ProdBackward

Autograd node for the multi-axis reduction product $y = \prod_{i \in \text{axes}} x_i$.

The gradient is the "product of all other elements", which can be recovered cheaply from the saved output: $\partial y / \partial x_i = y / x_i$. Both the forward input ($x$) and the forward output ($y$) are saved so grad_formula can reconstruct the ratio without rerunning the reduction.

Because no single IBackend overload spans every Accelerate / MLX combination, prod provides explicit cpu_kernel and gpu_kernel overloads instead of a shared dispatch.

Math