Convergence Analysis and Implicit Regularization of Feedback Alignment for Deep Linear Networks

Manuela Girotti, Ioannis Mitliagkas, Gauthier Gidel

Keywords: feedback alignement, optimization, convergence guarantees, implicit regularization

Abstract: We theoretically analyze the Feedback Alignment (FA) algorithm, an efficient alternative to backpropagation for training neural networks. We provide convergence guarantees with rates for deep linear networks for both continuous and discrete dynamics. Additionally, we study incremental learning phenomena for shallow linear networks. Interestingly, certain specific initializations imply that negligible components are learned {before} the principal ones, thus potentially negatively affecting the effectiveness of such a learning algorithm; a phenomenon we classify as implicit anti-regularization. We also provide initialization schemes where the components of the problem are approximately learned by decreasing order of importance, thus providing a form of implicit regularization.

One-sentence Summary: we present convergence results for the Feedback Alignment algorithm and we analyze incremental learning phenomena