This loss combines a Sigmoid layer and the BCELoss in one single class. This version is more numerically stable than using a plain Sigmoid followed by a BCELoss as, by combining the operations into one layer, we take advantage of the log-sum-exp trick for numerical stability.

## Usage

nn_bce_with_logits_loss(weight = NULL, reduction = "mean", pos_weight = NULL)

## Arguments

weight

(Tensor, optional): a manual rescaling weight given to the loss of each batch element. If given, has to be a Tensor of size nbatch.

reduction

(string, optional): Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed.

pos_weight

(Tensor, optional): a weight of positive examples. Must be a vector with length equal to the number of classes.

## Details

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

$$\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = - w_n \left[ y_n \cdot \log \sigma(x_n) + (1 - y_n) \cdot \log (1 - \sigma(x_n)) \right],$$

where $$N$$ is the batch size. If reduction is not 'none' (default 'mean'), then

$$\ell(x, y) = \begin{array}{ll} \mbox{mean}(L), & \mbox{if reduction} = \mbox{'mean';}\\ \mbox{sum}(L), & \mbox{if reduction} = \mbox{'sum'.} \end{array}$$

This is used for measuring the error of a reconstruction in for example an auto-encoder. Note that the targets t[i] should be numbers between 0 and 1. It's possible to trade off recall and precision by adding weights to positive examples. In the case of multi-label classification the loss can be described as:

$$\ell_c(x, y) = L_c = \{l_{1,c},\dots,l_{N,c}\}^\top, \quad l_{n,c} = - w_{n,c} \left[ p_c y_{n,c} \cdot \log \sigma(x_{n,c}) + (1 - y_{n,c}) \cdot \log (1 - \sigma(x_{n,c})) \right],$$ where $$c$$ is the class number ($$c > 1$$ for multi-label binary classification,

$$c = 1$$ for single-label binary classification), $$n$$ is the number of the sample in the batch and $$p_c$$ is the weight of the positive answer for the class $$c$$. $$p_c > 1$$ increases the recall, $$p_c < 1$$ increases the precision. For example, if a dataset contains 100 positive and 300 negative examples of a single class, then pos_weight for the class should be equal to $$\frac{300}{100}=3$$. The loss would act as if the dataset contains $$3\times 100=300$$ positive examples.

## Shape

• Input: $$(N, *)$$ where $$*$$ means, any number of additional dimensions

• Target: $$(N, *)$$, same shape as the input

• Output: scalar. If reduction is 'none', then $$(N, *)$$, same shape as input.

## Examples

if (torch_is_installed()) {
loss <- nn_bce_with_logits_loss()
input <- torch_randn(3, requires_grad = TRUE)
target <- torch_empty(3)$random_(1, 2) output <- loss(input, target) output$backward()

target <- torch_ones(10, 64, dtype = torch_float32()) # 64 classes, batch size = 10
output <- torch_full(c(10, 64), 1.5) # A prediction (logit)
pos_weight <- torch_ones(64) # All weights are equal to 1
criterion <- nn_bce_with_logits_loss(pos_weight = pos_weight)
criterion(output, target) # -log(sigmoid(1.5))
}
#> torch_tensor
#> 0.201413
#> [ CPUFloatType{} ]