Frame Theoretical Derivation of Three Factor Learning Rule for Oja's Subspace Rule

TL;DR

This paper derives a biologically plausible three-factor learning rule for PCA from Oja's subspace rule using frame theory, providing a principled mathematical foundation.

Contribution

It offers a systematic, non-heuristic derivation of EGHR-PCA from Oja's rule via frame theory, linking biologically plausible and canonical learning rules.

Findings

EGHR-PCA is equivalent to Oja's subspace rule under Gaussian inputs.

The global third factor in EGHR-PCA corresponds to a frame coefficient.

Provides a mathematically principled derivation of a biologically plausible learning rule.

Abstract

We show that the error-gated Hebbian rule for PCA (EGHR-PCA), a three-factor learning rule equivalent to Oja's subspace rule under Gaussian inputs, can be systematically derived from Oja's subspace rule using frame theory. The global third factor in EGHR-PCA arises exactly as a frame coefficient when the learning rule is expanded with respect to a natural frame on the space of symmetric matrices. This provides a principled, non-heuristic derivation of a biologically plausible learning rule from its mathematically canonical counterpart.