Frame Theoretical Derivation of Three Factor Learning Rule for Oja's Subspace Rule
This provides a principled derivation for a biologically plausible learning rule, which is incremental as it builds on existing mathematical frameworks.
The paper tackled the problem of deriving a biologically plausible three-factor learning rule from Oja's subspace rule for PCA, showing that the error-gated Hebbian rule (EGHR-PCA) can be systematically derived using frame theory, with the third factor emerging as a frame coefficient.
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.