Beyond exploding and vanishing gradients: analysing RNN training using attractors and smoothness

TL;DR

This paper refines the understanding of RNN training challenges by analyzing attractors and smoothness, offering new insights into gradient issues and recent advances like stable and orthogonal RNNs.

Contribution

It introduces a refined perspective on exploding and vanishing gradients by linking them to cost function smoothness and attractor dynamics, explaining recent RNN developments.

Findings

Reformulation of exploding gradients via cost function smoothness

Clarification of the role of attractors in RNN expressiveness

Insights into stable and orthogonal RNNs

Abstract

The exploding and vanishing gradient problem has been the major conceptual principle behind most architecture and training improvements in recurrent neural networks (RNNs) during the last decade. In this paper, we argue that this principle, while powerful, might need some refinement to explain recent developments. We refine the concept of exploding gradients by reformulating the problem in terms of the cost function smoothness, which gives insight into higher-order derivatives and the existence of regions with many close local minima. We also clarify the distinction between vanishing gradients and the need for the RNN to learn attractors to fully use its expressive power. Through the lens of these refinements, we shed new light on recent developments in the RNN field, namely stable RNN and unitary (or orthogonal) RNNs.