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.

翻译：我们证明，主成分分析中的误差门控赫布规则（EGHR-PCA）——一种在高斯输入下等价于Oja子空间规则的三因子学习规则——可以利用框架理论从Oja子空间规则中系统地推导出来。EGHR-PCA中的全局第三因子恰好是在对称矩阵空间上以自然框架展开学习规则时产生的框架系数。这为从数学上的标准规则推导出生物学上合理的学习规则提供了原则性、非启发式的途径。