Reviving and Improving Recurrent Back-Propagation

TL;DR

This paper revisits the recurrent back-propagation algorithm, identifies stability issues, and proposes two variants that improve efficiency and memory usage, demonstrating their effectiveness across various neural network applications.

Contribution

The paper introduces two novel RBP variants, CG-RBP and Neumann-RBP, that enhance stability and reduce memory requirements in training recurrent neural networks.

Findings

Neumann-RBP matches TBPTT in time complexity but uses constant memory.

All RBP variants outperform traditional methods in efficiency and effectiveness.

Neumann-RBP is particularly suitable for large-scale recurrent network training.

Abstract

In this paper, we revisit the recurrent back-propagation (RBP) algorithm, discuss the conditions under which it applies as well as how to satisfy them in deep neural networks. We show that RBP can be unstable and propose two variants based on conjugate gradient on the normal equations (CG-RBP) and Neumann series (Neumann-RBP). We further investigate the relationship between Neumann-RBP and back propagation through time (BPTT) and its truncated version (TBPTT). Our Neumann-RBP has the same time complexity as TBPTT but only requires constant memory, whereas TBPTT's memory cost scales linearly with the number of truncation steps. We examine all RBP variants along with BPTT and TBPTT in three different application domains: associative memory with continuous Hopfield networks, document classification in citation networks using graph neural networks and hyperparameter optimization for fully connected networks. All experiments demonstrate that RBPs, especially the Neumann-RBP variant, are efficient and effective for optimizing convergent recurrent neural networks. Code is released at: \url{https://github.com/lrjconan/RBP}.