How Important is Weight Symmetry in Backpropagation?

TL;DR

This study investigates the necessity of weight symmetry in backpropagation, revealing that sign alignment and certain normalization techniques are crucial, and symmetric weights are not strictly required for effective learning.

Contribution

The paper demonstrates that weight symmetry is not essential for backpropagation, highlighting the importance of sign concordance and normalization methods for asymmetric feedback learning.

Findings

Feedback weight magnitudes do not affect performance.

Sign alignment between feedback and feedforward weights is crucial.

Asymmetric feedback with normalization can match or outperform symmetric backpropagation.

Abstract

Gradient backpropagation (BP) requires symmetric feedforward and feedback connections -- the same weights must be used for forward and backward passes. This "weight transport problem" (Grossberg 1987) is thought to be one of the main reasons to doubt BP's biologically plausibility. Using 15 different classification datasets, we systematically investigate to what extent BP really depends on weight symmetry. In a study that turned out to be surprisingly similar in spirit to Lillicrap et al.'s demonstration (Lillicrap et al. 2014) but orthogonal in its results, our experiments indicate that: (1) the magnitudes of feedback weights do not matter to performance (2) the signs of feedback weights do matter -- the more concordant signs between feedforward and their corresponding feedback connections, the better (3) with feedback weights having random magnitudes and 100% concordant signs, we were able to achieve the same or even better performance than SGD. (4) some normalizations/stabilizations are indispensable for such asymmetric BP to work, namely Batch Normalization (BN) (Ioffe and Szegedy 2015) and/or a "Batch Manhattan" (BM) update rule.