Editing Openai/69371729-f090-8004-b69b-aa9f25ca0b40 (section)

=== Assistant: Short answer first: Correct. ===
Short answer first: Correct. Standard matrix multiplications used in (most) artificial neural networks (e.g., fully connected layers doing y=Wx+by = Wx+by=Wx+b and weight updates computed by backprop) are not Hebbian updates. Hebbian learning is a biologically-inspired local rule like “cells that fire together wire together” that directly updates weights using pre- and postsynaptic activity (no global error gradient required). Modern deep nets typically use global error signals and gradient descent rather than pure Hebbian updates — although Hebbian-like terms can be mixed into training.

Below I’ll (1) give the simplest mathematical Hebbian model, (2) show small stabilizing variants so weights don’t blow up, and (3) show simple, practical mechanisms to expand (grow) and delete (prune) connections (“abundancy control”). I’ll finish with a short worked numeric example and a compact algorithm you can implement.