Dynamical Isometry and a Mean Field Theory of LSTMs and GRUs

TL;DR

This paper develops a mean field theory for LSTMs and GRUs to understand signal propagation, leading to a new initialization scheme that improves training stability and performance on long sequence tasks.

Contribution

The authors introduce a mean field theory for LSTMs and GRUs, deriving an initialization scheme that reduces training instabilities and enhances generalization.

Findings

New initialization scheme improves training stability on long sequences

Scheme enables successful training where standard methods fail

Observed better generalization with the proposed initialization

Abstract

Training recurrent neural networks (RNNs) on long sequence tasks is plagued with difficulties arising from the exponential explosion or vanishing of signals as they propagate forward or backward through the network. Many techniques have been proposed to ameliorate these issues, including various algorithmic and architectural modifications. Two of the most successful RNN architectures, the LSTM and the GRU, do exhibit modest improvements over vanilla RNN cells, but they still suffer from instabilities when trained on very long sequences. In this work, we develop a mean field theory of signal propagation in LSTMs and GRUs that enables us to calculate the time scales for signal propagation as well as the spectral properties of the state-to-state Jacobians. By optimizing these quantities in terms of the initialization hyperparameters, we derive a novel initialization scheme that eliminates or reduces training instabilities. We demonstrate the efficacy of our initialization scheme on multiple sequence tasks, on which it enables successful training while a standard initialization either fails completely or is orders of magnitude slower. We also observe a beneficial effect on generalization performance using this new initialization.