++ed by:
18 non-PAUSE users
Sergey V. Kolychev

# NAME

    AI::MXNet::Gluon::Loss - Base class for loss.

## DESCRIPTION

    Base class for loss.

Parameters
----------
weight : float or None
Global scalar weight for loss.
batch_axis : int, default 0
The axis that represents mini-batch.

## _apply_weighting

    Apply weighting to loss.

Parameters
----------
loss : Symbol
The loss to be weighted.
weight : float or None
Global scalar weight for loss.
sample_weight : Symbol or None
Per sample weighting. Must be broadcastable to
the same shape as loss. For example, if loss has
shape (64, 10) and you want to weight each sample
in the batch separately, sample_weight should have
shape (64, 1).

Returns
-------
loss : Symbol
Weighted loss

# NAME

    AI::MXNet::Gluon::L2Loss

# DESCRIPTION

    Calculates the mean squared error between output and label:

Output and label can have arbitrary shape as long as they have the same
number of elements.

Parameters
----------
weight : float or None
Global scalar weight for loss.
sample_weight : Symbol or None
Per sample weighting. Must be broadcastable to
the same shape as loss. For example, if loss has
shape (64, 10) and you want to weight each sample
in the batch, sample_weight should have shape (64, 1).
batch_axis : int, default 0
The axis that represents mini-batch.

# NAME

    AI::MXNet::Gluon::L1Loss

# DESCRIPTION

    Calculates the mean absolute error between output and label:

.. math::
L = \\frac{1}{2}\\sum_i \\vert {output}_i - {label}_i \\vert.

Output and label must have the same shape.

Parameters
----------
weight : float or None
Global scalar weight for loss.
sample_weight : Symbol or None
Per sample weighting. Must be broadcastable to
the same shape as loss. For example, if loss has
shape (64, 10) and you want to weight each sample
in the batch, sample_weight should have shape (64, 1).
batch_axis : int, default 0
The axis that represents mini-batch.

# NAME

    AI::MXNet::Gluon::SigmoidBinaryCrossEntropyLoss

# DESCRIPTION

    The cross-entropy loss for binary classification. (alias: SigmoidBCELoss)

BCE loss is useful when training logistic regression.

.. math::
loss(o, t) = - 1/n \sum_i (t[i] * log(o[i]) + (1 - t[i]) * log(1 - o[i]))

Parameters
----------
from_sigmoid : bool, default is False
Whether the input is from the output of sigmoid. Set this to false will make
the loss calculate sigmoid and then BCE, which is more numerically stable through
log-sum-exp trick.
weight : float or None
Global scalar weight for loss.
sample_weight : Symbol or None
Per sample weighting. Must be broadcastable to
the same shape as loss. For example, if loss has
shape (64, 10) and you want to weight each sample
in the batch, sample_weight should have shape (64, 1).
batch_axis : int, default 0
The axis that represents mini-batch.

# NAME

    AI::MXNet::Gluon::SoftmaxCrossEntropyLoss

# DESCRIPTION

    Computes the softmax cross entropy loss. (alias: SoftmaxCELoss)

If sparse_label is True, label should contain integer category indicators:

.. math::
p = {softmax}({output})

L = -\\sum_i {log}(p_{i,{label}_i})

Label's shape should be output's shape without the axis dimension. i.e. for
output.shape = (1,2,3,4) and axis = 2, label.shape should be (1,2,4).

If sparse_label is False, label should contain probability distribution
with the same shape as output:

.. math::
p = {softmax}({output})

L = -\\sum_i \\sum_j {label}_j {log}(p_{ij})

Parameters
----------
axis : int, default -1
The axis to sum over when computing softmax and entropy.
sparse_label : bool, default True
Whether label is an integer array instead of probability distribution.
from_logits : bool, default False
Whether input is a log probability (usually from log_softmax) instead
of unnormalized numbers.
weight : float or None
Global scalar weight for loss.
sample_weight : Symbol or None
Per sample weighting. Must be broadcastable to
the same shape as loss. For example, if loss has
shape (64, 10) and you want to weight each sample
in the batch, sample_weight should have shape (64, 1).
batch_axis : int, default 0
The axis that represents mini-batch.

# NAME

    AI::MXNet::Gluon::KLDivLoss

# DESCRIPTION

    The Kullback-Leibler divergence loss.

KL divergence is a useful distance measure for continuous distributions
and is often useful when performing direct regression over the space of
(discretely sampled) continuous output distributions.

.. _Kullback-Leibler divergence:
https://en.wikipedia.org/wiki/Kullback-Leibler_divergence
.. math::
L = 1/n \\sum_i (label_i * (log(label_i) - output_i))

Label's shape should be the same as output's.

Parameters
----------
from_logits : bool, default is True
Whether the input is log probability (usually from log_softmax) instead
of unnormalized numbers.
weight : float or None
Global scalar weight for loss.
axis : int, default -1
The dimension along with to compute softmax. Only used when from_logits
is False.
sample_weight : Symbol or None
Per sample weighting. Must be broadcastable to
the same shape as loss. For example, if loss has
shape (64, 10) and you want to weight each sample
in the batch, sample_weight should have shape (64, 1).
batch_axis : int, default 0
The axis that represents mini-batch.

# NAME

    AI::MXNet::Gluon::CTCLoss

# DESCRIPTION

    Connectionist Temporal Classification Loss.

See "Connectionist Temporal Classification: Labelling Unsegmented
Sequence Data with Recurrent Neural Networks"

Parameters
----------
layout : str, default 'NTC'
Layout of the output sequence activation vector.
label_layout : str, default 'NT'
Layout of the labels.
weight : float or None
Global scalar weight for loss.
sample_weight : Symbol or None
Per sample weighting. Must be broadcastable to
the same shape as loss. For example, if loss has
shape (64, 10) and you want to weight each sample
in the batch, sample_weight should have shape (64, 1).
This should be used as the fifth argument when calling this loss.

Input shapes:
data is an activation tensor (i.e. before softmax).
Its shape depends on layout. For layout='TNC', this
input has shape (sequence_length, batch_size, alphabet_size)
Note that the last dimension with index alphabet_size-1 is reserved for special
blank character.

label is the label index matrix with zero-indexed labels.
Its shape depends on label_layout. For label_layout='TN', this
input has shape (label_sequence_length, batch_size). Padding mask of value -1
is available for dealing with unaligned label lengths.
When label_lengths is specified, label lengths are directly used and padding mask
is not allowed in the label.
When label_lengths is not specified, the first occurrence of -1
in each sample marks the end of the label sequence of that sample.

For example, suppose the vocabulary is [a, b, c], and in one batch we have three
sequences 'ba', 'cbb', and 'abac'. We can index the labels as {'a': 0, 'b': 1, 'c': 2}.
The alphabet size should be 4, and we reserve the channel index 3 for blank label
in data tensor. The padding mask value for extra length is -1, so the resulting label
tensor should be padded to be::

[[1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2]]

data_lengths is optional and defaults to None.
When specified, it represents the actual lengths of data.
The shape should be (batch_size,).
If None, the data lengths are treated as being equal to the max sequence length.
This should be used as the third argument when calling this loss.

label_lengths is optional and defaults to None.
When specified, it represents the actual lengths of labels.
The shape should be (batch_size,).
If None, the label lengths are derived from the first occurrence of
the value specified by padding_mask.
This should be used as the fourth argument when calling this loss.

Output shape:
The CTC loss output has the shape (batch_size,).

# NAME

    AI::MXNet::Gluon::HuberLoss

# DESCRIPTION

    Calculates smoothed L1 loss that is equal to L1 loss if absolute error
exceeds rho but is equal to L2 loss otherwise. Also called SmoothedL1 loss.

.. math::
L = \sum_i \begin{cases} \frac{1}{2 {rho}} ({pred}_i - {label}_i)^2 &
\text{ if } |{pred}_i - {label}_i| < {rho} \\
|{pred}_i - {label}_i| - \frac{{rho}}{2} &
\text{ otherwise }
\end{cases}

pred and label can have arbitrary shape as long as they have the same
number of elements.

Parameters
----------
rho : float, default 1
Threshold for trimmed mean estimator.
weight : float or None
Global scalar weight for loss.
batch_axis : int, default 0
The axis that represents mini-batch.

Inputs:
- **pred**: prediction tensor with arbitrary shape
- **label**: target tensor with the same size as pred.
- **sample_weight**: element-wise weighting tensor. Must be broadcastable
to the same shape as pred. For example, if pred has shape [64, 10]
and you want to weigh each sample in the batch separately,
sample_weight should have shape [64, 1].

Outputs:
- **loss**: loss tensor with shape [batch_size]. Dimenions other than
batch_axis are averaged out.

# NAME

    AI::MXNet::Gluon::HingeLoss

# DESCRIPTION

    Calculates the hinge loss function often used in SVMs:

.. math::
L = \sum_i max(0, {margin} - {pred}_i \cdot {label}_i)

where pred is the classifier prediction and label is the target tensor
containing values -1 or 1. pred and label must have the same number of
elements.

Parameters
----------
margin : float
The margin in hinge loss. Defaults to 1.0
weight : float or None
Global scalar weight for loss.
batch_axis : int, default 0
The axis that represents mini-batch.

Inputs:
- **pred**: prediction tensor with arbitrary shape.
- **label**: truth tensor with values -1 or 1. Must have the same size
as pred.
- **sample_weight**: element-wise weighting tensor. Must be broadcastable
to the same shape as pred. For example, if pred has shape (64, 10)
and you want to weigh each sample in the batch separately,
sample_weight should have shape (64, 1).

Outputs:
- **loss**: loss tensor with shape (batch_size,). Dimenions other than
batch_axis are averaged out.

# NAME

    AI::MXNet::Gluon::SquaredHingeLoss

# DESCRIPTION

    Calculates the soft-margin loss function used in SVMs:

.. math::
L = \sum_i max(0, {margin} - {pred}_i \cdot {label}_i)^2

where pred is the classifier prediction and label is the target tensor
containing values -1 or 1. pred and label can have arbitrary shape as
long as they have the same number of elements.

Parameters
----------
margin : float
The margin in hinge loss. Defaults to 1.0
weight : float or None
Global scalar weight for loss.
batch_axis : int, default 0
The axis that represents mini-batch.

Inputs:
- **pred**: prediction tensor with arbitrary shape
- **label**: truth tensor with values -1 or 1. Must have the same size
as pred.
- **sample_weight**: element-wise weighting tensor. Must be broadcastable
to the same shape as pred. For example, if pred has shape (64, 10)
and you want to weigh each sample in the batch separately,
sample_weight should have shape (64, 1).

Outputs:
- **loss**: loss tensor with shape (batch_size,). Dimenions other than
batch_axis are averaged out.

# NAME

    AI::MXNet::Gluon::LogisticLoss

# DESCRIPTION

    Calculates the logistic loss (for binary losses only):

.. math::
L = \sum_i \log(1 + \exp(- {pred}_i \cdot {label}_i))

where pred is the classifier prediction and label is the target tensor
containing values -1 or 1 (0 or 1 if label_format is binary).
pred and label can have arbitrary shape as long as they have the same number of elements.

Parameters
----------
weight : float or None
Global scalar weight for loss.
batch_axis : int, default 0
The axis that represents mini-batch.
label_format : str, default 'signed'
Can be either 'signed' or 'binary'. If the label_format is 'signed', all label values should
be either -1 or 1. If the label_format is 'binary', all label values should be either
0 or 1.

Inputs:
- **pred**: prediction tensor with arbitrary shape.
- **label**: truth tensor with values -1/1 (label_format is 'signed')
or 0/1 (label_format is 'binary'). Must have the same size as pred.
- **sample_weight**: element-wise weighting tensor. Must be broadcastable
to the same shape as pred. For example, if pred has shape (64, 10)
and you want to weigh each sample in the batch separately,
sample_weight should have shape (64, 1).

Outputs:
- **loss**: loss tensor with shape (batch_size,). Dimenions other than
batch_axis are averaged out.

# NAME

    AI::MXNet::Gluon::TripletLoss

# DESCRIPTION

    Calculates triplet loss given three input tensors and a positive margin.
Triplet loss measures the relative similarity between prediction, a positive
example and a negative example:

.. math::
L = \sum_i \max(\Vert {pred}_i - {pos_i} \Vert_2^2 -
\Vert {pred}_i - {neg_i} \Vert_2^2 + {margin}, 0)

pred, positive and negative can have arbitrary shape as long as they
have the same number of elements.

Parameters
----------
margin : float
Margin of separation between correct and incorrect pair.
weight : float or None
Global scalar weight for loss.
batch_axis : int, default 0
The axis that represents mini-batch.

Inputs:
- **pred**: prediction tensor with arbitrary shape
- **positive**: positive example tensor with arbitrary shape. Must have
the same size as pred.
- **negative**: negative example tensor with arbitrary shape Must have
the same size as pred.

Outputs:
- **loss**: loss tensor with shape (batch_size,).

# NAME

    AI::MXNet::Gluon::PoissonNLLLoss

# DESCRIPTION

    For a target (Random Variable) in a Poisson distribution, the function calculates the Negative
Log likelihood loss.
PoissonNLLLoss measures the loss accrued from a poisson regression prediction made by the model.

.. math::
L = \text{pred} - \text{target} * \log(\text{pred}) +\log(\text{target!})

pred, target can have arbitrary shape as long as they have the same number of elements.

Parameters
----------
from_logits : boolean, default True
indicating whether log(predicted) value has already been computed. If True, the loss is computed as
:math:\exp(\text{pred}) - \text{target} * \text{pred}, and if False, then loss is computed as
:math:\text{pred} - \text{target} * \log(\text{pred}+\text{epsilon}).The default value
weight : float or None
Global scalar weight for loss.
batch_axis : int, default 0
The axis that represents mini-batch.
compute_full: boolean, default False
Indicates whether to add an approximation(Stirling factor) for the Factorial term in the formula for the loss.
The Stirling factor is:
:math:\text{target} * \log(\text{target}) - \text{target} + 0.5 * \log(2 * \pi * \text{target})
epsilon: float, default 1e-08
This is to avoid calculating log(0) which is not defined.

Inputs:
- **pred**:   Predicted value
- **target**: Random variable(count or number) which belongs to a Poisson distribution.
- **sample_weight**: element-wise weighting tensor. Must be broadcastable
to the same shape as pred. For example, if pred has shape (64, 10)
and you want to weigh each sample in the batch separately,
sample_weight should have shape (64, 1).

Outputs:
- **loss**: Average loss (shape=(1,1)) of the loss tensor with shape (batch_size,).

# NAME

    AI::MXNet::Gluon::CosineEmbeddingLoss

# DESCRIPTION

    For a target label 1 or -1, vectors input1 and input2, the function computes the cosine distance
between the vectors. This can be interpreted as how similar/dissimilar two input vectors are.

.. math::

L = \sum_i \begin{cases} 1 - {cos\_sim({input1}_i, {input2}_i)} & \text{ if } {label}_i = 1\\
{cos\_sim({input1}_i, {input2}_i)} & \text{ if } {label}_i = -1 \end{cases}\\
cos\_sim(input1, input2) = \frac{{input1}_i.{input2}_i}{||{input1}_i||.||{input2}_i||}

input1, input2 can have arbitrary shape as long as they have the same number of elements.

Parameters
----------
weight : float or None
Global scalar weight for loss.
batch_axis : int, default 0
The axis that represents mini-batch.
margin : float
Margin of separation between correct and incorrect pair.

Inputs:
- **input1**: a tensor with arbitrary shape
- **input2**: another tensor with same shape as pred to which input1 is
compared for similarity and loss calculation
- **label**: A 1-D tensor indicating for each pair input1 and input2, target label is 1 or -1
- **sample_weight**: element-wise weighting tensor. Must be broadcastable
to the same shape as input1. For example, if input1 has shape (64, 10)
and you want to weigh each sample in the batch separately,
sample_weight should have shape (64, 1).

Outputs:
- **loss**: The loss tensor with shape (batch_size,).