The negative log likelihood loss. It is useful to train a classification problem with C classes.

## Usage

nn_nll_loss(weight = NULL, ignore_index = -100, reduction = "mean")

## Arguments

weight

(Tensor, optional): a manual rescaling weight given to each class. If given, it has to be a Tensor of size C. Otherwise, it is treated as if having all ones.

ignore_index

(int, optional): Specifies a target value that is ignored and does not contribute to the input gradient.

reduction

(string, optional): Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the weighted mean of the output is taken, 'sum': the output will be summed.

## Details

If provided, the optional argument weight 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 call is expected to contain log-probabilities of each class. input has to be a Tensor of size either $$(minibatch, C)$$ or $$(minibatch, C, d_1, d_2, ..., d_K)$$ with $$K \geq 1$$ for the K-dimensional case (described later).

Obtaining log-probabilities in a neural network is easily achieved by adding a LogSoftmax layer in the last layer of your network.

You may use CrossEntropyLoss instead, if you prefer not to add an extra layer.

The target that this loss expects should be a class index in the range $$[0, C-1]$$ where C = number of classes; if ignore_index is specified, this loss also accepts this class index (this index may not necessarily be in the class range).

The unreduced (i.e. with reduction set to 'none') loss can be described as:

$$\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = - w_{y_n} x_{n,y_n}, \quad w_{c} = \mbox{weight}[c] \cdot \mbox{1}\{c \not= \mbox{ignore\_index}\},$$

where $$x$$ is the input, $$y$$ is the target, $$w$$ is the weight, and $$N$$ is the batch size. If reduction is not 'none' (default 'mean'), then

$$\ell(x, y) = \begin{array}{ll} \sum_{n=1}^N \frac{1}{\sum_{n=1}^N w_{y_n}} l_n, & \mbox{if reduction} = \mbox{'mean';}\\ \sum_{n=1}^N l_n, & \mbox{if reduction} = \mbox{'sum'.} \end{array}$$

Can also be used for higher dimension inputs, such as 2D images, by providing an input of size $$(minibatch, C, d_1, d_2, ..., d_K)$$ with $$K \geq 1$$, where $$K$$ is the number of dimensions, and a target of appropriate shape (see below). In the case of images, it computes NLL loss per-pixel.

## Shape

• Input: $$(N, C)$$ where C = number of classes, or $$(N, C, d_1, d_2, ..., d_K)$$ with $$K \geq 1$$ in the case of K-dimensional loss.

• Target: $$(N)$$ where each value is $$0 \leq \mbox{targets}[i] \leq C-1$$, or $$(N, d_1, d_2, ..., d_K)$$ with $$K \geq 1$$ in the case of K-dimensional loss.

• Output: scalar.

If reduction is 'none', then the same size as the target: $$(N)$$, or $$(N, d_1, d_2, ..., d_K)$$ with $$K \geq 1$$ in the case of K-dimensional loss.

## Examples

if (torch_is_installed()) {
m <- nn_log_softmax(dim = 2)
loss <- nn_nll_loss()
# input is of size N x C = 3 x 5
input <- torch_randn(3, 5, requires_grad = TRUE)
# each element in target has to have 0 <= value < C
target <- torch_tensor(c(2, 1, 5), dtype = torch_long())
output <- loss(m(input), target)
output$backward() # 2D loss example (used, for example, with image inputs) N <- 5 C <- 4 loss <- nn_nll_loss() # input is of size N x C x height x width data <- torch_randn(N, 16, 10, 10) conv <- nn_conv2d(16, C, c(3, 3)) m <- nn_log_softmax(dim = 1) # each element in target has to have 0 <= value < C target <- torch_empty(N, 8, 8, dtype = torch_long())$random_(1, C)
output <- loss(m(conv(data)), target)
output\$backward()
}