Learning Long Term Dependencies via Fourier Recurrent Units

TL;DR

The paper introduces Fourier Recurrent Units (FRU), a novel RNN architecture that stabilizes gradients for long-term dependencies and outperforms existing models with fewer parameters.

Contribution

FRU uses Fourier basis functions to stabilize gradients and enhance expressive power, addressing long-term dependency challenges in RNNs.

Findings

FRU stabilizes gradients regardless of sequence length.

FRU outperforms other RNNs on multiple tasks.

FRU requires fewer parameters for better performance.

Abstract

It is a known fact that training recurrent neural networks for tasks that have long term dependencies is challenging. One of the main reasons is the vanishing or exploding gradient problem, which prevents gradient information from propagating to early layers. In this paper we propose a simple recurrent architecture, the Fourier Recurrent Unit (FRU), that stabilizes the gradients that arise in its training while giving us stronger expressive power. Specifically, FRU summarizes the hidden states $h^{(t)}$ along the temporal dimension with Fourier basis functions. This allows gradients to easily reach any layer due to FRU's residual learning structure and the global support of trigonometric functions. We show that FRU has gradient lower and upper bounds independent of temporal dimension. We also show the strong expressivity of sparse Fourier basis, from which FRU obtains its strong expressive power. Our experimental study also demonstrates that with fewer parameters the proposed architecture outperforms other recurrent architectures on many tasks.