2.,  2.,  2.]


Defined in src/operator/tensor/elemwise_unary_op.cc:L300

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.rmsprop_update(weight=None, grad=None, n=None, lr=_Null, gamma1=_Null, epsilon=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, clip_weights=_Null, name=None, attr=None, out=None, **kwargs)

Update function for RMSProp optimizer.

RMSprop is a variant of stochastic gradient descent where the gradients are divided by a cache which grows with the sum of squares of recent gradients?

RMSProp is similar to AdaGrad, a popular variant of SGD which adaptively tunes the learning rate of each parameter. AdaGrad lowers the learning rate for each parameter monotonically over the course of training. While this is analytically motivated for convex optimizations, it may not be ideal for non-convex problems. RMSProp deals with this heuristically by allowing the learning rates to rebound as the denominator decays over time.

Define the Root Mean Square (RMS) error criterion of the gradient as $$RMS[g]_t = \sqrt{E[g^2]_t + \epsilon}$$, where $$g$$ represents gradient and $$E[g^2]_t$$ is the decaying average over past squared gradient.

The $$E[g^2]_t$$ is given by:

$E[g^2]_t = \gamma * E[g^2]_{t-1} + (1-\gamma) * g_t^2$

The update step is

$\theta_{t+1} = \theta_t - \frac{\eta}{RMS[g]_t} g_t$

The RMSProp code follows the version in http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf Tieleman & Hinton, 2012.

Hinton suggests the momentum term $$\gamma$$ to be 0.9 and the learning rate $$\eta$$ to be 0.001.

Defined in src/operator/optimizer_op.cc:L196

mxnet.symbol.rmspropalex_update(weight=None, grad=None, n=None, g=None, delta=None, lr=_Null, gamma1=_Null, gamma2=_Null, epsilon=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, clip_weights=_Null, name=None, attr=None, out=None, **kwargs)

Update function for RMSPropAlex optimizer.

RMSPropAlex is non-centered version of RMSProp.

Define $$E[g^2]_t$$ is the decaying average over past squared gradient and $$E[g]_t$$ is the decaying average over past gradient.

$\begin{split}E[g^2]_t = \gamma_1 * E[g^2]_{t-1} + (1 - \gamma_1) * g_t^2\\ E[g]_t = \gamma_1 * E[g]_{t-1} + (1 - \gamma_1) * g_t\\ \Delta_t = \gamma_2 * \Delta_{t-1} - \frac{\eta}{\sqrt{E[g^2]_t - E[g]_t^2 + \epsilon}} g_t\\\end{split}$

The update step is

$\theta_{t+1} = \theta_t + \Delta_t$

The RMSPropAlex code follows the version in http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013.

Graves suggests the momentum term $$\gamma_1$$ to be 0.95, $$\gamma_2$$ to be 0.9 and the learning rate $$\eta$$ to be 0.0001.

Defined in src/operator/optimizer_op.cc:L235

mxnet.symbol.round(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise rounded value to the nearest integer of the input.

Example:

round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2.,  2., -2.,  2.,  2.]


Defined in src/operator/tensor/elemwise_unary_op.cc:L284

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.rsqrt(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise inverse square-root value of the input.

$rsqrt(x) = 1/\sqrt{x}$

Example:

rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25]


Defined in src/operator/tensor/elemwise_unary_op.cc:L401

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sample_exponential(lam=None, shape=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Concurrent sampling from multiple exponential distributions with parameters lambda (rate).

The parameters of the distributions are provided as an input array. Let [s] be the shape of the input array, n be the dimension of [s], [t] be the shape specified as the parameter of the operator, and m be the dimension of [t]. Then the output will be a (n+m)-dimensional array with shape [s]x[t].

For any valid n-dimensional index i with respect to the input array, output[i] will be an m-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input value at index i. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input array.

Examples:

lam = [ 1.0, 8.5 ]

// Draw a single sample for each distribution
sample_exponential(lam) = [ 0.51837951,  0.09994757]

// Draw a vector containing two samples for each distribution
sample_exponential(lam, shape=(2)) = [[ 0.51837951,  0.19866663],
[ 0.09994757,  0.50447971]]


Defined in src/operator/random/multisample_op.cc:L388

Parameters: lam (Symbol) – Lambda (rate) parameters of the distributions. shape (Shape(tuple), optional, default=()) – Shape to be sampled from each random distribution. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sample_gamma(alpha=None, beta=None, shape=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Concurrent sampling from multiple gamma distributions with parameters alpha (shape) and beta (scale).

The parameters of the distributions are provided as input arrays. Let [s] be the shape of the input arrays, n be the dimension of [s], [t] be the shape specified as the parameter of the operator, and m be the dimension of [t]. Then the output will be a (n+m)-dimensional array with shape [s]x[t].

For any valid n-dimensional index i with respect to the input arrays, output[i] will be an m-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index i. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays.

Examples:

alpha = [ 0.0, 2.5 ]
beta = [ 1.0, 0.7 ]

// Draw a single sample for each distribution
sample_gamma(alpha, beta) = [ 0.        ,  2.25797319]

// Draw a vector containing two samples for each distribution
sample_gamma(alpha, beta, shape=(2)) = [[ 0.        ,  0.        ],
[ 2.25797319,  1.70734084]]


Defined in src/operator/random/multisample_op.cc:L386

Parameters: alpha (Symbol) – Alpha (shape) parameters of the distributions. shape (Shape(tuple), optional, default=()) – Shape to be sampled from each random distribution. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). beta (Symbol) – Beta (scale) parameters of the distributions. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sample_generalized_negative_binomial(mu=None, alpha=None, shape=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Concurrent sampling from multiple generalized negative binomial distributions with parameters mu (mean) and alpha (dispersion).

The parameters of the distributions are provided as input arrays. Let [s] be the shape of the input arrays, n be the dimension of [s], [t] be the shape specified as the parameter of the operator, and m be the dimension of [t]. Then the output will be a (n+m)-dimensional array with shape [s]x[t].

For any valid n-dimensional index i with respect to the input arrays, output[i] will be an m-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index i. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays.

Samples will always be returned as a floating point data type.

Examples:

mu = [ 2.0, 2.5 ]
alpha = [ 1.0, 0.1 ]

// Draw a single sample for each distribution
sample_generalized_negative_binomial(mu, alpha) = [ 0.,  3.]

// Draw a vector containing two samples for each distribution
sample_generalized_negative_binomial(mu, alpha, shape=(2)) = [[ 0.,  3.],
[ 3.,  1.]]


Defined in src/operator/random/multisample_op.cc:L397

Parameters: mu (Symbol) – Means of the distributions. shape (Shape(tuple), optional, default=()) – Shape to be sampled from each random distribution. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). alpha (Symbol) – Alpha (dispersion) parameters of the distributions. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sample_multinomial(data=None, shape=_Null, get_prob=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Concurrent sampling from multiple multinomial distributions.

data is an n dimensional array whose last dimension has length k, where k is the number of possible outcomes of each multinomial distribution. This operator will draw shape samples from each distribution. If shape is empty one sample will be drawn from each distribution.

If get_prob is true, a second array containing log likelihood of the drawn samples will also be returned. This is usually used for reinforcement learning where you can provide reward as head gradient for this array to estimate gradient.

Note that the input distribution must be normalized, i.e. data must sum to 1 along its last axis.

Examples:

probs = [[0, 0.1, 0.2, 0.3, 0.4], [0.4, 0.3, 0.2, 0.1, 0]]

// Draw a single sample for each distribution
sample_multinomial(probs) = [3, 0]

// Draw a vector containing two samples for each distribution
sample_multinomial(probs, shape=(2)) = [[4, 2],
[0, 0]]

// requests log likelihood
sample_multinomial(probs, get_prob=True) = [2, 1], [0.2, 0.3]

Parameters: data (Symbol) – Distribution probabilities. Must sum to one on the last axis. shape (Shape(tuple), optional, default=()) – Shape to be sampled from each random distribution. get_prob (boolean, optional, default=False) – Whether to also return the log probability of sampled result. This is usually used for differentiating through stochastic variables, e.g. in reinforcement learning. dtype ({'int32'},optional, default='int32') – DType of the output in case this can’t be inferred. Only support int32 for now. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sample_negative_binomial(k=None, p=None, shape=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Concurrent sampling from multiple negative binomial distributions with parameters k (failure limit) and p (failure probability).

The parameters of the distributions are provided as input arrays. Let [s] be the shape of the input arrays, n be the dimension of [s], [t] be the shape specified as the parameter of the operator, and m be the dimension of [t]. Then the output will be a (n+m)-dimensional array with shape [s]x[t].

For any valid n-dimensional index i with respect to the input arrays, output[i] will be an m-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index i. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays.

Samples will always be returned as a floating point data type.

Examples:

k = [ 20, 49 ]
p = [ 0.4 , 0.77 ]

// Draw a single sample for each distribution
sample_negative_binomial(k, p) = [ 15.,  16.]

// Draw a vector containing two samples for each distribution
sample_negative_binomial(k, p, shape=(2)) = [[ 15.,  50.],
[ 16.,  12.]]


Defined in src/operator/random/multisample_op.cc:L393

Parameters: k (Symbol) – Limits of unsuccessful experiments. shape (Shape(tuple), optional, default=()) – Shape to be sampled from each random distribution. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). p (Symbol) – Failure probabilities in each experiment. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sample_normal(mu=None, sigma=None, shape=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Concurrent sampling from multiple normal distributions with parameters mu (mean) and sigma (standard deviation).

The parameters of the distributions are provided as input arrays. Let [s] be the shape of the input arrays, n be the dimension of [s], [t] be the shape specified as the parameter of the operator, and m be the dimension of [t]. Then the output will be a (n+m)-dimensional array with shape [s]x[t].

For any valid n-dimensional index i with respect to the input arrays, output[i] will be an m-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index i. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays.

Examples:

mu = [ 0.0, 2.5 ]
sigma = [ 1.0, 3.7 ]

// Draw a single sample for each distribution
sample_normal(mu, sigma) = [-0.56410581,  0.95934606]

// Draw a vector containing two samples for each distribution
sample_normal(mu, sigma, shape=(2)) = [[-0.56410581,  0.2928229 ],
[ 0.95934606,  4.48287058]]


Defined in src/operator/random/multisample_op.cc:L383

Parameters: mu (Symbol) – Means of the distributions. shape (Shape(tuple), optional, default=()) – Shape to be sampled from each random distribution. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). sigma (Symbol) – Standard deviations of the distributions. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sample_poisson(lam=None, shape=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Concurrent sampling from multiple Poisson distributions with parameters lambda (rate).

The parameters of the distributions are provided as an input array. Let [s] be the shape of the input array, n be the dimension of [s], [t] be the shape specified as the parameter of the operator, and m be the dimension of [t]. Then the output will be a (n+m)-dimensional array with shape [s]x[t].

For any valid n-dimensional index i with respect to the input array, output[i] will be an m-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input value at index i. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input array.

Samples will always be returned as a floating point data type.

Examples:

lam = [ 1.0, 8.5 ]

// Draw a single sample for each distribution
sample_poisson(lam) = [  0.,  13.]

// Draw a vector containing two samples for each distribution
sample_poisson(lam, shape=(2)) = [[  0.,   4.],
[ 13.,   8.]]


Defined in src/operator/random/multisample_op.cc:L390

Parameters: lam (Symbol) – Lambda (rate) parameters of the distributions. shape (Shape(tuple), optional, default=()) – Shape to be sampled from each random distribution. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sample_uniform(low=None, high=None, shape=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Concurrent sampling from multiple uniform distributions on the intervals given by [low,high).

The parameters of the distributions are provided as input arrays. Let [s] be the shape of the input arrays, n be the dimension of [s], [t] be the shape specified as the parameter of the operator, and m be the dimension of [t]. Then the output will be a (n+m)-dimensional array with shape [s]x[t].

For any valid n-dimensional index i with respect to the input arrays, output[i] will be an m-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input values at index i. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input arrays.

Examples:

low = [ 0.0, 2.5 ]
high = [ 1.0, 3.7 ]

// Draw a single sample for each distribution
sample_uniform(low, high) = [ 0.40451524,  3.18687344]

// Draw a vector containing two samples for each distribution
sample_uniform(low, high, shape=(2)) = [[ 0.40451524,  0.18017688],
[ 3.18687344,  3.68352246]]


Defined in src/operator/random/multisample_op.cc:L381

Parameters: low (Symbol) – Lower bounds of the distributions. shape (Shape(tuple), optional, default=()) – Shape to be sampled from each random distribution. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). high (Symbol) – Upper bounds of the distributions. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sgd_mom_update(weight=None, grad=None, mom=None, lr=_Null, momentum=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, name=None, attr=None, out=None, **kwargs)

Momentum update function for Stochastic Gradient Descent (SDG) optimizer.

Momentum update has better convergence rates on neural networks. Mathematically it looks like below:

$\begin{split}v_1 = \alpha * \nabla J(W_0)\\ v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\ W_t = W_{t-1} + v_t\end{split}$

v = momentum * v - learning_rate * gradient
weight += v


Where the parameter momentum is the decay rate of momentum estimates at each epoch.

Defined in src/operator/optimizer_op.cc:L73

mxnet.symbol.sgd_update(weight=None, grad=None, lr=_Null, wd=_Null, rescale_grad=_Null, clip_gradient=_Null, name=None, attr=None, out=None, **kwargs)

Update function for Stochastic Gradient Descent (SDG) optimizer.

weight = weight - learning_rate * gradient


Defined in src/operator/optimizer_op.cc:L43

mxnet.symbol.sigmoid(data=None, name=None, attr=None, out=None, **kwargs)

Computes sigmoid of x element-wise.

$y = 1 / (1 + exp(-x))$

Defined in src/operator/tensor/elemwise_unary_op.cc:L54

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sign(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise sign of the input.

Example:

sign([-2, 0, 3]) = [-1, 0, 1]


Defined in src/operator/tensor/elemwise_unary_op.cc:L269

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sin(data=None, name=None, attr=None, out=None, **kwargs)

Computes the element-wise sine of the input array.

The input should be in radians ($$2\pi$$ rad equals 360 degrees).

$sin([0, \pi/4, \pi/2]) = [0, 0.707, 1]$

Defined in src/operator/tensor/elemwise_unary_op.cc:L466

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sinh(data=None, name=None, attr=None, out=None, **kwargs)

Returns the hyperbolic sine of the input array, computed element-wise.

$sinh(x) = 0.5\times(exp(x) - exp(-x))$

Defined in src/operator/tensor/elemwise_unary_op.cc:L617

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.slice(data=None, begin=_Null, end=_Null, name=None, attr=None, out=None, **kwargs)

Slices a contiguous region of the array.

Note

crop is deprecated. Use slice instead.

This function returns a sliced continuous region of the array between the indices given by begin and end.

For an input array of n dimensions, slice operation with begin=(b_0, b_1...b_n-1) indices and end=(e_1, e_2, ... e_n) indices will result in an array with the shape (e_1-b_0, ..., e_n-b_n-1).

The resulting array’s k-th dimension contains elements from the k-th dimension of the input array with the open range [b_k, e_k).

Example:

x = [[  1.,   2.,   3.,   4.],
[  5.,   6.,   7.,   8.],
[  9.,  10.,  11.,  12.]]

slice(x, begin=(0,1), end=(2,4)) = [[ 2.,  3.,  4.],
[ 6.,  7.,  8.]]


Defined in src/operator/tensor/matrix_op.cc:L275

Parameters: data (Symbol) – Source input begin (Shape(tuple), required) – starting indices for the slice operation, supports negative indices. end (Shape(tuple), required) – ending indices for the slice operation, supports negative indices. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.slice_axis(data=None, axis=_Null, begin=_Null, end=_Null, name=None, attr=None, out=None, **kwargs)

Slices along a given axis.

Returns an array slice along a given axis starting from the begin index to the end index.

Examples:

x = [[  1.,   2.,   3.,   4.],
[  5.,   6.,   7.,   8.],
[  9.,  10.,  11.,  12.]]

slice_axis(x, axis=0, begin=1, end=3) = [[  5.,   6.,   7.,   8.],
[  9.,  10.,  11.,  12.]]

slice_axis(x, axis=1, begin=0, end=2) = [[  1.,   2.],
[  5.,   6.],
[  9.,  10.]]

slice_axis(x, axis=1, begin=-3, end=-1) = [[  2.,   3.],
[  6.,   7.],
[ 10.,  11.]]


Defined in src/operator/tensor/matrix_op.cc:L355

Parameters: data (Symbol) – Source input axis (int, required) – Axis along which to be sliced, supports negative indexes. begin (int, required) – The beginning index along the axis to be sliced, supports negative indexes. end (int or None, required) – The ending index along the axis to be sliced, supports negative indexes. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.smooth_l1(data=None, scalar=_Null, name=None, attr=None, out=None, **kwargs)

Calculate Smooth L1 Loss(lhs, scalar) by summing

$\begin{split}f(x) = \begin{cases} (\sigma x)^2/2,& \text{if }x < 1/\sigma^2\\ |x|-0.5/\sigma^2,& \text{otherwise} \end{cases}\end{split}$

where $$x$$ is an element of the tensor lhs and $$\sigma$$ is the scalar.

Example:

smooth_l1([1, 2, 3, 4], sigma=1) = [0.5, 1.5, 2.5, 3.5]


Defined in src/operator/tensor/elemwise_binary_scalar_op_extended.cc:L97

Parameters: data (Symbol) – source input scalar (float) – scalar input name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.softmax(data=None, axis=_Null, name=None, attr=None, out=None, **kwargs)

Applies the softmax function.

The resulting array contains elements in the range (0,1) and the elements along the given axis sum up to 1.

$softmax(\mathbf{z})_j = \frac{e^{z_j}}{\sum_{k=1}^K e^{z_k}}$

for $$j = 1, ..., K$$

Example:

x = [[ 1.  1.  1.]
[ 1.  1.  1.]]

softmax(x,axis=0) = [[ 0.5  0.5  0.5]
[ 0.5  0.5  0.5]]

softmax(x,axis=1) = [[ 0.33333334,  0.33333334,  0.33333334],
[ 0.33333334,  0.33333334,  0.33333334]]


Defined in src/operator/nn/softmax.cc:L53

Parameters: data (Symbol) – The input array. axis (int, optional, default='-1') – The axis along which to compute softmax. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.softmax_cross_entropy(data=None, label=None, name=None, attr=None, out=None, **kwargs)

Calculate cross entropy of softmax output and one-hot label.

• This operator computes the cross entropy in two steps: - Applies softmax function on the input array. - Computes and returns the cross entropy loss between the softmax output and the labels.

• The softmax function and cross entropy loss is given by:

• Softmax Function:
$\text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}$
• Cross Entropy Function:
$\text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)$

Example:

x = [[1, 2, 3],
[11, 7, 5]]

label = [2, 0]

softmax(x) = [[0.09003057, 0.24472848, 0.66524094],
[0.97962922, 0.01794253, 0.00242826]]

softmax_cross_entropy(data, label) = - log(0.66524084) - log(0.97962922) = 0.4281871


Defined in src/operator/loss_binary_op.cc:L58

Parameters: data (Symbol) – Input data label (Symbol) – Input label name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sort(data=None, axis=_Null, is_ascend=_Null, name=None, attr=None, out=None, **kwargs)

Returns a sorted copy of an input array along the given axis.

Examples:

x = [[ 1, 4],
[ 3, 1]]

// sorts along the last axis
sort(x) = [[ 1.,  4.],
[ 1.,  3.]]

// flattens and then sorts
sort(x) = [ 1.,  1.,  3.,  4.]

// sorts along the first axis
sort(x, axis=0) = [[ 1.,  1.],
[ 3.,  4.]]

// in a descend order
sort(x, is_ascend=0) = [[ 4.,  1.],
[ 3.,  1.]]


Defined in src/operator/tensor/ordering_op.cc:L125

Parameters: data (Symbol) – The input array axis (int or None, optional, default='-1') – Axis along which to choose sort the input tensor. If not given, the flattened array is used. Default is -1. is_ascend (boolean, optional, default=True) – Whether to sort in ascending or descending order. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.split(data=None, num_outputs=_Null, axis=_Null, squeeze_axis=_Null, name=None, attr=None, out=None, **kwargs)

Splits an array along a particular axis into multiple sub-arrays.

Note

SliceChannel is deprecated. Use split instead.

Note that num_outputs should evenly divide the length of the axis along which to split the array.

Example:

x  = [[[ 1.]
[ 2.]]
[[ 3.]
[ 4.]]
[[ 5.]
[ 6.]]]
x.shape = (3, 2, 1)

y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1)
y = [[[ 1.]]
[[ 3.]]
[[ 5.]]]

[[[ 2.]]
[[ 4.]]
[[ 6.]]]

y[0].shape = (3, 1, 1)

z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1)
z = [[[ 1.]
[ 2.]]]

[[[ 3.]
[ 4.]]]

[[[ 5.]
[ 6.]]]

z[0].shape = (1, 2, 1)


squeeze_axis=1 removes the axis with length 1 from the shapes of the output arrays. Note that setting squeeze_axis to 1 removes axis with length 1 only along the axis which it is split. Also squeeze_axis can be set to true only if input.shape[axis] == num_outputs.

Example:

z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1)
z = [[ 1.]
[ 2.]]

[[ 3.]
[ 4.]]

[[ 5.]
[ 6.]]
z[0].shape = (2 ,1 )


Defined in src/operator/slice_channel.cc:L106

Parameters: data (Symbol) – The input num_outputs (int, required) – Number of splits. Note that this should evenly divide the length of the axis. axis (int, optional, default='1') – Axis along which to split. squeeze_axis (boolean, optional, default=False) – If true, Removes the axis with length 1 from the shapes of the output arrays. Note that setting squeeze_axis to true removes axis with length 1 only along the axis which it is split. Also squeeze_axis can be set to true only if input.shape[axis] == num_outputs. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sqrt(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise square-root value of the input.

$\textrm{sqrt}(x) = \sqrt{x}$

Example:

sqrt([4, 9, 16]) = [2, 3, 4]


Defined in src/operator/tensor/elemwise_unary_op.cc:L383

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.square(data=None, name=None, attr=None, out=None, **kwargs)

Returns element-wise squared value of the input.

$square(x) = x^2$

Example:

square([2, 3, 4]) = [4, 9, 16]


Defined in src/operator/tensor/elemwise_unary_op.cc:L365

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.stack(*data, **kwargs)

Join a sequence of arrays along a new axis.

The axis parameter specifies the index of the new axis in the dimensions of the result. For example, if axis=0 it will be the first dimension and if axis=-1 it will be the last dimension.

Examples:

x = [1, 2]
y = [3, 4]

stack(x, y) = [[1, 2],
[3, 4]]
stack(x, y, axis=1) = [[1, 3],
[2, 4]]


This function support variable length of positional input.

Parameters: data (Symbol[]) – List of arrays to stack axis (int, optional, default='0') – The axis in the result array along which the input arrays are stacked. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.stop_gradient(data=None, name=None, attr=None, out=None, **kwargs)

Stops the accumulated gradient of the inputs from flowing through this operator in the backward direction. In other words, this operator prevents the contribution of its inputs to be taken into account for computing gradients.

Example:

v1 = [1, 2]
v2 = [0, 1]
a = Variable('a')
b = Variable('b')

executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2))
executor.forward(is_train=True, a=v1, b=v2)
executor.outputs
[ 1.  5.]

executor.backward()
[ 0.  0.]
[ 1.  1.]


Defined in src/operator/tensor/elemwise_unary_op.cc:L117

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sum(data=None, axis=_Null, keepdims=_Null, exclude=_Null, name=None, attr=None, out=None, **kwargs)

Computes the sum of array elements over given axes.

Note

sum and sum_axis are equivalent.

Example:

data = [[[1,2],[2,3],[1,3]],
[[1,4],[4,3],[5,2]],
[[7,1],[7,2],[7,3]]]

sum(data, axis=1)
[[  4.   8.]
[ 10.   9.]
[ 21.   6.]]

sum(data, axis=[1,2])
[ 12.  19.  27.]


Parameters: data (Symbol) – The input axis (Shape(tuple), optional, default=()) – The axis or axes along which to perform the reduction. The default, axis=(), will compute over all elements into a scalar array with shape (1,). If axis is int, a reduction is performed on a particular axis. If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If exclude is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims (boolean, optional, default=False) – If this is set to True, the reduced axes are left in the result as dimension with size one. exclude (boolean, optional, default=False) – Whether to perform reduction on axis that are NOT in axis instead. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.sum_axis(data=None, axis=_Null, keepdims=_Null, exclude=_Null, name=None, attr=None, out=None, **kwargs)

Computes the sum of array elements over given axes.

Note

sum and sum_axis are equivalent.

Example:

data = [[[1,2],[2,3],[1,3]],
[[1,4],[4,3],[5,2]],
[[7,1],[7,2],[7,3]]]

sum(data, axis=1)
[[  4.   8.]
[ 10.   9.]
[ 21.   6.]]

sum(data, axis=[1,2])
[ 12.  19.  27.]


Parameters: data (Symbol) – The input axis (Shape(tuple), optional, default=()) – The axis or axes along which to perform the reduction. The default, axis=(), will compute over all elements into a scalar array with shape (1,). If axis is int, a reduction is performed on a particular axis. If axis is a tuple of ints, a reduction is performed on all the axes specified in the tuple. If exclude is true, reduction will be performed on the axes that are NOT in axis instead. Negative values means indexing from right to left. keepdims (boolean, optional, default=False) – If this is set to True, the reduced axes are left in the result as dimension with size one. exclude (boolean, optional, default=False) – Whether to perform reduction on axis that are NOT in axis instead. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.swapaxes(data=None, dim1=_Null, dim2=_Null, name=None, attr=None, out=None, **kwargs)

Interchanges two axes of an array.

Examples:

 x = [[1, 2, 3]])
swapaxes(x, 0, 1) = [[ 1],
[ 2],
[ 3]]

x = [[[ 0, 1],
[ 2, 3]],
[[ 4, 5],
[ 6, 7]]]  // (2,2,2) array

swapaxes(x, 0, 2) = [[[ 0, 4],
[ 2, 6]],
[[ 1, 5],
[ 3, 7]]]


Defined in src/operator/swapaxis.cc:L69

Parameters: data (Symbol) – Input array. dim1 (int (non-negative), optional, default=0) – the first axis to be swapped. dim2 (int (non-negative), optional, default=0) – the second axis to be swapped. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.take(a=None, indices=None, axis=_Null, mode=_Null, name=None, attr=None, out=None, **kwargs)

Takes elements from an input array along the given axis.

This function slices the input array along a particular axis with the provided indices.

Given an input array with shape (d0, d1, d2) and indices with shape (i0, i1), the output will have shape (i0, i1, d1, d2), computed by:

output[i,j,:,:] = input[indices[i,j],:,:]


Note

• axis- Only slicing along axis 0 is supported for now.
• mode- Only clip mode is supported for now.

Examples:

x = [[ 1.,  2.],
[ 3.,  4.],
[ 5.,  6.]]

// takes elements with specified indices along axis 0
take(x, [[0,1],[1,2]]) = [[[ 1.,  2.],
[ 3.,  4.]],

[[ 3.,  4.],
[ 5.,  6.]]]


Defined in src/operator/tensor/indexing_op.cc:L135

Parameters: a (Symbol) – The input array. indices (Symbol) – The indices of the values to be extracted. axis (int, optional, default='0') – The axis of input array to be taken. mode ({'clip', 'raise', 'wrap'},optional, default='clip') – Specify how out-of-bound indices bahave. “clip” means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis. “wrap” means to wrap around. “raise” means to raise an error. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.tan(data=None, name=None, attr=None, out=None, **kwargs)

Computes the element-wise tangent of the input array.

The input should be in radians ($$2\pi$$ rad equals 360 degrees).

$tan([0, \pi/4, \pi/2]) = [0, 1, -inf]$

Defined in src/operator/tensor/elemwise_unary_op.cc:L525

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.tanh(data=None, name=None, attr=None, out=None, **kwargs)

Returns the hyperbolic tangent of the input array, computed element-wise.

$tanh(x) = sinh(x) / cosh(x)$

Defined in src/operator/tensor/elemwise_unary_op.cc:L645

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.tile(data=None, reps=_Null, name=None, attr=None, out=None, **kwargs)

Repeats the whole array multiple times.

If reps has length d, and input array has dimension of n. There are there cases:

• n=d. Repeat i-th dimension of the input by reps[i] times:

x = [[1, 2],
[3, 4]]

tile(x, reps=(2,3)) = [[ 1.,  2.,  1.,  2.,  1.,  2.],
[ 3.,  4.,  3.,  4.,  3.,  4.],
[ 1.,  2.,  1.,  2.,  1.,  2.],
[ 3.,  4.,  3.,  4.,  3.,  4.]]

• n>d. reps is promoted to length n by pre-pending 1’s to it. Thus for an input shape (2,3), repos=(2,) is treated as (1,2):

tile(x, reps=(2,)) = [[ 1.,  2.,  1.,  2.],
[ 3.,  4.,  3.,  4.]]

• n<d. The input is promoted to be d-dimensional by prepending new axes. So a shape (2,2) array is promoted to (1,2,2) for 3-D replication:

tile(x, reps=(2,2,3)) = [[[ 1.,  2.,  1.,  2.,  1.,  2.],
[ 3.,  4.,  3.,  4.,  3.,  4.],
[ 1.,  2.,  1.,  2.,  1.,  2.],
[ 3.,  4.,  3.,  4.,  3.,  4.]],

[[ 1.,  2.,  1.,  2.,  1.,  2.],
[ 3.,  4.,  3.,  4.,  3.,  4.],
[ 1.,  2.,  1.,  2.,  1.,  2.],
[ 3.,  4.,  3.,  4.,  3.,  4.]]]


Defined in src/operator/tensor/matrix_op.cc:L578

Parameters: data (Symbol) – Input data array reps (Shape(tuple), required) – The number of times for repeating the tensor a. If reps has length d, the result will have dimension of max(d, a.ndim); If a.ndim < d, a is promoted to be d-dimensional by prepending new axes. If a.ndim > d, reps is promoted to a.ndim by pre-pending 1’s to it. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.topk(data=None, axis=_Null, k=_Null, ret_typ=_Null, is_ascend=_Null, name=None, attr=None, out=None, **kwargs)

Returns the top k elements in an input array along the given axis.

Examples:

x = [[ 0.3,  0.2,  0.4],
[ 0.1,  0.3,  0.2]]

// returns an index of the largest element on last axis
topk(x) = [[ 2.],
[ 1.]]

// returns the value of top-2 largest elements on last axis
topk(x, ret_typ='value', k=2) = [[ 0.4,  0.3],
[ 0.3,  0.2]]

// returns the value of top-2 smallest elements on last axis
topk(x, ret_typ='value', k=2, is_ascend=1) = [[ 0.2 ,  0.3],
[ 0.1 ,  0.2]]

// returns the value of top-2 largest elements on axis 0
topk(x, axis=0, ret_typ='value', k=2) = [[ 0.3,  0.3,  0.4],
[ 0.1,  0.2,  0.2]]

// flattens and then returns list of both values and indices
topk(x, ret_typ='both', k=2) = [[[ 0.4,  0.3], [ 0.3,  0.2]] ,  [[ 2.,  0.], [ 1.,  2.]]]


Defined in src/operator/tensor/ordering_op.cc:L62

Parameters: data (Symbol) – The input array axis (int or None, optional, default='-1') – Axis along which to choose the top k indices. If not given, the flattened array is used. Default is -1. k (int, optional, default='1') – Number of top elements to select, should be always smaller than or equal to the element number in the given axis. A global sort is performed if set k < 1. ret_typ ({'both', 'indices', 'mask', 'value'},optional, default='indices') – The return type. “value” means to return the top k values, “indices” means to return the indices of the top k values, “mask” means to return a mask array containing 0 and 1. 1 means the top k values. “both” means to return a list of both values and indices of top k elements. is_ascend (boolean, optional, default=False) – Whether to choose k largest or k smallest elements. Top K largest elements will be chosen if set to false. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.transpose(data=None, axes=_Null, name=None, attr=None, out=None, **kwargs)

Permutes the dimensions of an array.

Examples:

x = [[ 1, 2],
[ 3, 4]]

transpose(x) = [[ 1.,  3.],
[ 2.,  4.]]

x = [[[ 1.,  2.],
[ 3.,  4.]],

[[ 5.,  6.],
[ 7.,  8.]]]

transpose(x) = [[[ 1.,  5.],
[ 3.,  7.]],

[[ 2.,  6.],
[ 4.,  8.]]]

transpose(x, axes=(1,0,2)) = [[[ 1.,  2.],
[ 5.,  6.]],

[[ 3.,  4.],
[ 7.,  8.]]]


Defined in src/operator/tensor/matrix_op.cc:L195

Parameters: data (Symbol) – Source input axes (Shape(tuple), optional, default=()) – Target axis order. By default the axes will be inverted. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.trunc(data=None, name=None, attr=None, out=None, **kwargs)

Return the element-wise truncated value of the input.

The truncated value of the scalar x is the nearest integer i which is closer to zero than x is. In short, the fractional part of the signed number x is discarded.

Example:

trunc([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1.,  1.,  1.,  2.]


Defined in src/operator/tensor/elemwise_unary_op.cc:L340

Parameters: data (Symbol) – The input array. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.uniform(low=_Null, high=_Null, shape=_Null, ctx=_Null, dtype=_Null, name=None, attr=None, out=None, **kwargs)

Draw random samples from a uniform distribution.

Note

The existing alias uniform is deprecated.

Samples are uniformly distributed over the half-open interval [low, high) (includes low, but excludes high).

Example:

random_uniform(low=0, high=1, shape=(2,2)) = [[ 0.60276335,  0.85794562],
[ 0.54488319,  0.84725171]]


Defined in src/operator/random/sample_op.cc:L63

Parameters: low (float, optional, default=0) – Lower bound of the distribution. high (float, optional, default=1) – Upper bound of the distribution. shape (Shape(tuple), optional, default=()) – Shape of the output. ctx (string, optional, default='') – Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls. dtype ({'None', 'float16', 'float32', 'float64'},optional, default='None') – DType of the output in case this can’t be inferred. Defaults to float32 if not defined (dtype=None). name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.where(condition=None, x=None, y=None, name=None, attr=None, out=None, **kwargs)

Given three ndarrays, condition, x, and y, return an ndarray with the elements from x or y, depending on the elements from condition are true or false. x and y must have the same shape. If condition has the same shape as x, each element in the output array is from x if the corresponding element in the condition is true, and from y if false. If condition does not have the same shape as x, it must be a 1D array whose size is the same as x’s first dimension size. Each row of the output array is from x’s row if the corresponding element from condition is true, and from y’s row if false.

From:src/operator/tensor/control_flow_op.cc:39

Parameters: condition (Symbol) – condition array x (Symbol) – y (Symbol) – name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.symbol.zeros_like(data=None, name=None, attr=None, out=None, **kwargs)

Return an array of zeros with the same shape and type as the input array.

Examples:

x = [[ 1.,  1.,  1.],
[ 1.,  1.,  1.]]

zeros_like(x) = [[ 0.,  0.,  0.],
[ 0.,  0.,  0.]]

Parameters: data (Symbol) – The input name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol

Symbol namespace used to register contrib functions

mxnet.contrib.symbol.CTCLoss(data=None, label=None, name=None, attr=None, out=None, **kwargs)

Connectionist Temporal Classification Loss.

The shapes of the inputs and outputs:

• data: (sequence_length, batch_size, alphabet_size + 1)
• label: (batch_size, label_sequence_length)
• out: (batch_size).

label is a tensor of integers between 1 and alphabet_size. If a sequence of labels is shorter than label_sequence_length, use the special padding character 0 at the end of the sequence to conform it to the correct length. For example, if label_sequence_length = 4, and one has two sequences of labels [2, 1] and [3, 2, 2], the resulting label tensor should be padded to be:

[[2, 1, 0, 0], [3, 2, 2, 0]]


The data tensor consists of sequences of activation vectors. The layer applies a softmax to each vector, which then becomes a vector of probabilities over the alphabet. Note that the 0th element of this vector is reserved for the special blank character.

out is a list of CTC loss values, one per example in the batch.

See Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks, A. Graves et al. for more information.

Defined in src/operator/contrib/ctc_loss.cc:L99

Parameters: data (Symbol) – Input data to the ctc_loss op. label (Symbol) – Ground-truth labels for the loss. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.contrib.symbol.DeformableConvolution(data=None, offset=None, weight=None, bias=None, kernel=_Null, stride=_Null, dilate=_Null, pad=_Null, num_filter=_Null, num_group=_Null, num_deformable_group=_Null, workspace=_Null, no_bias=_Null, layout=_Null, name=None, attr=None, out=None, **kwargs)

Compute 2-D deformable convolution on 4-D input.

The deformable convolution operation is described in https://arxiv.org/abs/1703.06211

For 2-D deformable convolution, the shapes are

• data: (batch_size, channel, height, width)
• offset: (batch_size, num_deformable_group * kernel[0] * kernel[1], height, width)
• weight: (num_filter, channel, kernel[0], kernel[1])
• bias: (num_filter,)
• out: (batch_size, num_filter, out_height, out_width).

Define:

f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1


then we have:

out_height=f(height, kernel[0], pad[0], stride[0], dilate[0])


If no_bias is set to be true, then the bias term is ignored.

The default data layout is NCHW, namely (batch_size, channle, height, width).

If num_group is larger than 1, denoted by g, then split the input data evenly into g parts along the channel axis, and also evenly split weight along the first dimension. Next compute the convolution on the i-th part of the data with the i-th weight part. The output is obtained by concating all the g results.

If num_deformable_group is larger than 1, denoted by dg, then split the input offset evenly into dg parts along the channel axis, and also evenly split out evenly into dg parts along the channel axis. Next compute the deformable convolution, apply the i-th part of the offset part on the i-th out.

Both weight and bias are learnable parameters.

Defined in src/operator/contrib/deformable_convolution.cc:L100

Parameters: data (Symbol) – Input data to the DeformableConvolutionOp. offset (Symbol) – Input offset to the DeformableConvolutionOp. weight (Symbol) – Weight matrix. bias (Symbol) – Bias parameter. kernel (Shape(tuple), required) – convolution kernel size: (h, w) or (d, h, w) stride (Shape(tuple), optional, default=()) – convolution stride: (h, w) or (d, h, w) dilate (Shape(tuple), optional, default=()) – convolution dilate: (h, w) or (d, h, w) pad (Shape(tuple), optional, default=()) – pad for convolution: (h, w) or (d, h, w) num_filter (int (non-negative), required) – convolution filter(channel) number num_group (int (non-negative), optional, default=1) – Number of group partitions. num_deformable_group (int (non-negative), optional, default=1) – Number of deformable group partitions. workspace (long (non-negative), optional, default=1024) – Maximum temperal workspace allowed for convolution (MB). no_bias (boolean, optional, default=False) – Whether to disable bias parameter. layout ({None, 'NCDHW', 'NCHW', 'NCW'},optional, default='None') – Set layout for input, output and weight. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.contrib.symbol.DeformablePSROIPooling(data=None, rois=None, trans=None, spatial_scale=_Null, output_dim=_Null, group_size=_Null, pooled_size=_Null, part_size=_Null, sample_per_part=_Null, trans_std=_Null, no_trans=_Null, name=None, attr=None, out=None, **kwargs)

Performs deformable position-sensitive region-of-interest pooling on inputs.The DeformablePSROIPooling operation is described in https://arxiv.org/abs/1703.06211 .batch_size will change to the number of region bounding boxes after DeformablePSROIPooling

Parameters: data (Symbol) – Input data to the pooling operator, a 4D Feature maps rois (Symbol) – Bounding box coordinates, a 2D array of [[batch_index, x1, y1, x2, y2]]. (x1, y1) and (x2, y2) are top left and down right corners of designated region of interest. batch_index indicates the index of corresponding image in the input data trans (Symbol) – transition parameter spatial_scale (float, required) – Ratio of input feature map height (or w) to raw image height (or w). Equals the reciprocal of total stride in convolutional layers output_dim (int, required) – fix output dim group_size (int, required) – fix group size pooled_size (int, required) – fix pooled size part_size (int, optional, default='0') – fix part size sample_per_part (int, optional, default='1') – fix samples per part trans_std (float, optional, default=0) – fix transition std no_trans (boolean, optional, default=False) – Whether to disable trans parameter. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.contrib.symbol.MultiBoxDetection(cls_prob=None, loc_pred=None, anchor=None, clip=_Null, threshold=_Null, background_id=_Null, nms_threshold=_Null, force_suppress=_Null, variances=_Null, nms_topk=_Null, name=None, attr=None, out=None, **kwargs)

Convert multibox detection predictions.

Parameters: cls_prob (Symbol) – Class probabilities. loc_pred (Symbol) – Location regression predictions. anchor (Symbol) – Multibox prior anchor boxes clip (boolean, optional, default=True) – Clip out-of-boundary boxes. threshold (float, optional, default=0.01) – Threshold to be a positive prediction. background_id (int, optional, default='0') – Background id. nms_threshold (float, optional, default=0.5) – Non-maximum suppression threshold. force_suppress (boolean, optional, default=False) – Suppress all detections regardless of class_id. variances (, optional, default=(0.1,0.1,0.2,0.2)) – Variances to be decoded from box regression output. nms_topk (int, optional, default='-1') – Keep maximum top k detections before nms, -1 for no limit. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.contrib.symbol.MultiBoxPrior(data=None, sizes=_Null, ratios=_Null, clip=_Null, steps=_Null, offsets=_Null, name=None, attr=None, out=None, **kwargs)

Generate prior(anchor) boxes from data, sizes and ratios.

Parameters: data (Symbol) – Input data. sizes (, optional, default=(1,)) – List of sizes of generated MultiBoxPriores. ratios (, optional, default=(1,)) – List of aspect ratios of generated MultiBoxPriores. clip (boolean, optional, default=False) – Whether to clip out-of-boundary boxes. steps (, optional, default=(-1,-1)) – Priorbox step across y and x, -1 for auto calculation. offsets (, optional, default=(0.5,0.5)) – Priorbox center offsets, y and x respectively name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.contrib.symbol.MultiBoxTarget(anchor=None, label=None, cls_pred=None, overlap_threshold=_Null, ignore_label=_Null, negative_mining_ratio=_Null, negative_mining_thresh=_Null, minimum_negative_samples=_Null, variances=_Null, name=None, attr=None, out=None, **kwargs)

Compute Multibox training targets

Parameters: anchor (Symbol) – Generated anchor boxes. label (Symbol) – Object detection labels. cls_pred (Symbol) – Class predictions. overlap_threshold (float, optional, default=0.5) – Anchor-GT overlap threshold to be regarded as a possitive match. ignore_label (float, optional, default=-1) – Label for ignored anchors. negative_mining_ratio (float, optional, default=-1) – Max negative to positive samples ratio, use -1 to disable mining negative_mining_thresh (float, optional, default=0.5) – Threshold used for negative mining. minimum_negative_samples (int, optional, default='0') – Minimum number of negative samples. variances (, optional, default=(0.1,0.1,0.2,0.2)) – Variances to be encoded in box regression target. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.contrib.symbol.MultiProposal(cls_score=None, bbox_pred=None, im_info=None, rpn_pre_nms_top_n=_Null, rpn_post_nms_top_n=_Null, threshold=_Null, rpn_min_size=_Null, scales=_Null, ratios=_Null, feature_stride=_Null, output_score=_Null, iou_loss=_Null, name=None, attr=None, out=None, **kwargs)

Generate region proposals via RPN

Parameters: cls_score (Symbol) – Score of how likely proposal is object. bbox_pred (Symbol) – BBox Predicted deltas from anchors for proposals im_info (Symbol) – Image size and scale. rpn_pre_nms_top_n (int, optional, default='6000') – Number of top scoring boxes to keep after applying NMS to RPN proposals rpn_post_nms_top_n (int, optional, default='300') – Overlap threshold used for non-maximumsuppresion(suppress boxes with IoU >= this threshold threshold (float, optional, default=0.7) – NMS value, below which to suppress. rpn_min_size (int, optional, default='16') – Minimum height or width in proposal scales (, optional, default=(4,8,16,32)) – Used to generate anchor windows by enumerating scales ratios (, optional, default=(0.5,1,2)) – Used to generate anchor windows by enumerating ratios feature_stride (int, optional, default='16') – The size of the receptive field each unit in the convolution layer of the rpn,for example the product of all stride’s prior to this layer. output_score (boolean, optional, default=False) – Add score to outputs iou_loss (boolean, optional, default=False) – Usage of IoU Loss name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.contrib.symbol.PSROIPooling(data=None, rois=None, spatial_scale=_Null, output_dim=_Null, pooled_size=_Null, group_size=_Null, name=None, attr=None, out=None, **kwargs)

Performs region-of-interest pooling on inputs. Resize bounding box coordinates by spatial_scale and crop input feature maps accordingly. The cropped feature maps are pooled by max pooling to a fixed size output indicated by pooled_size. batch_size will change to the number of region bounding boxes after PSROIPooling

Parameters: data (Symbol) – Input data to the pooling operator, a 4D Feature maps rois (Symbol) – Bounding box coordinates, a 2D array of [[batch_index, x1, y1, x2, y2]]. (x1, y1) and (x2, y2) are top left and down right corners of designated region of interest. batch_index indicates the index of corresponding image in the input data spatial_scale (float, required) – Ratio of input feature map height (or w) to raw image height (or w). Equals the reciprocal of total stride in convolutional layers output_dim (int, required) – fix output dim pooled_size (int, required) – fix pooled size group_size (int, optional, default='0') – fix group size name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.contrib.symbol.Proposal(cls_score=None, bbox_pred=None, im_info=None, rpn_pre_nms_top_n=_Null, rpn_post_nms_top_n=_Null, threshold=_Null, rpn_min_size=_Null, scales=_Null, ratios=_Null, feature_stride=_Null, output_score=_Null, iou_loss=_Null, name=None, attr=None, out=None, **kwargs)

Generate region proposals via RPN

Parameters: cls_score (Symbol) – Score of how likely proposal is object. bbox_pred (Symbol) – BBox Predicted deltas from anchors for proposals im_info (Symbol) – Image size and scale. rpn_pre_nms_top_n (int, optional, default='6000') – Number of top scoring boxes to keep after applying NMS to RPN proposals rpn_post_nms_top_n (int, optional, default='300') – Overlap threshold used for non-maximumsuppresion(suppress boxes with IoU >= this threshold threshold (float, optional, default=0.7) – NMS value, below which to suppress. rpn_min_size (int, optional, default='16') – Minimum height or width in proposal scales (, optional, default=(4,8,16,32)) – Used to generate anchor windows by enumerating scales ratios (, optional, default=(0.5,1,2)) – Used to generate anchor windows by enumerating ratios feature_stride (int, optional, default='16') – The size of the receptive field each unit in the convolution layer of the rpn,for example the product of all stride’s prior to this layer. output_score (boolean, optional, default=False) – Add score to outputs iou_loss (boolean, optional, default=False) – Usage of IoU Loss name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.contrib.symbol.count_sketch(data=None, h=None, s=None, out_dim=_Null, processing_batch_size=_Null, name=None, attr=None, out=None, **kwargs)

Apply CountSketch to input: map a d-dimension data to k-dimension data”

Note

count_sketch is only available on GPU.

Assume input data has shape (N, d), sign hash table s has shape (N, d), index hash table h has shape (N, d) and mapping dimension out_dim = k, each element in s is either +1 or -1, each element in h is random integer from 0 to k-1. Then the operator computs:

$out[h[i]] += data[i] * s[i]$
Example::

out_dim = 5 x = [[1.2, 2.5, 3.4],[3.2, 5.7, 6.6]] h = [0, 3, 4] s = [1, -1, 1] mx.contrib.ndarray.count_sketch(data=x, h=h, s=s, out_dim = 5) = [[1.2, 0, 0, -2.5, 3.4],

[3.2, 0, 0, -5.7, 6.6]]

Defined in src/operator/contrib/count_sketch.cc:L65

Parameters: data (Symbol) – Input data to the CountSketchOp. h (Symbol) – The index vector s (Symbol) – The sign vector out_dim (int, required) – The output dimension. processing_batch_size (int, optional, default='32') – How many sketch vectors to process at one time. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.contrib.symbol.ctc_loss(data=None, label=None, name=None, attr=None, out=None, **kwargs)

Connectionist Temporal Classification Loss.

The shapes of the inputs and outputs:

• data: (sequence_length, batch_size, alphabet_size + 1)
• label: (batch_size, label_sequence_length)
• out: (batch_size).

label is a tensor of integers between 1 and alphabet_size. If a sequence of labels is shorter than label_sequence_length, use the special padding character 0 at the end of the sequence to conform it to the correct length. For example, if label_sequence_length = 4, and one has two sequences of labels [2, 1] and [3, 2, 2], the resulting label tensor should be padded to be:

[[2, 1, 0, 0], [3, 2, 2, 0]]


The data tensor consists of sequences of activation vectors. The layer applies a softmax to each vector, which then becomes a vector of probabilities over the alphabet. Note that the 0th element of this vector is reserved for the special blank character.

out is a list of CTC loss values, one per example in the batch.

See Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks, A. Graves et al. for more information.

Defined in src/operator/contrib/ctc_loss.cc:L99

Parameters: data (Symbol) – Input data to the ctc_loss op. label (Symbol) – Ground-truth labels for the loss. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.contrib.symbol.dequantize(input=None, min_range=None, max_range=None, out_type=_Null, name=None, attr=None, out=None, **kwargs)

Dequantize the input tensor into a float tensor. [min_range, max_range] are scalar floats that spcify the range for the output data.

Each value of the tensor will undergo the following:

out[i] = min_range + (in[i] * (max_range - min_range) / range(INPUT_TYPE))

here range(T) = numeric_limits<T>::max() - numeric_limits<T>::min()

Defined in src/operator/contrib/dequantize.cc:L40

Parameters: input (Symbol) – A ndarray/symbol of type uint8 min_range (Symbol) – The minimum scalar value possibly produced for the input max_range (Symbol) – The maximum scalar value possibly produced for the input out_type ({'float32'}, required) – Output data type. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.contrib.symbol.fft(data=None, compute_size=_Null, name=None, attr=None, out=None, **kwargs)

Apply 1D FFT to input”

Note

fft is only available on GPU.

Currently accept 2 input data shapes: (N, d) or (N1, N2, N3, d), data can only be real numbers. The output data has shape: (N, 2*d) or (N1, N2, N3, 2*d). The format is: [real0, imag0, real1, imag1, ...].

Example::
data = np.random.normal(0,1,(3,4)) out = mx.contrib.ndarray.fft(data = mx.nd.array(data,ctx = mx.gpu(0)))

Defined in src/operator/contrib/fft.cc:L58

Parameters: data (Symbol) – Input data to the FFTOp. compute_size (int, optional, default='128') – Maximum size of sub-batch to be forwarded at one time name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.contrib.symbol.ifft(data=None, compute_size=_Null, name=None, attr=None, out=None, **kwargs)

Apply 1D ifft to input”

Note

ifft is only available on GPU.

Currently accept 2 input data shapes: (N, d) or (N1, N2, N3, d). Data is in format: [real0, imag0, real1, imag1, ...]. Last dimension must be an even number. The output data has shape: (N, d/2) or (N1, N2, N3, d/2). It is only the real part of the result.

Example::
data = np.random.normal(0,1,(3,4)) out = mx.contrib.ndarray.ifft(data = mx.nd.array(data,ctx = mx.gpu(0)))

Defined in src/operator/contrib/ifft.cc:L60

Parameters: data (Symbol) – Input data to the IFFTOp. compute_size (int, optional, default='128') – Maximum size of sub-batch to be forwarded at one time name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol
mxnet.contrib.symbol.quantize(input=None, min_range=None, max_range=None, out_type=_Null, name=None, attr=None, out=None, **kwargs)

Quantize a input tensor from float to out_type, with user-specified min_range and max_range.

[min_range, max_range] are scalar floats that spcify the range for the input data. Each value of the tensor will undergo the following:

out[i] = (in[i] - min_range) * range(OUTPUT_TYPE) / (max_range - min_range)

here range(T) = numeric_limits<T>::max() - numeric_limits<T>::min()

Defined in src/operator/contrib/quantize.cc:L40

Parameters: input (Symbol) – A ndarray/symbol of type float32 min_range (Symbol) – The minimum scalar value possibly produced for the input max_range (Symbol) – The maximum scalar value possibly produced for the input out_type ({'uint8'},optional, default='uint8') – Output data type. name (string, optional.) – Name of the resulting symbol. The result symbol. Symbol