Target Propagation via Regularized Inversion

Vincent Roulet, Zaid Harchaoui

Keywords: Target propagation, differentiable programming, recurrent neural networks

Abstract: Target Propagation (TP) algorithms compute targets instead of gradients along neural networks and propagate them backward in a way that is similar yet different than gradient back-propagation (BP). The idea was first presented as a perturbative alternative to back-propagation that may achieve greater accuracy in gradient evaluation when training multi-layer neural networks (LeCun et al., 1989). However, TP has remained more of a template algorithm with many variations than a well-identified algorithm. Revisiting insights of LeCun et al., (1989) and more recently of Lee et al. (2015), we present a simple version of target propagation based on regularized inversion of network layers, easily implementable in a differentiable programming framework. We compare its computational complexity to the one of BP and delineate the regimes in which TP can be attractive compared to BP. We show how our TP can be used to train recurrent neural networks with long sequences on various sequence modeling problems. The experimental results underscore the importance of regularization in TP in practice.

One-sentence Summary: We implement target propagation for RNNs with the actual formulation of the inverse and not with a parameterized inverse; our experiments show the effectiveness of the approach and paves the way for a better understanding of the approach.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2112.01453/code)