<a name="nn.Criterions"></a>
# Criterions #

[`Criterions`](#nn.Criterion) are helpful to train a neural network. Given an input and a
target, they compute a gradient according to a given loss function.

  * Classification criterions:
    * [`BCECriterion`](#nn.BCECriterion): binary cross-entropy for [`Sigmoid`](transfer.md#nn.Sigmoid) (two-class version of [`ClassNLLCriterion`](#nn.ClassNLLCriterion));
    * [`ClassNLLCriterion`](#nn.ClassNLLCriterion): negative log-likelihood for [`LogSoftMax`](transfer.md#nn.LogSoftMax) (multi-class);
    * [`CrossEntropyCriterion`](#nn.CrossEntropyCriterion): combines [`LogSoftMax`](transfer.md#nn.LogSoftMax) and [`ClassNLLCriterion`](#nn.ClassNLLCriterion);
    * [`ClassSimplexCriterion`](#nn.ClassSimplexCriterion): A simplex embedding criterion for classification.
    * [`MarginCriterion`](#nn.MarginCriterion): two class margin-based loss;
    * [`SoftMarginCriterion`](#nn.SoftMarginCriterion): two class softmargin-based loss;
    * [`MultiMarginCriterion`](#nn.MultiMarginCriterion): multi-class margin-based loss;
    * [`MultiLabelMarginCriterion`](#nn.MultiLabelMarginCriterion): multi-class multi-classification margin-based loss;
    * [`MultiLabelSoftMarginCriterion`](#nn.MultiLabelSoftMarginCriterion): multi-class multi-classification loss based on binary cross-entropy;
  * Regression criterions:
    * [`AbsCriterion`](#nn.AbsCriterion): measures the mean absolute value of the element-wise difference between input;
    * [`SmoothL1Criterion`](#nn.SmoothL1Criterion): a smooth version of the AbsCriterion;
    * [`MSECriterion`](#nn.MSECriterion): mean square error (a classic);
    * [`SpatialAutoCropMSECriterion`](#nn.SpatialAutoCropMSECriterion): Spatial mean square error when the input is spatially smaller than the target, by only comparing their spatial overlap;
    * [`DistKLDivCriterion`](#nn.DistKLDivCriterion): Kullback–Leibler divergence (for fitting continuous probability distributions);
  * Embedding criterions (measuring whether two inputs are similar or dissimilar):
    * [`HingeEmbeddingCriterion`](#nn.HingeEmbeddingCriterion): takes a distance as input;
    * [`L1HingeEmbeddingCriterion`](#nn.L1HingeEmbeddingCriterion): L1 distance between two inputs;
    * [`CosineEmbeddingCriterion`](#nn.CosineEmbeddingCriterion): cosine distance between two inputs;
    * [`DistanceRatioCriterion`](#nn.DistanceRatioCriterion): Probabilistic criterion for training siamese model with triplets.
  * Miscelaneus criterions:
    * [`MultiCriterion`](#nn.MultiCriterion) : a weighted sum of other criterions each applied to the same input and target;
    * [`ParallelCriterion`](#nn.ParallelCriterion) : a weighted sum of other criterions each applied to a different input and target;
    * [`MarginRankingCriterion`](#nn.MarginRankingCriterion): ranks two inputs;
    * [`ModuleCriterion`](#nn.ModuleCriterion) : adds an optional `inputModule` and `targetModule` before a decorated criterion;

<a name="nn.Criterion"></a>
## Criterion ##

This is an abstract class which declares methods defined in all criterions.
This class is [serializable](https://github.com/torch/torch7/blob/master/doc/file.md#serialization-methods).

<a name="nn.Criterion.forward"></a>
### [output] forward(input, target) ###

Given an `input` and a `target`, compute the loss function associated to the criterion and return the result.
In general `input` and `target` are [`Tensor`s](https://github.com/torch/torch7/blob/master/doc/tensor.md), but some specific criterions might require some other type of object.

The `output` returned should be a scalar in general.

The state variable [`self.output`](#nn.Criterion.output) should be updated after a call to `forward()`.


<a name="nn.Criterion.backward"></a>
### [gradInput] backward(input, target) ###

Given an `input` and a `target`, compute the gradients of the loss function associated to the criterion and return the result.
In general `input`, `target` and `gradInput` are [`Tensor`s](..:torch:tensor), but some specific criterions might require some other type of object.

The state variable [`self.gradInput`](#nn.Criterion.gradInput) should be updated after a call to `backward()`.


<a name="nn.Criterion.output"></a>
### State variable: output ###

State variable which contains the result of the last [`forward(input, target)`](#nn.Criterion.forward) call.


<a name="nn.Criterion.gradInput"></a>
### State variable: gradInput ###

State variable which contains the result of the last [`backward(input, target)`](#nn.Criterion.backward) call.


<a name="nn.AbsCriterion"></a>
## AbsCriterion ##

```lua
criterion = nn.AbsCriterion()
```

Creates a criterion that measures the mean absolute value of the element-wise difference between input `x` and target `y`:

```lua
loss(x, y)  = 1/n \sum |x_i - y_i|
```

If `x` and `y` are `d`-dimensional `Tensor`s with a total of `n` elements, the sum operation still operates over all the elements, and divides by `n`.

The division by `n` can be avoided if one sets the internal variable `sizeAverage` to `false`:

```lua
criterion = nn.AbsCriterion()
criterion.sizeAverage = false
```


<a name="nn.ClassNLLCriterion"></a>
## ClassNLLCriterion ##

```lua
criterion = nn.ClassNLLCriterion([weights, sizeAverage, ignoreIndex])
```

The negative log likelihood (NLL) criterion. It is useful to train a classification problem with `n` classes.
If provided, the optional argument `weights` should be a 1D `Tensor` assigning weight to each of the classes.
This is particularly useful when you have an unbalanced training set.

The `input` given through a `forward()` is expected to contain _log-probabilities_ of each class: `input` has to be a 1D `Tensor` of size `n`.
Obtaining log-probabilities in a neural network is easily achieved by adding a [`LogSoftMax`](transfer.md#nn.LogSoftMax) layer in the last layer of your neural network.
You may use [`CrossEntropyCriterion`](#nn.CrossEntropyCriterion) instead, if you prefer not to add an extra layer to your network.
This criterion expects a class index (1 to the number of class) as `target` when calling [`forward(input, target`)](#nn.CriterionForward) and [`backward(input, target)`](#nn.CriterionBackward).

The loss can be described as:

```lua
loss(x, class) = -x[class]
```

or in the case of the `weights` argument, it is specified as follows:
```lua
loss(x, class) = -weights[class] * x[class]
```

or in the case of the `ignoreIndex` argument:
```
loss(x, class) = class != ignoreIndex ? -weights[class] * x[class] : 0
```

Indeed, the `ignoreIndex` (defaults to -100) specifies a value for targets to be ignored.
The commensurate `gradInput` for that target will be zero.
When `sizeAverage=true` (the default), the `gradInput` and `output` are averaged over non-ignored targets.

Due to the behaviour of the backend code, it is necessary to set `sizeAverage` to false when calculating losses *in non-batch mode*.

The following is a code fragment showing how to make a gradient step given an input `x`, a desired output `y` (an integer `1` to `n`, in this case `n = 2` classes), a network `mlp` and a learning rate `learningRate`:

```lua
function gradUpdate(mlp, x, y, learningRate)
   local criterion = nn.ClassNLLCriterion()
   local pred = mlp:forward(x)
   local err = criterion:forward(pred, y)
   mlp:zeroGradParameters()
   local t = criterion:backward(pred, y)
   mlp:backward(x, t)
   mlp:updateParameters(learningRate)
end
```

By default, the losses are averaged over observations for each minibatch. However, if the argument `sizeAverage` is set to `false`, the losses are instead summed for each minibatch.


<a name="nn.CrossEntropyCriterion"></a>
## CrossEntropyCriterion ##

```lua
criterion = nn.CrossEntropyCriterion([weights])
```

This criterion combines [`LogSoftMax`](#nn.LogSoftMax) and [`ClassNLLCriterion`](#nn.ClassNLLCriterion) in one single class.

It is useful to train a classification problem with `n` classes.
If provided, the optional argument `weights` should be a 1D `Tensor` assigning weight to each of the classes. This is particularly useful when you have an unbalanced training set.

The `input` given through a `forward()` is expected to contain scores for each class: `input` has to be a 1D `Tensor` of size `n`.
This criterion expect a class index (1 to the number of class) as `target` when calling [`forward(input, target)`](#nn.CriterionForward) and [`backward(input, target)`](#nn.CriterionBackward).

The loss can be described as:

```lua
loss(x, class) = -log(exp(x[class]) / (\sum_j exp(x[j])))
               = -x[class] + log(\sum_j exp(x[j]))
```

or in the case of the `weights` argument being specified:

```lua
loss(x, class) = weights[class] * (-x[class] + log(\sum_j exp(x[j])))
```
Due to the behaviour of the backend code, it is necessary to set sizeAverage to false when calculating losses *in non-batch mode*.
```lua
crit = nn.CrossEntropyCriterion(weights)
crit.nll.sizeAverage = false
```
The losses are averaged across observations for each minibatch.

<a name="nn.ClassSimplexCriterion"></a>
## ClassSimplexCriterion ##

```lua
criterion = nn.ClassSimplexCriterion(nClasses)
```

ClassSimplexCriterion implements a criterion for classification.
It learns an embedding per class, where each class' embedding is a point on an (N-1)-dimensional simplex,
where N is the number of classes.

The `input` given through a `forward()` is expected to be the output of a Normalized Linear layer with no bias:
- `input` has to be a 1D `Tensor` of size `n` for a single sample
- a 2D `Tensor` of size `batchSize x n` for a mini-batch of samples

This Criterion is best used in combination with a neural network where the last layers are:
- a weight-normalized bias-less Linear layer. [Example source code](https://gist.github.com/soumith/4d0273f592956199739b)
- followed by an output normalization layer (nn.Normalize).

The loss is described in detail in the paper [Scale-invariant learning and convolutional networks](http://arxiv.org/abs/1506.08230).


The following is a code fragment showing how to make a gradient step given an input `x`, a desired output `y` (an integer `1` to `n`, in this case `n = 30` classes), a network `mlp` and a learning rate `learningRate`:

```lua
nInput = 10
nClasses = 30
nHidden = 100
mlp = nn.Sequential()
mlp:add(nn.Linear(nInput, nHidden)):add(nn.ReLU())
mlp:add(nn.NormalizedLinearNoBias(nHidden, nClasses))
mlp:add(nn.Normalize(2))

criterion = nn.ClassSimplexCriterion(nClasses)

function gradUpdate(mlp, x, y, learningRate)
   pred = mlp:forward(x)
   local err = criterion:forward(pred, y)
   mlp:zeroGradParameters()
   local t = criterion:backward(pred, y)
   mlp:backward(x, t)
   mlp:updateParameters(learningRate)
end
```

This criterion also provides two helper functions `getPredictions(input)` and `getTopPrediction(input)` that return the raw predictions and the top prediction index respectively, given an input sample.

<a name="nn.DistKLDivCriterion"></a>
## DistKLDivCriterion ##

```lua
criterion = nn.DistKLDivCriterion()
```

The [Kullback–Leibler divergence](http://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence) criterion.
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.
As with ClassNLLCriterion, the `input` given through a `forward()` is expected to contain _log-probabilities_, however unlike ClassNLLCriterion, `input` is not restricted to a 1D or 2D vector (as the criterion is applied element-wise).

This criterion expect a `target` `Tensor` of the same size as the `input` `Tensor` when calling [`forward(input, target)`](#nn.CriterionForward) and [`backward(input, target)`](#nn.CriterionBackward).

The loss can be described as:

```lua
loss(x, target) = 1/n \sum(target_i * (log(target_i) - x_i))
```

By default, the losses are averaged for each minibatch over observations *as well as* over dimensions. However, if the field `sizeAverage` is set to `false`, the losses are instead summed.


<a name="nn.BCECriterion"></a>
## BCECriterion

```lua
criterion = nn.BCECriterion([weights])
```

Creates a criterion that measures the Binary Cross Entropy between the target and the output:

```lua
loss(o, t) = - 1/n sum_i (t[i] * log(o[i]) + (1 - t[i]) * log(1 - o[i]))
```

or in the case of the weights argument being specified:

```lua
loss(o, t) = - 1/n sum_i weights[i] * (t[i] * log(o[i]) + (1 - t[i]) * log(1 - o[i]))
```

This is used for measuring the error of a reconstruction in for example an auto-encoder. Note that the outputs `o[i]` should be numbers between 0 and 1, for instance, the output of an [`nn.Sigmoid`](transfer.md#nn.Sigmoid) layer and should be interpreted as the probability of predicting `t[i] = 1`. Note `t[i]` can be either 0 or 1.

By default, the losses are averaged for each minibatch over observations *as well as* over dimensions. However, if the field `sizeAverage` is set to `false`, the losses are instead summed.


<a name="nn.MarginCriterion"></a>
## MarginCriterion ##

```lua
criterion = nn.MarginCriterion([margin])
```

Creates a criterion that optimizes a two-class classification hinge loss (margin-based loss) between input `x` (a `Tensor` of dimension `1`) and output `y` (which is a tensor containing either `1`s or `-1`s).
`margin`, if unspecified, is by default `1`.

```lua
loss(x, y) = sum_i (max(0, margin - y[i]*x[i])) / x:nElement()
```

The normalization by the number of elements in the input can be disabled by
setting `self.sizeAverage` to `false`.

### Example

```lua
function gradUpdate(mlp, x, y, criterion, learningRate)
   local pred = mlp:forward(x)
   local err = criterion:forward(pred, y)
   local gradCriterion = criterion:backward(pred, y)
   mlp:zeroGradParameters()
   mlp:backward(x, gradCriterion)
   mlp:updateParameters(learningRate)
end

mlp = nn.Sequential()
mlp:add(nn.Linear(5, 1))

x1 = torch.rand(5)
x1_target = torch.Tensor{1}
x2 = torch.rand(5)
x2_target = torch.Tensor{-1}
criterion=nn.MarginCriterion(1)

for i = 1, 1000 do
   gradUpdate(mlp, x1, x1_target, criterion, 0.01)
   gradUpdate(mlp, x2, x2_target, criterion, 0.01)
end

print(mlp:forward(x1))
print(mlp:forward(x2))

print(criterion:forward(mlp:forward(x1), x1_target))
print(criterion:forward(mlp:forward(x2), x2_target))
```

gives the output:

```lua
 1.0043
[torch.Tensor of dimension 1]


-1.0061
[torch.Tensor of dimension 1]

0
0
```

i.e. the mlp successfully separates the two data points such that they both have a `margin` of `1`, and hence a loss of `0`.

By default, the losses are averaged over observations for each minibatch. However, if the field `sizeAverage` is set to `false`, the losses are instead summed.

<a name="nn.SoftMarginCriterion"></a>
## SoftMarginCriterion ##

```lua
criterion = nn.SoftMarginCriterion()
```

Creates a criterion that optimizes a two-class classification logistic loss between input `x` (a `Tensor` of dimension `1`) and output `y` (which is a tensor containing either `1`s or `-1`s).

```lua
loss(x, y) = sum_i (log(1 + exp(-y[i]*x[i]))) / x:nElement()
```

The normalization by the number of elements in the input can be disabled by
setting `self.sizeAverage` to `false`.

### Example

```lua
function gradUpdate(mlp, x, y, criterion, learningRate)
   local pred = mlp:forward(x)
   local err = criterion:forward(pred, y)
   local gradCriterion = criterion:backward(pred, y)
   mlp:zeroGradParameters()
   mlp:backward(x, gradCriterion)
   mlp:updateParameters(learningRate)
end

mlp = nn.Sequential()
mlp:add(nn.Linear(5, 1))

x1 = torch.rand(5)
x1_target = torch.Tensor{1}
x2 = torch.rand(5)
x2_target = torch.Tensor{-1}
criterion=nn.SoftMarginCriterion(1)

for i = 1, 1000 do
   gradUpdate(mlp, x1, x1_target, criterion, 0.01)
   gradUpdate(mlp, x2, x2_target, criterion, 0.01)
end

print(mlp:forward(x1))
print(mlp:forward(x2))

print(criterion:forward(mlp:forward(x1), x1_target))
print(criterion:forward(mlp:forward(x2), x2_target))
```

gives the output:

```lua

 0.7471
[torch.DoubleTensor of size 1]

-0.9607
[torch.DoubleTensor of size 1]

0.38781049558836
0.32399356957564

```

i.e. the mlp successfully separates the two data points.

By default, the losses are averaged over observations for each minibatch. However, if the field `sizeAverage` is set to `false`, the losses are instead summed.

<a name="nn.MultiMarginCriterion"></a>
## MultiMarginCriterion ##

```lua
criterion = nn.MultiMarginCriterion(p, [weights], [margin])
```

Creates a criterion that optimizes a multi-class classification hinge loss (margin-based loss) between input `x`  (a `Tensor` of dimension 1) and output `y` (which is a target class index, `1` <= `y` <= `x:size(1)`):

```lua
loss(x, y) = sum_i(max(0, (margin - x[y] + x[i]))^p) / x:size(1)
```

where `i == 1` to `x:size(1)` and `i ~= y`.
Note that this criterion also works with 2D inputs and 1D targets.

Optionally, you can give non-equal weighting on the classes by passing a 1D `weights` tensor into the constructor.
The loss function then becomes:

```lua
loss(x, y) = sum_i(max(0, w[y] * (margin - x[y] + x[i]))^p) / x:size(1)
```

This criterion is especially useful for classification when used in conjunction with a module ending in the following output layer:

```lua
mlp = nn.Sequential()
mlp:add(nn.Euclidean(n, m)) -- outputs a vector of distances
mlp:add(nn.MulConstant(-1)) -- distance to similarity
```

By default, the losses are averaged over observations for each minibatch. However, if the field `sizeAverage` is set to `false`, the losses are instead summed.


<a name="nn.MultiLabelMarginCriterion"></a>
## MultiLabelMarginCriterion ##

```lua
criterion = nn.MultiLabelMarginCriterion()
```

Creates a criterion that optimizes a multi-class multi-classification hinge loss (margin-based loss) between input `x`  (a 1D `Tensor`) and output `y` (which is a 1D `Tensor` of target class indices):

```lua
loss(x, y) = sum_ij(max(0, 1 - (x[y[j]] - x[i]))) / x:size(1)
```

where `i == 1` to `x:size(1)`, `j == 1` to `y:size(1)`, `y[j] ~= 0`, and `i ~= y[j]` for all `i` and `j`.
Note that this criterion also works with 2D inputs and targets.

`y` and `x` must have the same size.
The criterion only considers the first non zero `y[j]` targets.
This allows for different samples to have variable amounts of target classes:

```lua
criterion = nn.MultiLabelMarginCriterion()
input = torch.randn(2, 4)
target = torch.Tensor{{1, 3, 0, 0}, {4, 0, 0, 0}} -- zero-values are ignored
criterion:forward(input, target)
```

<a name="nn.MultiLabelSoftMarginCriterion"></a>
## MultiLabelSoftMarginCriterion ##

```lua
criterion = nn.MultiLabelSoftMarginCriterion()
```

Creates a criterion that optimizes a multi-label one-versus-all loss based on max-entropy, between input `x`  (a 1D `Tensor`) and target `y` (a binary 1D `Tensor`):

```lua
loss(x, y) = - sum_i (y[i] log( exp(x[i]) / (1 + exp(x[i]))) + (1-y[i]) log(1/(1+exp(x[i])))) / x:nElement()
```

where `i == 1` to `x:nElement()`, `y[i]  in {0,1}`.
Note that this criterion also works with 2D inputs and targets.

`y` and `x` must have the same size.

<a name="nn.MSECriterion"></a>
## MSECriterion ##

```lua
criterion = nn.MSECriterion()
```

Creates a criterion that measures the mean squared error between `n` elements in the input `x` and output `y`:

```lua
loss(x, y) = 1/n \sum |x_i - y_i|^2 .
```

If `x` and `y` are `d`-dimensional `Tensor`s with a total of `n` elements, the sum operation still operates over all the elements, and divides by `n`.
The two `Tensor`s must have the same number of elements (but their sizes might be different).

The division by `n` can be avoided if one sets the internal variable `sizeAverage` to `false`:

```lua
criterion = nn.MSECriterion()
criterion.sizeAverage = false
```

By default, the losses are averaged over observations for each minibatch. However, if the field `sizeAverage` is set to `false`, the losses are instead summed.


<a name="nn.SpatialAutoCropMSECriterion"></a>
## SpatialAutoCropMSECriterion ##

```lua
criterion = nn.SpatialAutoCropMSECriterion()
```

Creates a criterion that measures the mean squared error between the input and target, even if the target is spatially larger than the input. It achieves this by center-cropping the target to the same spatial resolution as the input, the mean squared error is then calculated between the input and this cropped target.

If the input and cropped target tensors are `d`-dimensional `Tensor`s with a total of `n` elements, the sum operation operates over all the elements, and divides by `n`.

The division by `n` can be avoided if one sets the internal variable `sizeAverage` to `false`:

```lua
criterion = nn.SpatialAutoCropMSECriterion()
criterion.sizeAverage = false
```


<a name="nn.MultiCriterion"></a>
## MultiCriterion ##

```lua
criterion = nn.MultiCriterion()
```

This returns a Criterion which is a weighted sum of other Criterion.
Criterions are added using the method:

```lua
criterion:add(singleCriterion [, weight])
```

where `weight` is a scalar (default 1). Each criterion is applied to the same `input` and `target`.

Example :

```lua
input = torch.rand(2,10)
target = torch.IntTensor{1,8}
nll = nn.ClassNLLCriterion()
nll2 = nn.CrossEntropyCriterion()
mc = nn.MultiCriterion():add(nll, 0.5):add(nll2)
output = mc:forward(input, target)
```

<a name="nn.ParallelCriterion"></a>
## ParallelCriterion ##

```lua
criterion = nn.ParallelCriterion([repeatTarget])
```

This returns a Criterion which is a weighted sum of other Criterion.
Criterions are added using the method:

```lua
criterion:add(singleCriterion [, weight])
```

where `weight` is a scalar (default 1). The criterion expects an `input` and `target` table.
Each criterion is applied to the commensurate `input` and `target` element in the tables.
However, if `repeatTarget=true`, the `target` is repeatedly presented to each criterion (with a different `input`).

Example :

```lua
input = {torch.rand(2,10), torch.randn(2,10)}
target = {torch.IntTensor{1,8}, torch.randn(2,10)}
nll = nn.ClassNLLCriterion()
mse = nn.MSECriterion()
pc = nn.ParallelCriterion():add(nll, 0.5):add(mse)
output = pc:forward(input, target)
```


<a name="nn.SmoothL1Criterion"></a>
## SmoothL1Criterion ##

```lua
criterion = nn.SmoothL1Criterion()
```

Creates a criterion that can be thought of as a smooth version of the [`AbsCriterion`](#nn.AbsCriterion). It uses a squared term if the absolute element-wise error falls below 1. It is less sensitive to outliers than the [`MSECriterion`](#nn.MSECriterion) and in some cases prevents exploding gradients (e.g. see "Fast R-CNN" paper by Ross Girshick).

```lua
                      ⎧ 0.5 * (x_i - y_i)^2, if |x_i - y_i| < 1
loss(x, y) = 1/n \sum ⎨
                      ⎩ |x_i - y_i| - 0.5,   otherwise
```

If `x` and `y` are `d`-dimensional `Tensor`s with a total of `n` elements, the sum operation still operates over all the elements, and divides by `n`.

The division by `n` can be avoided if one sets the internal variable `sizeAverage` to `false`:

```lua
criterion = nn.SmoothL1Criterion()
criterion.sizeAverage = false
```

By default, the losses are averaged over observations for each minibatch. However, if the field `sizeAverage` is set to `false`, the losses are instead summed.


<a name="nn.HingeEmbeddingCriterion"></a>
## HingeEmbeddingCriterion ##

```lua
criterion = nn.HingeEmbeddingCriterion([margin])
```

Creates a criterion that measures the loss given an input `x` which is a 1-dimensional vector and a label `y` (`1` or `-1`).
This is usually used for measuring whether two inputs are similar or dissimilar, e.g. using the L1 pairwise distance, and is typically used for learning nonlinear embeddings or semi-supervised learning.

```lua
                 ⎧ x_i,                  if y_i ==  1
loss(x, y) = 1/n ⎨
                 ⎩ max(0, margin - x_i), if y_i == -1
```

If `x` and `y` are `n`-dimensional `Tensor`s, the sum operation still operates over all the elements, and divides by `n` (this can be avoided if one sets the internal variable `sizeAverage` to `false`). The `margin` has a default value of `1`, or can be set in the constructor.

### Example

```lua
-- imagine we have one network we are interested in, it is called "p1_mlp"
p1_mlp = nn.Sequential(); p1_mlp:add(nn.Linear(5, 2))

-- But we want to push examples towards or away from each other so we make another copy
-- of it called p2_mlp; this *shares* the same weights via the set command, but has its
-- own set of temporary gradient storage that's why we create it again (so that the gradients
-- of the pair don't wipe each other)
p2_mlp = nn.Sequential(); p2_mlp:add(nn.Linear(5, 2))
p2_mlp:get(1).weight:set(p1_mlp:get(1).weight)
p2_mlp:get(1).bias:set(p1_mlp:get(1).bias)

-- we make a parallel table that takes a pair of examples as input.
-- They both go through the same (cloned) mlp
prl = nn.ParallelTable()
prl:add(p1_mlp)
prl:add(p2_mlp)

-- now we define our top level network that takes this parallel table
-- and computes the pairwise distance betweem the pair of outputs
mlp = nn.Sequential()
mlp:add(prl)
mlp:add(nn.PairwiseDistance(1))

-- and a criterion for pushing together or pulling apart pairs
crit = nn.HingeEmbeddingCriterion(1)

-- lets make two example vectors
x = torch.rand(5)
y = torch.rand(5)


-- Use a typical generic gradient update function
function gradUpdate(mlp, x, y, criterion, learningRate)
local pred = mlp:forward(x)
local err = criterion:forward(pred, y)
local gradCriterion = criterion:backward(pred, y)
mlp:zeroGradParameters()
mlp:backward(x, gradCriterion)
mlp:updateParameters(learningRate)
end

-- push the pair x and y together, notice how then the distance between them given
-- by print(mlp:forward({x, y})[1]) gets smaller
for i = 1, 10 do
   gradUpdate(mlp, {x, y}, 1, crit, 0.01)
   print(mlp:forward({x, y})[1])
end

-- pull apart the pair x and y, notice how then the distance between them given
-- by print(mlp:forward({x, y})[1]) gets larger

for i = 1, 10 do
   gradUpdate(mlp, {x, y}, -1, crit, 0.01)
   print(mlp:forward({x, y})[1])
end
```

By default, the losses are averaged over observations for each minibatch. However, if the field `sizeAverage` is set to `false`, the losses are instead summed.


<a name="nn.L1HingeEmbeddingCriterion"></a>
## L1HingeEmbeddingCriterion ##

```lua
criterion = nn.L1HingeEmbeddingCriterion([margin])
```

Creates a criterion that measures the loss given  an input `x` = `{x1, x2}`, a table of two `Tensor`s, and a label `y` (`1` or `-1`): this is used for measuring whether two inputs are similar or dissimilar, using the L1 distance, and is typically used for learning nonlinear embeddings or semi-supervised learning.

```lua
             ⎧ ||x1 - x2||_1,                  if y ==  1
loss(x, y) = ⎨
             ⎩ max(0, margin - ||x1 - x2||_1), if y == -1
```

The `margin` has a default value of `1`, or can be set in the constructor.

<a name="nn.CosineEmbeddingCriterion"></a>
## CosineEmbeddingCriterion ##

```lua
criterion = nn.CosineEmbeddingCriterion([margin])
```

Creates a criterion that measures the loss given  an input `x` = `{x1, x2}`, a table of two `Tensor`s, and a `Tensor` label `y`  with values 1 or -1.
This is used for measuring whether two inputs are similar or dissimilar, using the cosine distance, and is typically used for learning nonlinear embeddings or semi-supervised learning.

`margin` should be a number from `-1` to `1`, `0` to `0.5` is suggested.
`Forward` and `Backward` have to be used alternately. If `margin` is missing, the default value is `0`.

The loss function for each sample is:

```lua
             ⎧ 1 - cos(x1, x2),              if y ==  1
loss(x, y) = ⎨
             ⎩ max(0, cos(x1, x2) - margin), if y == -1
```

For batched inputs, if the internal variable `sizeAverage` is equal to `true`, the loss function averages the loss over the batch samples; if `sizeAverage` is `false`, then the loss function sums over the batch samples. By default, `sizeAverage` equals to `true`.

By default, the losses are averaged over observations for each minibatch. However, if the field `sizeAverage` is set to `false`, the losses are instead summed.

<a name="nn.DistanceRatioCriterion"></a>
## DistanceRatioCriterion ##
Ref A. [Unsupervised Learning through Spatial Contrasting](https://arxiv.org/pdf/1610.00243.pdf)

```lua
criterion = nn.DistanceRatioCriterion(sizeAverage)
```

This criterion is probabilistic treatment of margin cost. The model is trained using sample triplets `{Xs, Xa, Xd}` where `Xa` is anchor sample, `Xs` is sample similar to anchor sample and `Xd` is a sample not similar to anchor sample. Let `Ds` be distance between embeddings of `{Xs, Xa}` and `Dd` be distance between embeddings of `{Xa, Xd}` then the loss is defined as follow

```lua
   loss = -log( exp(-Ds) / ( exp(-Ds) + exp(-Dd) ) )
```

Sample example
```lua
   torch.setdefaulttensortype("torch.FloatTensor")

   require 'nn'

   -- triplet : with batchSize of 32 and dimensionality 512
   sample = {torch.rand(32, 512), torch.rand(32, 512), torch.rand(32, 512)}

   embeddingModel = nn.Sequential()
   embeddingModel:add(nn.Linear(512, 96)):add(nn.ReLU())

   tripleModel = nn.ParallelTable()
   tripleModel:add(embeddingModel)
   tripleModel:add(embeddingModel:clone('weight', 'bias',
                                        'gradWeight', 'gradBias'))
   tripleModel:add(embeddingModel:clone('weight', 'bias',
                                        'gradWeight', 'gradBias'))

   -- Similar sample distance w.r.t anchor sample
   posDistModel = nn.Sequential()
   posDistModel:add(nn.NarrowTable(1,2)):add(nn.PairwiseDistance())

   -- Different sample distance w.r.t anchor sample
   negDistModel = nn.Sequential()
   negDistModel:add(nn.NarrowTable(2,2)):add(nn.PairwiseDistance())

   distanceModel = nn.ConcatTable():add(posDistModel):add(negDistModel)

   -- Complete Model
   model = nn.Sequential():add(tripleModel):add(distanceModel)

   -- DistanceRatioCriterion
   criterion = nn.DistanceRatioCriterion(true)

   -- Forward & Backward
   output = model:forward(sample)
   loss   = criterion:forward(output)
   dLoss  = criterion:backward(output)
   model:backward(sample, dLoss)
```

<a name="nn.MarginRankingCriterion"></a>
## MarginRankingCriterion ##

```lua
criterion = nn.MarginRankingCriterion(margin)
```

Creates a criterion that measures the loss given  an input `x` = `{x1, x2}`, a table of two `Tensor`s of size 1 (they contain only scalars), and a label `y` (`1` or `-1`).
In batch mode, `x` is a table of two `Tensor`s of size `batchsize`, and `y` is a `Tensor` of size `batchsize` containing `1` or `-1` for each corresponding pair of elements in the input `Tensor`.

If `y == 1` then it assumed the first input should be ranked higher (have a larger value) than the second input, and vice-versa for `y == -1`.

The loss function is:

```lua
loss(x, y) = max(0, -y * (x[1] - x[2]) + margin)
```

For batched inputs, if the internal variable `sizeAverage` is equal to `true`, the loss function averages the loss over the batch samples; if `sizeAverage` is `false`, then the loss function sums over the batch samples. By default, `sizeAverage` equals to `true`.
By default, the losses are averaged over observations for each minibatch. However, if the field `sizeAverage` is set to `false`, the losses are instead summed.

### Example

```lua
p1_mlp = nn.Linear(5, 2)
p2_mlp = p1_mlp:clone('weight', 'bias')

prl = nn.ParallelTable()
prl:add(p1_mlp)
prl:add(p2_mlp)

mlp1 = nn.Sequential()
mlp1:add(prl)
mlp1:add(nn.DotProduct())

mlp2 = mlp1:clone('weight', 'bias')

mlpa = nn.Sequential()
prla = nn.ParallelTable()
prla:add(mlp1)
prla:add(mlp2)
mlpa:add(prla)

crit = nn.MarginRankingCriterion(0.1)

x=torch.randn(5)
y=torch.randn(5)
z=torch.randn(5)

-- Use a typical generic gradient update function
function gradUpdate(mlp, x, y, criterion, learningRate)
   local pred = mlp:forward(x)
   local err = criterion:forward(pred, y)
   local gradCriterion = criterion:backward(pred, y)
   mlp:zeroGradParameters()
   mlp:backward(x, gradCriterion)
   mlp:updateParameters(learningRate)
end

for i = 1, 100 do
   gradUpdate(mlpa, {{x, y}, {x, z}}, 1, crit, 0.01)
   if true then
      o1 = mlp1:forward{x, y}[1]
      o2 = mlp2:forward{x, z}[1]
      o = crit:forward(mlpa:forward{{x, y}, {x, z}}, 1)
      print(o1, o2, o)
   end
end

print "--"

for i = 1, 100 do
   gradUpdate(mlpa, {{x, y}, {x, z}}, -1, crit, 0.01)
   if true then
      o1 = mlp1:forward{x, y}[1]
      o2 = mlp2:forward{x, z}[1]
      o = crit:forward(mlpa:forward{{x, y}, {x, z}}, -1)
      print(o1, o2, o)
   end
end
```

<a name='nn.ModuleCriterion'></a>
## ModuleCriterion ##

```lua
criterion = nn.ModuleCriterion(criterion [, inputModule, targetModule, castTarget])
```

This criterion decorates a `criterion` by allowing the `input` and `target` to be
fed through an optional `inputModule` and `targetModule` before being passed to the
`criterion`. The `inputModule` must not contain parameters as these would not be updated.

When `castTarget = true` (the default), the `targetModule` is cast along with the `inputModule` and
`criterion`. Otherwise, the `targetModule` isn't.