Fading memory as inductive bias in residual recurrent networks

TL;DR

This paper explores how residual connections in recurrent neural networks influence their dynamics and fading memory, revealing that certain residual structures enhance expressivity and memory properties, especially near the edge of chaos.

Contribution

It introduces weakly coupled residual recurrent networks (WCRNNs) and demonstrates how specific residual connections improve network expressivity and memory by affecting dynamics and spectral properties.

Findings

Residual connections near the edge of chaos enhance expressivity.

Certain spectral properties of data are exploited by residual networks.

Heterogeneous memory properties emerge from specific residual structures.

Abstract

Residual connections have been proposed as an architecture-based inductive bias to mitigate the problem of exploding and vanishing gradients and increased task performance in both feed-forward and recurrent networks (RNNs) when trained with the backpropagation algorithm. Yet, little is known about how residual connections in RNNs influence their dynamics and fading memory properties. Here, we introduce weakly coupled residual recurrent networks (WCRNNs) in which residual connections result in well-defined Lyapunov exponents and allow for studying properties of fading memory. We investigate how the residual connections of WCRNNs influence their performance, network dynamics, and memory properties on a set of benchmark tasks. We show that several distinct forms of residual connections yield effective inductive biases that result in increased network expressivity. In particular, those are residual connections that (i) result in network dynamics at the proximity of the edge of chaos, (ii) allow networks to capitalize on characteristic spectral properties of the data, and (iii) result in heterogeneous memory properties. In addition, we demonstrate how our results can be extended to non-linear residuals and introduce a weakly coupled residual initialization scheme that can be used for Elman RNNs.