Add Binary Cross Entropy With Logit Loss to nn crate (#1157)

* add bce with logit loss

* add bce with logit loss

* remove imports

* fix tiny bug

* add test documentation and refactor function

* fix test cases and formatting

candle-nn/src/loss.rs

@@ -48,3 +48,25 @@ pub fn cross_entropy(inp: &Tensor, target: &Tensor) -> Result<Tensor> {
 pub fn mse(inp: &Tensor, target: &Tensor) -> Result<Tensor> {
     (inp - target)?.sqr()?.mean_all()
 }
+
+/// The binary cross-entropy with logit loss.
+///
+/// Arguments
+///
+/// * [inp]: The input tensor of dimensions `N, C` where `N` is the batch size and `C` the number
+///          of categories. This is expected to raw logits.
+/// * [target]: The ground truth labels as a tensor of u32 of dimension `N, C` where `N` is the batch size and `C` the number
+///          of categories.
+///
+/// The resulting tensor is a scalar containing the average value over the batch.
+pub fn binary_cross_entropy_with_logit(inp: &Tensor, target: &Tensor) -> Result<Tensor> {
+    let inp = crate::ops::sigmoid(inp)?;
+
+    let left_side = target * inp.log()?;
+    let right_side = (target.affine(-1., 1.))? * inp.affine(-1., 1.)?.log()?;
+
+    let loss = left_side? + right_side?;
+    let loss = loss?.neg()?.mean_all()?;
+
+    Ok(loss)
+}