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:
Related reading
Theory mainline index — Return to the site hub and grouped directory.
- Backpropagation, Adjoint Fields, and Physical Transport Constraints — The revised long-form analysis separates legitimate adjoint-field results from the derivation this archive withdraws.
- Hebbian Appearance, Instructive Signals, and Physical Credit Transport — A narrower hypothesis reframes the old claim around physically transported instructive signals and local plasticity.
- Wave / Credit Transport Research Notes | Macheng Shen — An evidence-layered index shows where this retired route now belongs within the broader research branch.
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