Binary Cross-Entropy with Logits

Computing sigmoid then log loses precision and can produce log(0). The fused, stable form for logit $z$ and target $y$ is

\ell = \max(z, 0) - z y + \log(1 + e^{-|z|})

Implement bce_with_logits(z, y, pos_weight=1.0) returning the mean loss, where pos_weight multiplies the positive term (as in PyTorch): $\ell = -[w\,y\log\sigma(z) + (1-y)\log(1-\sigma(z))]$ . Also implement bce_with_logits_grad(z, y, pos_weight=1.0), the gradient of the mean loss with respect to z.