Symbol API

Overview

This document lists the routines of the symbolic expression package:

mxnet.symbol Symbolic configuration API of MXNet.

A symbol declares computation. It is composited by operators, such as simple matrix operations (e.g. “+”), or a neural network layer (e.g. convolution layer). We can bind data to a symbol to execute the computation.

>>> 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 http://mxnet.io/tutorials/python/symbol.html.

Note

most operators provided in symbol are similar to ndarray. But also note that symbol differs to ndarray in several aspects:

  • symbol adopts declare programming. In other words, we need to first composite the computations, and then feed with data to execute.
  • Most binary operators such as + and > are not enabled broadcasting. We need to call the broadcasted version 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__ Compose symbol on 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__(y) <=> -x
Symbol.__mul__ x.__mul__(y) <=> x*y
Symbol.__div__ x.__div__(y) <=> x/y
Symbol.__rdiv__ x.__rdiv__(y) <=> y/x
Symbol.__pow__ x.__pow__(y) <=> x**y

Comparison operators

Symbol.__lt__ x.__lt__(y) <=> x<y
Symbol.__le__ x.__le__(y) <=> 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 Get 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 Gets attribute string 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 all outputs in a list
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 Bind current symbol to get an executor.
Symbol.simple_bind Bind current symbol to get an executor, allocate all the ndarrays needed.

Save

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

Symbol creation routines

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

Symbol manipulation routines

Changing shape and type

cast Casts all elements of the input to the new type.
reshape Reshapes the input array into a new shape.
flatten Flattens the input array into a 2-D array by collapsing the higher dimensions.
expand_dims Insert a new axis with 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 Repeat elements of an array.
tile Repeat the whole array by multiple times.
pad Pad an array.

Rearranging elements

transpose Permute the dimensions of an array.
swapaxes Interchange two axes of an array.
flip Reverse elements of an array with axis

Joining and splitting symbols

concat Join input arrays along the given axis.
split Split an array along a particular axis into multiple sub-arrays.

Indexing routines

slice Slice a continuous region of the array.
slice_axis Slice 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.
negative Negate src
dot Dot product of two arrays.
batch_dot Batchwise dot product.
add_n Add all input arguments element-wise.

Trigonometric functions

sin Computes the element-wise sine of the input.
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 minimum left and right
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 Compute the sum of array elements over given axes.
nansum Compute the sum of array elements over given axes with NaN ignored
prod Compute the product of array elements over given axes.
nanprod Compute the product of array elements over given axes with NaN ignored
mean Compute the mean of array elements over given axes.
max Compute the max of array elements over given axes.
min Compute the min of array elements over given axes.
norm Computes the L2 norm of the input array.

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.

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

uniform Draw samples from a uniform distribution.
normal Draw random samples from a normal (Gaussian) distribution.
mxnet.random.seed Seed 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.

Miscellaneous

maximum maximum left and right
minimum minimum left and right
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 Clip (limit) 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 Apply a linear transformation: \(Y = XW^T + b\).
Convolution Compute N-D convolution on (N+2)-D input.
Activation Elementwise activation function.
BatchNorm Batch normalization.
Pooling Perform pooling on the input.
SoftmaxOutput Softmax with logit loss.
softmax Applies the softmax function.
log_softmax Compute the log softmax of the input.

More

Correlation Apply correlation to inputs
Deconvolution Apply deconvolution to input then add a bias.
RNN Apply a recurrent layer to input.
Embedding Maps integer indices to vector representations (embeddings).
LeakyReLU Leaky ReLu activation
InstanceNorm An operator taking in a n-dimensional input tensor (n > 2), and normalizing the input by subtracting the mean and variance calculated over the spatial dimensions.
L2Normalization Set the l2 norm of each instance to a constant.
LRN Apply convolution to input then add a bias.
ROIPooling Performs region of interest(ROI) pooling on the input array.
SoftmaxActivation Apply softmax activation to input.
Dropout Apply dropout to input.
BilinearSampler Apply bilinear sampling to input feature map, which is the key of “[NIPS2015] Spatial Transformer Networks” output[batch, channel, y_dst, x_dst] = G(data[batch, channel, y_src, x_src) x_dst, y_dst enumerate all spatial locations in output x_src = grid[batch, 0, y_dst, x_dst] y_src = grid[batch, 1, y_dst, x_dst] G() denotes the bilinear interpolation kernel The out-boundary points will be padded as zeros.
GridGenerator generate sampling grid for bilinear sampling.
UpSampling Perform nearest neighboor/bilinear up sampling to inputs This function support variable length of positional input.
SpatialTransformer Apply spatial transformer to input feature map.
LinearRegressionOutput LinearRegressionOutput computes and optimizes for squared loss.
LogisticRegressionOutput LogisticRegressionOutput applies a logistic function to the input.
MAERegressionOutput MAERegressionOutput function computes mean absolute error.
SVMOutput Computes support vector machine based transformation of the input.
softmax_cross_entropy Calculate cross_entropy(data, one_hot(label))
smooth_l1 Calculate Smooth L1 Loss(lhs, scalar)
IdentityAttachKLSparseReg Apply a sparse regularization to the output a sigmoid activation function.
MakeLoss Get output from a symbol and pass 1 gradient back.
BlockGrad Get output from a symbol and pass 0 gradient back
Custom Custom operator implemented in frontend.

API Reference

Symbolic configuration API of MXNet.

class mxnet.symbol.Symbol(handle)

Symbol is symbolic graph of the mxnet.

name

Get 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.
Return type:str
attr(key)

Gets attribute string from the symbol. This function only works for non-grouped symbols.

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

Gets all attributes from the symbol.

Returns:ret – A dicitonary mapping attribute keys to values.
Return type:dict of str to str
attr_dict()

Recursively gets all attributes from the symbol and its children.

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).
Return type: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.
Return type: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.
Return type: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.
Return type: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.
Return type: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.
Return type:list of string

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.

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.
Returns:

  • 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.
Returns:

  • 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.
Returns:

  • 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.

Returns:debug_str – Debug string of the symbol.
Return type:string
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 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 - s3://my-bucket/path/my-s3-symbol - hdfs://my-bucket/path/my-hdfs-symbol - /path-to/my-local-symbol

See also

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

Saves symbol to a JSON string.

See also

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

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

This function will ask user to pass in an NDArray of position they like to bind to, and it will automatically allocate the ndarray for arguments and auxiliary states that user did not specify explicitly.

Parameters:
  • ctx (Context) – The device context the generated executor to run on.
  • grad_req (string) – {‘write’, ‘add’, ‘null’}, or list of str or dict of str to str, optional Specifies how we should update the gradient to the args_grad. - ‘write’ means everytime gradient is write to specified args_grad NDArray. - ‘add’ means everytime gradient is add to the specified NDArray. - ‘null’ means no action is taken, the gradient may not be calculated.
  • type_dict (dict of str->numpy.dtype) – Input type dictionary, name->dtype
  • group2ctx (dict of string to mx.Context) – The dict mapping the ctx_group attribute to the context assignment.
  • kwargs (dict of str->shape) – Input shape dictionary, name->shape
Returns:

executor – The generated Executor

Return type:

mxnet.Executor

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

Bind current symbol to get an executor.

Parameters:
  • ctx (Context) – The device context the generated executor to run on.
  • args (list of NDArray or dict of str to NDArray) –

    Input arguments to the symbol.

    • If type is list of NDArray, the position is in the same order of list_arguments.
    • If type is dict of str to NDArray, then it maps the name of arguments to the corresponding NDArray.
    • In either case, all the arguments must be provided.
  • args_grad (list of NDArray or dict of str to NDArray, optional) –

    When specified, args_grad provide NDArrays to hold the result of gradient value in backward.

    • If type is list of NDArray, the position is in the same order of list_arguments.
    • If type is dict of str to NDArray, then it maps the name of arguments to the corresponding NDArray.
    • When the type is dict of str to NDArray, users only need to provide the dict for needed argument gradient. Only the specified argument gradient will be calculated.
  • grad_req ({'write', 'add', 'null'}, or list of str or dict of str to str, optional) –

    Specifies how we should update the gradient to the args_grad.

    • ‘write’ means everytime gradient is write to specified args_grad NDArray.
    • ‘add’ means everytime gradient is add to the specified NDArray.
    • ‘null’ means no action is taken, the gradient may not be calculated.
  • aux_states (list of NDArray, or dict of str to NDArray, optional) –

    Input auxiliary states to the symbol, only need to specify when list_auxiliary_states is not empty.

    • If type is list of NDArray, the position is in the same order of list_auxiliary_states.
    • If type is dict of str to NDArray, then it maps the name of auxiliary_states to the corresponding NDArray,
    • In either case, all the auxiliary_states need to be provided.
  • group2ctx (dict of string to mx.Context) – The dict mapping the ctx_group attribute to the context assignment.
  • shared_exec (mx.executor.Executor) – Executor to share memory with. This is intended for runtime reshaping, variable length sequences, etc. The returned executor shares state with shared_exec, and should not be used in parallel with it.
Returns:

executor – The generated Executor

Return type:

Executor

Notes

Auxiliary states are special states of symbols that do not correspond to an argument, and do not have gradient. But still be 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.

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

grad(wrt)

Get 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.
Returns:grad – A gradient Symbol with returns to be the corresponding gradients.
Return type:Symbol
eval(ctx=cpu(0), **kwargs)

Evaluate 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. Eval allows simpler syntax for less cumbersome introspection.

Parameters:
  • ctx (Context) – The device context the generated executor to run on.
  • kwargs (list of NDArray or dict of str to NDArray) –

    Input arguments to the symbol.

    • If type is list of NDArray, the position is in the same order of list_arguments.
    • If type is dict of str to NDArray, then it maps the name of arguments to the corresponding NDArray.
    • In either case, all the arguments must be provided.
Returns:

  • 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.

mxnet.symbol.var(name, attr=None, shape=None, lr_mult=None, wd_mult=None, dtype=None, init=None, **kwargs)

Create a symbolic variable with specified name.

Parameters:
  • name (str) – Name of the variable.
  • attr (dict of string -> string) – Additional attributes to set on the variable.
  • shape (tuple) – The shape of a variable. If specified, this will be used during shape inference. If the user 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 muliplier for this variable.
  • wd_mult (float) – Weight decay muliplier for this variable.
  • dtype (str or numpy.dtype) – The dtype for this variable. If not specified, this value will be inferred.
  • init (initializer (mxnet.init.*)) – Initializer for this variable to (optionally) override the default initializer
  • kwargs (other additional attribute variables) –
Returns:

variable – A symbol corresponding to an input to the computation graph.

Return type:

Symbol

mxnet.symbol.Variable(name, attr=None, shape=None, lr_mult=None, wd_mult=None, dtype=None, init=None, **kwargs)

Create a symbolic variable with specified name.

Parameters:
  • name (str) – Name of the variable.
  • attr (dict of string -> string) – Additional attributes to set on the variable.
  • shape (tuple) – The shape of a variable. If specified, this will be used during shape inference. If the user 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 muliplier for this variable.
  • wd_mult (float) – Weight decay muliplier for this variable.
  • dtype (str or numpy.dtype) – The dtype for this variable. If not specified, this value will be inferred.
  • init (initializer (mxnet.init.*)) – Initializer for this variable to (optionally) override the default initializer
  • kwargs (other additional attribute variables) –
Returns:

variable – A symbol corresponding to an input to the computation graph.

Return type:

Symbol

mxnet.symbol.Group(symbols)

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

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

Load 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
Returns:sym – The loaded symbol.
Return type:Symbol

See also

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

Load symbol from json string.

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

See also

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

Raise base to an exp.

Parameters:
Returns:

result

Return type:

Symbol or Number

mxnet.symbol.maximum(left, right)

maximum left and right

Parameters:
Returns:

result

Return type:

Symbol or Number

mxnet.symbol.minimum(left, right)

minimum left and right

Parameters:
Returns:

result

Return type:

Symbol or Number

mxnet.symbol.hypot(left, right)

minimum left and right

Parameters:
Returns:

result

Return type:

Symbol or Number

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

Return 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.
Returns:

out – The created Symbol.

Return type:

Symbol

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

Return 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.
Returns:

out – The created Symbol

Return type:

Symbol

mxnet.symbol.arange(start, stop=None, step=1.0, repeat=1, name=None, dtype=None)

Return 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.
Returns:

out – The created Symbol

Return type:

Symbol

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

Elementwise activation function. The activation operations are applied elementwisely to each array elements. The following types are supported:

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

Defined in src/operator/activation.cc:L76

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

The result symbol.

Return type:

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(*args, **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.cc:L79

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. Must be bigger 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
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.BilinearSampler(*args, **kwargs)
Apply bilinear sampling to input feature map, which is the key of “[NIPS2015] Spatial Transformer Networks”
output[batch, channel, y_dst, x_dst] = G(data[batch, channel, y_src, x_src) x_dst, y_dst enumerate all spatial locations in output x_src = grid[batch, 0, y_dst, x_dst] y_src = grid[batch, 1, y_dst, x_dst] G() denotes the bilinear interpolation kernel

The out-boundary points will be padded as zeros. (The boundary is defined to be [-1, 1]) The shape of output will be (data.shape[0], data.shape[1], grid.shape[2], grid.shape[3]) The operator assumes that grid has been nomalized. If you want to design a CustomOp to manipulate grid, please refer to GridGeneratorOp.

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.
Returns:

The result symbol.

Return type:

Symbol

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

Get output from a symbol and pass 0 gradient back

From:src/operator/tensor/elemwise_unary_op.cc:32

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Casts all elements of the input to the 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:L86

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

The result symbol.

Return type:

Symbol

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

Join input arrays along the 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 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:L80 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.
Returns:

The result symbol.

Return type:

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(*args, **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

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

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])
out_width=f(width, kernel[1], pad[1], stride[1], dilate[1])

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). 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 concating 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:L154

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 temperal 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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.Convolution_v1(*args, **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.
Returns:

The result symbol.

Return type:

Symbol

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

Apply correlation to inputs

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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.Crop(*args, **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:L31 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.
Returns:

The result symbol.

Return type:

Symbol

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

Custom operator implemented in frontend.

Parameters:
  • op_type (string) – Type of custom operator. Must be registered first.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Apply deconvolution to input then add a bias.

Parameters:
  • data (Symbol) – Input data to the DeconvolutionOp.
  • weight (Symbol) – Weight matrix.
  • bias (Symbol) – Bias parameter.
  • kernel (Shape(tuple), required) – deconvolution kernel size: (h, w) or (d, h, w)
  • stride (Shape(tuple), optional, default=()) – deconvolution stride: (h, w) or (d, h, w)
  • dilate (Shape(tuple), optional, default=()) – deconvolution dilate: (h, w) or (d, h, w)
  • pad (Shape(tuple), optional, default=()) – pad for deconvolution: (h, w) or (d, h, w). A good number is : (kernel-1)/2. If target_shape is set, pad will be ignored and computed accordingly
  • adj (Shape(tuple), optional, default=()) – adjustment for output shape: (h, w) or (d, h, w). If target_shape is set, ad will be ignored and computed accordingly
  • target_shape (Shape(tuple), optional, default=()) – output shape with target shape : (h, w) or (d, h, w)
  • num_filter (int (non-negative), required) – deconvolution filter(channel) number
  • 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 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.
Returns:

The result symbol.

Return type:

Symbol

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

Apply dropout to input. During training, each element of the input is randomly set to zero with probability p. And then the whole tensor is rescaled by 1/(1-p) to keep the expectation the same as before applying dropout. During the test time, this behaves as an identity map.

Parameters:
  • data (Symbol) – Input data to dropout.
  • p (float, optional, default=0.5) – Fraction of the input that gets dropped out at training time
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

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 all input arguments element-wise.

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

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

Defined in src/operator/tensor/elemwise_sum.cc:L63 This function support variable length of positional input.

Parameters:
  • args (Symbol[]) – Positional input arguments
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.Embedding(*args, **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:L55

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.
Returns:

The result symbol.

Return type:

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(*args, **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:L127

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

The result symbol.

Return type:

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(*args, **kwargs)

Apply 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:L74

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.
Returns:

The result symbol.

Return type:

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(*args, **kwargs)

generate sampling grid for bilinear sampling.

Parameters:
  • data (Symbol) – Input data to the GridGeneratorOp.
  • transform_type ({'affine', 'warp'}, required) – transformation type if transformation type is affine, data is affine matrix : (batch, 6) if transformation type is warp, data is optical flow : (batch, 2, h, w)
  • target_shape (Shape(tuple), optional, default=(0,0)) – if transformation type is affine, the operator need a target_shape : (H, W) if transofrmation type is warp, the operator will ignore target_shape
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.IdentityAttachKLSparseReg(*args, **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.
Returns:

The result symbol.

Return type:

Symbol

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

An operator taking in a n-dimensional input tensor (n > 2), and normalizing the input by subtracting the mean and variance calculated over the spatial dimensions. This is an implemention of the operator described in “Instance Normalization: The Missing Ingredient for Fast Stylization”, D. Ulyanov, A. Vedaldi, V. Lempitsky, 2016 (arXiv:1607.08022v2). This layer is similar to batch normalization, 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’.

Parameters:
  • data (Symbol) – A n-dimensional tensor (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) – Epsilon to prevent division by 0.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.L2Normalization(*args, **kwargs)

Set the l2 norm of each instance to a constant.

Parameters:
  • data (Symbol) – Input data to the L2NormalizationOp.
  • eps (float, optional, default=1e-10) – Epsilon to prevent div 0
  • mode ({'channel', 'instance', 'spatial'},optional, default='instance') – Normalization Mode. If set to instance, this operator will compute a norm for each instance in the batch; this is the default mode. If set to channel, this operator will compute a cross channel norm at each position of each instance. If set to spatial, this operator will compute a norm for each channel.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Apply convolution to input then add a bias.

Parameters:
  • data (Symbol) – Input data to the ConvolutionOp.
  • alpha (float, optional, default=0.0001) – value of the alpha variance scaling parameter in the normalization formula
  • beta (float, optional, default=0.75) – value of the beta power parameter in the normalization formula
  • knorm (float, optional, default=2) – value of the k parameter in normalization formula
  • nsize (int (non-negative), required) – normalization window width in elements.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Leaky ReLu activation

The following types are supported:

  • elu: y = x > 0 ? x : slop * (exp(x)-1)
  • leaky: y = x > 0 ? x : slope * x
  • prelu: same as leaky but the slope is learnable.
  • rrelu: same as leaky but the slope is uniformly 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:L36

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.
Returns:

The result symbol.

Return type:

Symbol

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

LinearRegressionOutput computes and optimizes for squared loss.

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:L45

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.
Returns:

The result symbol.

Return type:

Symbol

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

LogisticRegressionOutput 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:L87

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.
Returns:

The result symbol.

Return type:

Symbol

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

MAERegressionOutput function computes mean absolute error.

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:L66

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.
Returns:

The result symbol.

Return type:

Symbol

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

Get output from a symbol and pass 1 gradient back. This is used as a terminal loss if unary and binary operator are used to composite a loss with no declaration of backward dependency

Parameters:
  • data (Symbol) – Input data.
  • grad_scale (float, optional, default=1) – gradient scale as a supplement to unary and binary operators
  • valid_thresh (float, optional, default=0) – regard element valid when x > valid_thresh, this is used only in valid normalization mode.
  • normalization ({'batch', 'null', 'valid'},optional, default='null') – If set to null, op will not normalize on output gradient.If set to batch, op will normalize gradient by divide batch size.If set to valid, op will normalize gradient by divide # sample marked as valid
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Pad an array.

Only supports 4-D and 5-D input array.

Defined in src/operator/pad.cc:L407

Parameters:
  • data (Symbol) – An n-dimensional input tensor.
  • mode ({'constant', 'edge'}, required) – Padding type to use. “constant” pads all values with a constant value, the value of which can be specified with the constant_value option. “edge” uses the boundary values of the array as padding.
  • pad_width (Shape(tuple), required) – A tuple of padding widths of length 2*r, where r is the rank of the input tensor, specifying number of values padded to the edges of each axis. (before_1, after_1, ... , before_N, after_N) unique pad widths for each axis. Equivalent to pad_width in numpy.pad, but flattened.
  • constant_value (double, optional, default=0) – This option is only used when mode is “constant”. This value will be used as the padding value. Defaults to 0 if not specified.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Perform 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 defintion 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:L121

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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.Pooling_v1(*args, **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 defintion 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:L85

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.
Returns:

The result symbol.

Return type:

Symbol

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

Apply 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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.ROIPooling(*args, **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:L273

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.
Returns:

The result symbol.

Return type:

Symbol

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

Reshapes the input array into a new shape.

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:L87

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=(0,0)) – (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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.SVMOutput(*args, **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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.SequenceLast(*args, **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:L77

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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.SequenceMask(*args, **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
SequenceMask(x, y=[1,1], use_sequence_length=True) =
             [[[  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
SequenceMask(x, y=[2,3], use_sequence_length=True, value=1) =
             [[[  1.,   2.,   3.],
               [  4.,   5.,   6.]],

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

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

Defined in src/operator/sequence_mask.cc:L112

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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.SequenceReverse(*args, **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:L98

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.
Returns:

The result symbol.

Return type:

Symbol

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

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

Assume the input array has shape (d_0, ..., d_n) and we slice it into m (num_outputs=m) subarrays along axis k, then we will obtain a list of m arrays with each of which has shape (d_0, ..., d_k/m, ..., d_n).

For example:

x = [[1, 2],
     [3, 4],
     [5, 6],
     [7, 8]]  // 4x2 array

y = split(x, axis=0, num_outputs=4) // a list of 4 arrays
y[0] = [[ 1.,  2.]]  // 1x2 array

z = split(x, axis=0, num_outputs=2) // a list of 2 arrays
z[0] = [[ 1.,  2.],
        [ 3.,  4.]]

When setting optional argument squeeze_axis=1, then the k-dimension will be removed from the shape if it becomes 1:

y = split(x, axis=0, num_outputs=4, squeeze_axis=1)
y[0] = [ 1.,  2.]  // (2,) vector

Defined in src/operator/slice_channel.cc:L56

Parameters:
  • data (Symbol) – Source input
  • num_outputs (int, required) – Number of outputs to be sliced.
  • axis (int, optional, default='1') – Dimension along which to slice.
  • squeeze_axis (boolean, optional, default=False) – If true, the dimension will be squeezed. Also, input.shape[axis] must be the same as num_outputs when squeeze_axis is turned on.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Perform a softmax transformation on input. Please use SoftmaxOutput.. note:: Softmax` is deprecated. Use softmax

Parameters:
  • data (Symbol) – Input data to softmax.
  • grad_scale (float, optional, default=1) – Scale the gradient by a float factor
  • ignore_label (float, optional, default=-1) – the labels with value equals to ignore_label will be ignored during backward (only works if use_ignore is set to be true).
  • multi_output (boolean, optional, default=False) – If set to true, softmax will applied on axis 1
  • 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 true, softmax will applied on the last axis
  • normalization ({'batch', 'null', 'valid'},optional, default='null') – Normalize the gradient
  • out_grad (boolean, optional, default=False) – Apply weighting from output gradient
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Apply softmax activation to input. This is intended for internal layers. For output (loss layer) please use SoftmaxOutput. 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 num_channel-class softmax at each position of each instance; this can be used for fully convolutional network, image segmentation, etc.

Parameters:
  • data (Symbol) – Input data to activation function.
  • mode ({'channel', 'instance'},optional, default='instance') – Softmax Mode. If set to instance, this operator will compute a softmax for each instance in the batch; this is the default mode. If set to channel, this operator will compute a num_channel-class softmax at each position of each instance; this can be used for fully convolutional network, image segmentation, etc.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Softmax with logit loss.

In the forward pass, the softmax output is returned. Assume the input data has shape (n,k), then the output will have the same shape as the input, which is computed by

\[out[i,:] = softmax(data[i,:])\]

for \(i=0,...,n-1\), where

\[softmax(x) = \left[..., \frac{exp(x[j])}{exp(x[0])+...+exp(x[k-1])}, ...\right]\]

For general N-D input array with shape \((d_1, ..., d_n)\). Denoted by the size \(s=d_1d_2...d_n\). The way to compute softmax various:

  • preserve_shape is false (default). Reshape input into a 2-D array with shape \((d_1, s/d_1)\) beforing computing the softmax, and then reshaped back to the original shape.

  • preserve_shape is true. For all \(i_1, ..., i_{n-1}\), compute

    \[out[i_1, ..., i_{n-1}, :] = softmax(data[i_1, ..., i_{n-1},:])\]
  • multi_output is true. For all \(i_1, ..., i_{n-1}\), compute

    \[out[i_1, :, ..., i_{n-1}] = softmax(data[i_1, :, ..., i_{n-1}])\]

In the backward pass, the logit loss, also called cross-entroy loss, is added. The provided label can be a (N-1)-D label index array or a N-D label probability array.

Examples with a particular label can be ignored during backward by specifying ignore_label (also need use_ignore to be true).

A scale can be applied to the gradient by grad_scale, which is often used in mutli-loss object function in which we can given each loss different weight. It also supports various ways to normalize the gradient by normalization:

  • null: do nothing
  • batch: divide by batch size (number of examples)
  • valid: divide by the number of examples which are not ignored.

Defined in src/operator/softmax_output.cc:L77

Parameters:
  • data (Symbol) – Input data.
  • label (Symbol) – Ground truth label.
  • grad_scale (float, optional, default=1) – Scale the gradient by a float factor
  • ignore_label (float, optional, default=-1) – the labels with value equals to ignore_label will be ignored during backward (only works if use_ignore is set to be true).
  • multi_output (boolean, optional, default=False) – If set to true, softmax will applied on axis 1
  • 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 true, softmax will applied on the last axis
  • normalization ({'batch', 'null', 'valid'},optional, default='null') – Normalize the gradient
  • out_grad (boolean, optional, default=False) – Apply weighting from output gradient
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Apply 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.
Returns:

The result symbol.

Return type:

Symbol

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

Interchange 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:L55

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.
Returns:

The result symbol.

Return type:

Symbol

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

Perform nearest neighboor/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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.abs(*args, **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:L117

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Updater function for adam optimizer

Parameters:
  • weight (Symbol) – Weight
  • grad (Symbol) – Gradient
  • mean (Symbol) – Moving mean
  • var (Symbol) – Moving variance
  • lr (float, required) – learning_rate
  • beta1 (float, optional, default=0.9) – beta1
  • beta2 (float, optional, default=0.999) – beta2
  • epsilon (float, optional, default=1e-08) – epsilon
  • wd (float, optional, default=0) – weight decay
  • rescale_grad (float, optional, default=1) – rescale gradient as grad = rescale_grad*grad.
  • clip_gradient (float, optional, default=-1) – If greater than 0, clip gradient to grad = max(min(grad, -clip_gradient), clip_gradient). Otherwise turned off.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Add all input arguments element-wise.

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

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

Defined in src/operator/tensor/elemwise_sum.cc:L63 This function support variable length of positional input.

Parameters:
  • args (Symbol[]) – Positional input arguments
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.arccos(*args, **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:L404

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

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

Defined in src/operator/tensor/elemwise_unary_op.cc:L510

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.arcsin(*args, **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:L387

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

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

Defined in src/operator/tensor/elemwise_unary_op.cc:L500

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.arctan(*args, **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:L420

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

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

Defined in src/operator/tensor/elemwise_unary_op.cc:L520

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.argmax(*args, **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.]]

Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L31

Parameters:
  • data (Symbol) – The input
  • axis (int or None, optional, default='None') – int or None. The axis to perform the reduction. Negative values means indexing from right to left. If is None, a global reduction will be performed.
  • keepdims (boolean, optional, default=False) – If true, the axis which is reduced is left in the result as dimension with size one.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.argmax_channel(*args, **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.]

Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L76

Parameters:
  • data (Symbol) – The input array
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.argmin(*args, **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.]]

Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L56

Parameters:
  • data (Symbol) – The input
  • axis (int or None, optional, default='None') – int or None. The axis to perform the reduction. Negative values means indexing from right to left. If is None, a global reduction will be performed.
  • keepdims (boolean, optional, default=False) – If true, the axis which is reduced is left in the result as dimension with size one.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.argsort(*args, **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:L157

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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.batch_dot(*args, **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:L393

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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.batch_take(*args, **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:L172

Parameters:
  • a (Symbol) – The input array
  • indices (Symbol) – The index array
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

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

broadcast_plus is an alias to the function broadcast_add.

Example:

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

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

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

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

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L32

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_axes(*args, **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.]]]

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L137

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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_axis(*args, **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.]]]

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L137

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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_div(*args, **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.]]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L137

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_equal(*args, **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.]]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L27

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_greater(*args, **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.]]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L63

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_greater_equal(*args, **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.]]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L81

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_hypot(*args, **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.]]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L137

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_lesser(*args, **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.]]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L99

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_lesser_equal(*args, **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.]]

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

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_maximum(*args, **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.]]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L61

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_minimum(*args, **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.]]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L96

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

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

broadcast_minus is an alias to the function broadcast_sub.

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.]]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L71

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_mul(*args, **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.]]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L104

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_not_equal(*args, **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.]]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L45

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

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

broadcast_plus is an alias to the function broadcast_add.

Example:

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

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

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

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

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L32

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_power(*args, **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.]]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L26

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

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

broadcast_minus is an alias to the function broadcast_sub.

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.]]

Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L71

Parameters:
  • lhs (Symbol) – First input to the function
  • rhs (Symbol) – Second input to the function
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.broadcast_to(*args, **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.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L161

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.
Returns:

The result symbol.

Return type:

Symbol

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

Casts all elements of the input to the 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:L86

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

The result symbol.

Return type:

Symbol

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

Returns element-wise ceiling of the input.

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:L174

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.choose_element_0index(*args, **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.
Returns:

The result symbol.

Return type:

Symbol

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

Clip (limit) 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:L438

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.
Returns:

The result symbol.

Return type:

Symbol

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

Join input arrays along the 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 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:L80 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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.cos(*args, **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:L354

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.cosh(*args, **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:L476

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Slice a continuous region of the array.

Note

crop is deprecated. Use slice instead.

This function returns a sliced continous 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:L244

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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.degrees(*args, **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:L434

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.dot(*args, **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])
    

Defined in src/operator/tensor/matrix_op.cc:L357

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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.elemwise_add(*args, **kwargs)
Parameters:
  • lhs (Symbol) – first input
  • rhs (Symbol) – second input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.exp(*args, **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:L265

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Insert a new axis with 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:L204

Parameters:
  • data (Symbol) – Source input
  • axis (int (non-negative), required) – Position (amongst axes) where new axis is to be inserted.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.expm1(*args, **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:L338

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.fill_element_0index(*args, **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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.fix(*args, **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:L196

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.flatten(*args, **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:L127

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

The result symbol.

Return type:

Symbol

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

Reverse elements of an array with axis

From:src/operator/tensor/matrix_op.cc:557

Parameters:
  • data (Symbol) – Input data array
  • axis (Shape(tuple), required) – The axis which to reverse elements.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Returns element-wise floor of the input.

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:L185

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.gamma(*args, **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:530

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

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

From:src/operator/tensor/elemwise_unary_op.cc:540

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Returns a copy of the input.

From:src/operator/tensor/elemwise_unary_op.cc:15

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.log(*args, **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:L275

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.log10(*args, **kwargs)

Returns element-wise Base-10 logarithmic value of the input.

10**log10(x) = x

Defined in src/operator/tensor/elemwise_unary_op.cc:L285

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.log1p(*args, **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:L325

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.log2(*args, **kwargs)

Returns element-wise Base-2 logarithmic value of the input.

2**log2(x) = x

Defined in src/operator/tensor/elemwise_unary_op.cc:L295

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Compute 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
  • axis (int, optional, default='-1') – The axis along which to compute softmax.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Get output from a symbol and pass 1 gradient back. This is used as a terminal loss if unary and binary operator are used to composite a loss with no declaration of backward dependency

From:src/operator/tensor/elemwise_unary_op.cc:40

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Compute the max of array elements over given axes.

The argument axis specifies the axes to compute over:

  • (): compute over all elements into a scalar array with shape (1,). This is the default option.
  • int: compute over along a particular axis. If input has shape (n, m, k), use axis=0 will result in an array with shape (m, k).
  • tuple of int: compute over multiple axes. Again assume input shape (n, m, k), with axis=(0,2) we obtain a (m,) shape array.

If keepdims = 1, then the result array will has the same number of dimensions as the input, while the reduced axes will have size 1.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L98

Parameters:
  • data (Symbol) – The input
  • axis (Shape(tuple), optional, default=()) – The axes to perform the reduction.
  • keepdims (boolean, optional, default=False) – If true, the axes which are reduced are left in the result as dimension with size one.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Compute the max of array elements over given axes.

The argument axis specifies the axes to compute over:

  • (): compute over all elements into a scalar array with shape (1,). This is the default option.
  • int: compute over along a particular axis. If input has shape (n, m, k), use axis=0 will result in an array with shape (m, k).
  • tuple of int: compute over multiple axes. Again assume input shape (n, m, k), with axis=(0,2) we obtain a (m,) shape array.

If keepdims = 1, then the result array will has the same number of dimensions as the input, while the reduced axes will have size 1.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L98

Parameters:
  • data (Symbol) – The input
  • axis (Shape(tuple), optional, default=()) – The axes to perform the reduction.
  • keepdims (boolean, optional, default=False) – If true, the axes which are reduced are left in the result as dimension with size one.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Compute the mean of array elements over given axes.

The argument axis specifies the axes to compute over:

  • (): compute over all elements into a scalar array with shape (1,). This is the default option.
  • int: compute over along a particular axis. If input has shape (n, m, k), use axis=0 will result in an array with shape (m, k).
  • tuple of int: compute over multiple axes. Again assume input shape (n, m, k), with axis=(0,2) we obtain a (m,) shape array.

If keepdims = 1, then the result array will has the same number of dimensions as the input, while the reduced axes will have size 1.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L53

Parameters:
  • data (Symbol) – The input
  • axis (Shape(tuple), optional, default=()) – The axes to perform the reduction.
  • keepdims (boolean, optional, default=False) – If true, the axes which are reduced are left in the result as dimension with size one.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Compute the min of array elements over given axes.

The argument axis specifies the axes to compute over:

  • (): compute over all elements into a scalar array with shape (1,). This is the default option.
  • int: compute over along a particular axis. If input has shape (n, m, k), use axis=0 will result in an array with shape (m, k).
  • tuple of int: compute over multiple axes. Again assume input shape (n, m, k), with axis=(0,2) we obtain a (m,) shape array.

If keepdims = 1, then the result array will has the same number of dimensions as the input, while the reduced axes will have size 1.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L108

Parameters:
  • data (Symbol) – The input
  • axis (Shape(tuple), optional, default=()) – The axes to perform the reduction.
  • keepdims (boolean, optional, default=False) – If true, the axes which are reduced are left in the result as dimension with size one.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Compute the min of array elements over given axes.

The argument axis specifies the axes to compute over:

  • (): compute over all elements into a scalar array with shape (1,). This is the default option.
  • int: compute over along a particular axis. If input has shape (n, m, k), use axis=0 will result in an array with shape (m, k).
  • tuple of int: compute over multiple axes. Again assume input shape (n, m, k), with axis=(0,2) we obtain a (m,) shape array.

If keepdims = 1, then the result array will has the same number of dimensions as the input, while the reduced axes will have size 1.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L108

Parameters:
  • data (Symbol) – The input
  • axis (Shape(tuple), optional, default=()) – The axes to perform the reduction.
  • keepdims (boolean, optional, default=False) – If true, the axes which are reduced are left in the result as dimension with size one.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Compute the product of array elements over given axes with NaN ignored

Refer to prod for more details.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L88

Parameters:
  • data (Symbol) – The input
  • axis (Shape(tuple), optional, default=()) – The axes to perform the reduction.
  • keepdims (boolean, optional, default=False) – If true, the axes which are reduced are left in the result as dimension with size one.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Compute the sum of array elements over given axes with NaN ignored

Refer to sum for more details.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L75

Parameters:
  • data (Symbol) – The input
  • axis (Shape(tuple), optional, default=()) – The axes to perform the reduction.
  • keepdims (boolean, optional, default=False) – If true, the axes which are reduced are left in the result as dimension with size one.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Negate src

From:src/operator/tensor/elemwise_unary_op.cc:105

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Computes the L2 norm of the input array.

Flattens the input array and then computes the l2 norm.

Examples:

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

norm(x) = [5.47722578]

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L185

Parameters:
  • data (Symbol) – Source input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Draw random samples from a normal (Gaussian) distribution.

Examples:

normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478],
                                       [-1.23474145,  1.55807114]]

Defined in src/operator/tensor/sample_op.cc:L54

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=()) – The 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.one_hot(*args, **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:L218

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.
Returns:

The result symbol.

Return type:

Symbol

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

Return an array of ones with the same shape and type as the input array.

From:src/operator/tensor/init_op.cc:59

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Pad an array.

Only supports 4-D and 5-D input array.

Defined in src/operator/pad.cc:L407

Parameters:
  • data (Symbol) – An n-dimensional input tensor.
  • mode ({'constant', 'edge'}, required) – Padding type to use. “constant” pads all values with a constant value, the value of which can be specified with the constant_value option. “edge” uses the boundary values of the array as padding.
  • pad_width (Shape(tuple), required) – A tuple of padding widths of length 2*r, where r is the rank of the input tensor, specifying number of values padded to the edges of each axis. (before_1, after_1, ... , before_N, after_N) unique pad widths for each axis. Equivalent to pad_width in numpy.pad, but flattened.
  • constant_value (double, optional, default=0) – This option is only used when mode is “constant”. This value will be used as the padding value. Defaults to 0 if not specified.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.pick(*args, **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.

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.]]

Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L124

Parameters:
  • data (Symbol) – The input array
  • index (Symbol) – The index array
  • axis (int or None, optional, default='None') – int or None. The axis to perform the reduction. Negative values means indexing from right to left. If is None, a global reduction will be performed.
  • keepdims (boolean, optional, default=False) – If true, the axis which is reduced is left in the result as dimension with size one.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Compute the product of array elements over given axes.

The argument axis specifies the axes to compute over:

  • (): compute over all elements into a scalar array with shape (1,). This is the default option.
  • int: compute over along a particular axis. If input has shape (n, m, k), use axis=0 will result in an array with shape (m, k).
  • tuple of int: compute over multiple axes. Again assume input shape (n, m, k), with axis=(0,2) we obtain a (m,) shape array.

If keepdims = 1, then the result array will has the same number of dimensions as the input, while the reduced axes will have size 1.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L62

Parameters:
  • data (Symbol) – The input
  • axis (Shape(tuple), optional, default=()) – The axes to perform the reduction.
  • keepdims (boolean, optional, default=False) – If true, the axes which are reduced are left in the result as dimension with size one.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.radians(*args, **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:L448

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Sample an exponential distribution

Parameters:
  • lam (float, optional, default=1) – lambda parameter (rate) of the exponential distribution.
  • shape (Shape(tuple), optional, default=()) – The 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Sample a gamma distribution

Parameters:
  • alpha (float, optional, default=1) – alpha parameter (shape parameter) of the gamma distribution.
  • beta (float, optional, default=1) – beta parameter (scale parameter) of the gamma distribution.
  • shape (Shape(tuple), optional, default=()) – The 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Sample a generalized negative binomial distribution

Parameters:
  • mu (float, optional, default=1) – mean of the negative binomial distribution.
  • alpha (float, optional, default=1) – alpha parameter of the negative binomial distribution.
  • shape (Shape(tuple), optional, default=()) – The 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Sample a negative binomial distribution

Parameters:
  • k (int, optional, default='1') – limit of unsuccessful tries.
  • p (float, optional, default=1) – success probability.
  • shape (Shape(tuple), optional, default=()) – The 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Draw random samples from a normal (Gaussian) distribution.

Examples:

normal(loc=0, scale=1, shape=(2,2)) = [[ 1.89171135, -1.16881478],
                                       [-1.23474145,  1.55807114]]

Defined in src/operator/tensor/sample_op.cc:L54

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=()) – The 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Sample a Poisson distribution

Parameters:
  • lam (float, optional, default=1) – lambda parameter (rate) of the Poisson distribution.
  • shape (Shape(tuple), optional, default=()) – The 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Draw samples from a uniform distribution.

Samples are uniformly distributed over the half-open interval [low, high) (includes low, but excludes high):

nd.uniform(low=0, high=1, shape=(2,2)) = [[ 0.60276335,  0.85794562],
                                          [ 0.54488319,  0.84725171]]

Defined in src/operator/tensor/sample_op.cc:L41

Parameters:
  • low (float, optional, default=0) – The lower bound of distribution
  • high (float, optional, default=1) – The upper bound of distribution
  • shape (Shape(tuple), optional, default=()) – The 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Repeat elements of an array.

In default, repeat flatten the input array into 1-D and then repeat the elements:

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

repeat(x, repeats=2) = [ 1.,  1.,  2.,  2.,  3.,  3.,  4.,  4.]

We can also choose a particular axis to repeat, in which a negative axis is interpreted counting from the backward:

repeat(x, repeats=2, axis=1) = [[ 1.,  1.,  2.,  2.],
                                [ 3.,  3.,  4.,  4.]]

repeat(x, repeats=2, axis=-1) = [[ 1.,  2.],
                                 [ 1.,  2.],
                                 [ 3.,  4.],
                                 [ 3.,  4.]]

Defined in src/operator/tensor/matrix_op.cc:L477

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.
Returns:

The result symbol.

Return type:

Symbol

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

Reshapes the input array into a new shape.

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:L87

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=(0,0)) – (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.
Returns:

The result symbol.

Return type:

Symbol

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

Reverse elements of an array with axis

From:src/operator/tensor/matrix_op.cc:557

Parameters:
  • data (Symbol) – Input data array
  • axis (Shape(tuple), required) – The axis which to reverse elements.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.rint(*args, **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:L163

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Updater function for RMSProp optimizer. The RMSProp code follows the version in http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf Tieleman & Hinton, 2012.

Parameters:
  • weight (Symbol) – Weight
  • grad (Symbol) – Gradient
  • n (Symbol) – n
  • lr (float, required) – learning_rate
  • gamma1 (float, optional, default=0.95) – gamma1
  • epsilon (float, optional, default=1e-08) – epsilon
  • wd (float, optional, default=0) – weight decay
  • rescale_grad (float, optional, default=1) – rescale gradient as grad = rescale_grad*grad.
  • clip_gradient (float, optional, default=-1) – If greater than 0, clip gradient to grad = max(min(grad, -clip_gradient), clip_gradient). Otherwise turned off.
  • clip_weights (float, optional, default=-1) – If greater than 0, clip weights to weights = max(min(weights, -clip_weights), clip_weights). Otherwise turned off.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Updater function for RMSPropAlex optimizer. The RMSPropAlex code follows the version in http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013.

Parameters:
  • weight (Symbol) – Weight
  • grad (Symbol) – Gradient
  • n (Symbol) – n
  • g (Symbol) – g
  • delta (Symbol) – delta
  • lr (float, required) – learning_rate
  • gamma1 (float, optional, default=0.95) – gamma1
  • gamma2 (float, optional, default=0.9) – gamma2
  • epsilon (float, optional, default=1e-08) – epsilon
  • wd (float, optional, default=0) – weight decay
  • rescale_grad (float, optional, default=1) – rescale gradient as grad = rescale_grad*grad.
  • clip_gradient (float, optional, default=-1) – If greater than 0, clip gradient to grad = max(min(grad, -clip_gradient), clip_gradient). Otherwise turned off.
  • clip_weights (float, optional, default=-1) – If greater than 0, clip weights to weights = max(min(weights, -clip_weights), clip_weights). Otherwise turned off.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.round(*args, **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:L147

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.rsqrt(*args, **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:L246

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Multi-sampling from exponential distributions with parameters lambda. The parameters of the distributions are provided as input tensor(s). Let “[s]” be the shape of the input tensor(s), “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 tensor with shape [s]x[t]. For any valid n-dimensional index “i” with respect to the input tensor(s), output[i] will be an m-dimensional tensor 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 tensor has the same dimensions as the input tensor(s).

From:src/operator/tensor/multisample_op.cc:172

Parameters:
  • 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • lam (NDArray) –
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Multi-sampling from gamma distributions with parameters alpha and beta. The parameters of the distributions are provided as input tensor(s). Let “[s]” be the shape of the input tensor(s), “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 tensor with shape [s]x[t]. For any valid n-dimensional index “i” with respect to the input tensor(s), output[i] will be an m-dimensional tensor 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 tensor has the same dimensions as the input tensor(s).

From:src/operator/tensor/multisample_op.cc:170

Parameters:
  • 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • alpha (NDArray) –
  • beta (NDArray) –
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Multi-sampling from generalized negative binomial distributions with parameters mu (mean) and alpha (over dispersion). The parameters of the distributions are provided as input tensor(s). Let “[s]” be the shape of the input tensor(s), “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 tensor with shape [s]x[t]. For any valid n-dimensional index “i” with respect to the input tensor(s), output[i] will be an m-dimensional tensor 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 tensor has the same dimensions as the input tensor(s).

From:src/operator/tensor/multisample_op.cc:180

Parameters:
  • 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • mu (NDArray) –
  • alpha (NDArray) –
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Multi-sampling from negative binomial distributions with parameters k (failure limit) and p (failure probability). The parameters of the distributions are provided as input tensor(s). Let “[s]” be the shape of the input tensor(s), “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 tensor with shape [s]x[t]. For any valid n-dimensional index “i” with respect to the input tensor(s), output[i] will be an m-dimensional tensor 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 tensor has the same dimensions as the input tensor(s).

From:src/operator/tensor/multisample_op.cc:176

Parameters:
  • 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • k (NDArray) –
  • p (NDArray) –
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Multi-sampling from normal distributions with parameters mu and sigma. The parameters of the distributions are provided as input tensor(s). Let “[s]” be the shape of the input tensor(s), “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 tensor with shape [s]x[t]. For any valid n-dimensional index “i” with respect to the input tensor(s), output[i] will be an m-dimensional tensor 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 tensor has the same dimensions as the input tensor(s).

From:src/operator/tensor/multisample_op.cc:168

Parameters:
  • 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • mu (NDArray) –
  • sigma (NDArray) –
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Multi-sampling from Poisson distributions with parameters lambda. The parameters of the distributions are provided as input tensor(s). Let “[s]” be the shape of the input tensor(s), “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 tensor with shape [s]x[t]. For any valid n-dimensional index “i” with respect to the input tensor(s), output[i] will be an m-dimensional tensor 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 tensor has the same dimensions as the input tensor(s).

From:src/operator/tensor/multisample_op.cc:174

Parameters:
  • 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • lam (NDArray) –
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Multi-sampling from uniform distributions on the interval [low,high). The parameters of the distributions are provided as input tensor(s). Let “[s]” be the shape of the input tensor(s), “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 tensor with shape [s]x[t]. For any valid n-dimensional index “i” with respect to the input tensor(s), output[i] will be an m-dimensional tensor 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 tensor has the same dimensions as the input tensor(s).

From:src/operator/tensor/multisample_op.cc:166

Parameters:
  • 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • low (NDArray) –
  • high (NDArray) –
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Updater function for sgd optimizer

Parameters:
  • weight (Symbol) – Weight
  • grad (Symbol) – Gradient
  • mom (Symbol) – Momentum
  • lr (float, required) – learning_rate
  • momentum (float, optional, default=0) – momentum
  • wd (float, optional, default=0) – weight decay
  • rescale_grad (float, optional, default=1) – rescale gradient as grad = rescale_grad*grad.
  • clip_gradient (float, optional, default=-1) – If greater than 0, clip gradient to grad = max(min(grad, -clip_gradient), clip_gradient). Otherwise turned off.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Updater function for sgd optimizer

Parameters:
  • weight (Symbol) – Weight
  • grad (Symbol) – gradient
  • lr (float, required) – learning_rate
  • wd (float, optional, default=0) – weight decay
  • rescale_grad (float, optional, default=1) – rescale gradient as grad = rescale_grad*grad.
  • clip_gradient (float, optional, default=-1) – If greater than 0, clip gradient to grad = max(min(grad, -clip_gradient), clip_gradient). Otherwise turned off.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.sign(*args, **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:L132

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Computes the element-wise sine of the input.

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:L311

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.sinh(*args, **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:L462

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Slice a continuous region of the array.

Note

crop is deprecated. Use slice instead.

This function returns a sliced continous 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:L244

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.
Returns:

The result symbol.

Return type:

Symbol

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

Slice 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:L324

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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.smooth_l1(*args, **kwargs)

Calculate Smooth L1 Loss(lhs, scalar)

From:src/operator/tensor/elemwise_binary_scalar_op_extended.cc:63

Parameters:
  • data (Symbol) – source input
  • scalar (float) – scalar input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.softmax(*args, **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:L34

Parameters:
  • data (Symbol) – The input
  • axis (int, optional, default='-1') – The axis along which to compute softmax.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Calculate cross_entropy(data, one_hot(label))

From:src/operator/loss_binary_op.cc:12

Parameters:
  • data (Symbol) – Input data
  • label (Symbol) – Input label
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.sort(*args, **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:L107

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.
Returns:

The result symbol.

Return type:

Symbol

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

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

Assume the input array has shape (d_0, ..., d_n) and we slice it into m (num_outputs=m) subarrays along axis k, then we will obtain a list of m arrays with each of which has shape (d_0, ..., d_k/m, ..., d_n).

For example:

x = [[1, 2],
     [3, 4],
     [5, 6],
     [7, 8]]  // 4x2 array

y = split(x, axis=0, num_outputs=4) // a list of 4 arrays
y[0] = [[ 1.,  2.]]  // 1x2 array

z = split(x, axis=0, num_outputs=2) // a list of 2 arrays
z[0] = [[ 1.,  2.],
        [ 3.,  4.]]

When setting optional argument squeeze_axis=1, then the k-dimension will be removed from the shape if it becomes 1:

y = split(x, axis=0, num_outputs=4, squeeze_axis=1)
y[0] = [ 1.,  2.]  // (2,) vector

Defined in src/operator/slice_channel.cc:L56

Parameters:
  • data (Symbol) – Source input
  • num_outputs (int, required) – Number of outputs to be sliced.
  • axis (int, optional, default='1') – Dimension along which to slice.
  • squeeze_axis (boolean, optional, default=False) – If true, the dimension will be squeezed. Also, input.shape[axis] must be the same as num_outputs when squeeze_axis is turned on.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.sqrt(*args, **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:L228

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Returns element-wise squared value of the input.

\[square(x) = x^2\]

Example:

square([2, 3, 4]) = [3, 9, 16]

Defined in src/operator/tensor/elemwise_unary_op.cc:L210

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Get output from a symbol and pass 0 gradient back

From:src/operator/tensor/elemwise_unary_op.cc:32

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Compute the sum of array elements over given axes.

The argument axis specifies the axes to compute over:

  • (): compute over all elements into a scalar array with shape (1,). This is the default option.
  • int: compute over along a particular axis. If input has shape (n, m, k), use axis=0 will result in an array with shape (m, k).
  • tuple of int: compute over multiple axes. Again assume input shape (n, m, k), with axis=(0,2) we obtain a (m,) shape array.

If keepdims = 1, then the result array will has the same number of dimensions as the input, while the reduced axes will have size 1.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L44

Parameters:
  • data (Symbol) – The input
  • axis (Shape(tuple), optional, default=()) – The axes to perform the reduction.
  • keepdims (boolean, optional, default=False) – If true, the axes which are reduced are left in the result as dimension with size one.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Compute the sum of array elements over given axes.

The argument axis specifies the axes to compute over:

  • (): compute over all elements into a scalar array with shape (1,). This is the default option.
  • int: compute over along a particular axis. If input has shape (n, m, k), use axis=0 will result in an array with shape (m, k).
  • tuple of int: compute over multiple axes. Again assume input shape (n, m, k), with axis=(0,2) we obtain a (m,) shape array.

If keepdims = 1, then the result array will has the same number of dimensions as the input, while the reduced axes will have size 1.

Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L44

Parameters:
  • data (Symbol) – The input
  • axis (Shape(tuple), optional, default=()) – The axes to perform the reduction.
  • keepdims (boolean, optional, default=False) – If true, the axes which are reduced are left in the result as dimension with size one.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Interchange 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:L55

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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.take(*args, **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:L117

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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.tan(*args, **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:L370

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.tanh(*args, **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:L490

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Repeat the whole array by 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:L534

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.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.topk(*args, **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:L44

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.
Returns:

The result symbol.

Return type:

Symbol

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

Permute 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:L168

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.
Returns:

The result symbol.

Return type:

Symbol

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

Draw samples from a uniform distribution.

Samples are uniformly distributed over the half-open interval [low, high) (includes low, but excludes high):

nd.uniform(low=0, high=1, shape=(2,2)) = [[ 0.60276335,  0.85794562],
                                          [ 0.54488319,  0.84725171]]

Defined in src/operator/tensor/sample_op.cc:L41

Parameters:
  • low (float, optional, default=0) – The lower bound of distribution
  • high (float, optional, default=1) – The upper bound of distribution
  • shape (Shape(tuple), optional, default=()) – The 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. If output given, set to type of output.If output not given and type not defined (dtype=None), set to float32.
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

mxnet.symbol.where(*args, **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 condtion 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:21

Parameters:
  • condition (Symbol) – condition array
  • x (Symbol) –
  • y (Symbol) –
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol

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

Return an array of zeros with the same shape and type as the input array.

From:src/operator/tensor/init_op.cc:47

Parameters:
  • data (Symbol) – The input
  • name (string, optional.) – Name of the resulting symbol.
Returns:

The result symbol.

Return type:

Symbol