Lipschitz Recurrent Neural Networks

TL;DR

This paper introduces Lipschitz RNNs, a new recurrent unit with stability guarantees and improved robustness, outperforming existing units across various benchmark tasks in vision, language, and speech domains.

Contribution

It proposes a Lipschitz continuous recurrent unit with stability analysis, a novel hidden-to-hidden matrix construction, and demonstrates superior performance and robustness.

Findings

Outperforms existing RNNs on benchmark tasks

Provides stability conditions for recurrent units

Shows increased robustness to perturbations

Abstract

Viewing recurrent neural networks (RNNs) as continuous-time dynamical systems, we propose a recurrent unit that describes the hidden state's evolution with two parts: a well-understood linear component plus a Lipschitz nonlinearity. This particular functional form facilitates stability analysis of the long-term behavior of the recurrent unit using tools from nonlinear systems theory. In turn, this enables architectural design decisions before experimentation. Sufficient conditions for global stability of the recurrent unit are obtained, motivating a novel scheme for constructing hidden-to-hidden matrices. Our experiments demonstrate that the Lipschitz RNN can outperform existing recurrent units on a range of benchmark tasks, including computer vision, language modeling and speech prediction tasks. Finally, through Hessian-based analysis we demonstrate that our Lipschitz recurrent unit is more robust with respect to input and parameter perturbations as compared to other continuous-time RNNs.