Archive notice

Deriving Backpropagation from Wave Equations

This short note is being retired as a stand-alone derivation and kept only as a path-preserving archive page.

Updated position. The stronger claim is no longer that wave reflection has already provided a general first-principles derivation of backpropagation. The live project is now framed more cautiously as a study of credit transport and physically plausible implementations of instructive signals.

Please read the revised materials instead:

Research overview
Main working note
Exploratory adjoint / transport note