backprop-gradient-factors-to-oi-delta-j

IN premise — entries/2026/06/21/wiki-Backpropagation-chunk-4.md

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

The gradient ∂E/∂w_ij factors into the compact form o_i · δ_j, where o_i is the activation of the sending neuron and δ_j is the error signal at the receiving neuron.

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.