WavSpA: Wavelet Space Attention for Boosting Transformers' Long Sequence Learning Ability

TL;DR

WavSpA introduces a wavelet-based attention mechanism for Transformers, capturing both position and frequency information efficiently, leading to improved long sequence learning and reasoning extrapolation.

Contribution

The paper proposes Wavelet Space Attention (WavSpA), a novel method that replaces Fourier-based attention with wavelet transforms for better long-range sequence modeling in Transformers.

Findings

WavSpA outperforms Fourier-based methods on Long Range Arena tasks.

Learning in wavelet space enhances Transformer's reasoning over long distances.

Wavelet transforms improve efficiency by capturing multi-resolution features.

Abstract

Transformer and its variants are fundamental neural architectures in deep learning. Recent works show that learning attention in the Fourier space can improve the long sequence learning capability of Transformers. We argue that wavelet transform shall be a better choice because it captures both position and frequency information with linear time complexity. Therefore, in this paper, we systematically study the synergy between wavelet transform and Transformers. We propose Wavelet Space Attention (WavSpA) that facilitates attention learning in a learnable wavelet coefficient space which replaces the attention in Transformers by (1) applying forward wavelet transform to project the input sequences to multi-resolution bases, (2) conducting attention learning in the wavelet coefficient space, and (3) reconstructing the representation in input space via backward wavelet transform. Extensive experiments on the Long Range Arena demonstrate that learning attention in the wavelet space using either fixed or adaptive wavelets can consistently improve Transformer's performance and also significantly outperform learning in Fourier space. We further show our method can enhance Transformer's reasoning extrapolation capability over distance on the LEGO chain-of-reasoning task.