267. Backprop: Tanh (PyTorch)

Easy

Implement tanh as a torch.autograd.Function. Forward: y = tanh(x). Backward: dy/dx = 1 - y^2.

The rule: you may NOT call torch.tanh, x.tanh(), or nn.Tanh. Build the forward from .exp() and basic arithmetic.

Implement TanhFunction and the driver dispatches on 'forward' | 'grad_x' | 'gradcheck'. Save the output y for the backward.

Math

tanh (x) = \frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}}, tanh^{'} (x) = 1 - tanh^{2} (x)