A Theoretical Framework for Target Propagation

TL;DR

This paper provides a theoretical analysis of target propagation, relating it to Gauss-Newton optimization, and introduces a novel reconstruction loss to address its limitations, supported by experimental validation.

Contribution

It offers the first theoretical framework for target propagation, identifies its limitations, and proposes a new method with architectural flexibility and improved performance.

Findings

Target propagation is related to Gauss-Newton optimization.

Difference target propagation has fundamental limitations in non-invertible networks.

The proposed reconstruction loss improves feedback training and network performance.

Abstract

The success of deep learning, a brain-inspired form of AI, has sparked interest in understanding how the brain could similarly learn across multiple layers of neurons. However, the majority of biologically-plausible learning algorithms have not yet reached the performance of backpropagation (BP), nor are they built on strong theoretical foundations. Here, we analyze target propagation (TP), a popular but not yet fully understood alternative to BP, from the standpoint of mathematical optimization. Our theory shows that TP is closely related to Gauss-Newton optimization and thus substantially differs from BP. Furthermore, our analysis reveals a fundamental limitation of difference target propagation (DTP), a well-known variant of TP, in the realistic scenario of non-invertible neural networks. We provide a first solution to this problem through a novel reconstruction loss that improves feedback weight training, while simultaneously introducing architectural flexibility by allowing for direct feedback connections from the output to each hidden layer. Our theory is corroborated by experimental results that show significant improvements in performance and in the alignment of forward weight updates with loss gradients, compared to DTP.