backprop-delta-recursive-computation

IN premise — entries/2026/06/21/wiki-Backpropagation-chunk-2.md

Created 2026-06-21T09:55:49+00:00

The key intermediate quantity delta^l (gradient of the weighted input at layer l) is computed recursively from delta^(l+1) via δ^(l-1) = (f^(l-1))' ∘ (W^l)^T · δ^l, and is sufficient to compute all weight gradients at that layer.

Dependents

These beliefs depend on this one:

• IN backprop-efficient-recursive-gradient-factorization — Backpropagation's computational efficiency stems from a recursive factored structure: the error signal delta propagates backward layer-by-layer via matrix-vector products, each weight gradient factors into a compact o_i * delta_j form, and the full weight gradient is a simple outer product of local quantities — avoiding redundant computation entirely.