Custom autograd Functions verified with gradcheck

Write a numerically stable log-sum-exp and a fused softmax cross-entropy as custom Functions, pass float64 gradcheck, and compare against built-in operators.

The exercise happens on Self-directed project (PyTorch documentation). Canonical link: https://docs.pytorch.org/docs/stable/notes/extending.html. Link check: link responded (5 Oct 2026). Opened from this app 0 times; opening is not counted as an attempt.

Supports: Gradient derivation and verification skills used in research code and take-home exercises.