ReduceKernel

Forward entry point: run the reduction and wire the backward node.

Normalises axes_user (negative indices → positive, dedup), computes the output shape (respecting keepdims), enforces CPU contiguity, dispatches to the most specific kernel hook the Derived class exposes, and — when GradMode is enabled and the input requires grad — constructs the backward node with the extra reduction state (reduce_axes_, keepdims_, full_input_shape_) populated.

Storage-mode backward: delegate the full broadcast-and-scale to Derived::grad_formula.

Unlike UnaryKernel::apply, this method performs no reduce_grad_to_shape step — the reduction kernel's grad_formula is responsible for broadcasting the upstream gradient back to full_input_shape_ using the saved reduce_axes_ and keepdims_ fields, and for any reduction-specific scaling.

Graph-mode backward: rebuild the broadcast in tracked ops.

Re-inserts size-1 axes for any dims that were dropped because keepdims=False, runs broadcast_to_op to expand the gradient back to full_input_shape_, then defers to scale_graph_grad for the reduction-specific factor. The entire chain participates in the autograd graph so higher-order gradients work correctly.

Schema-derived op name, exposed to the IKernel virtual interface for error messages and profiler scopes.

Schema-derived node name used by the autograd graph display and create_graph error reports.

Graph-mode gradient scaling hook.

Default implementation passes the gradient through unchanged, matching the sum rule (every reduced element contributed with unit weight). Derived classes whose rule has a non-trivial scale — MeanBackward divides by $N$, ProdBackward multiplies by $y / x$, the argmax variants apply an indicator mask — override this method to inject their factor before the gradient is returned.