Skyformer: Remodel Self-Attention with Gaussian Kernel and Nystr\"om Method

TL;DR

Skyformer introduces a novel self-attention approximation using Gaussian kernels and Nyström method, significantly reducing computational costs while maintaining or improving performance on long-range tasks.

Contribution

The paper proposes Skyformer, a new self-attention model that replaces softmax with Gaussian kernels and uses Nyström approximation for efficiency, with theoretical and empirical validation.

Findings

Achieves comparable or better performance than full self-attention.

Reduces computational resources needed for long-range tasks.

Provides theoretical bounds on approximation error.

Abstract

Transformers are expensive to train due to the quadratic time and space complexity in the self-attention mechanism. On the other hand, although kernel machines suffer from the same computation bottleneck in pairwise dot products, several approximation schemes have been successfully incorporated to considerably reduce their computational cost without sacrificing too much accuracy. In this work, we leverage the computation methods for kernel machines to alleviate the high computational cost and introduce Skyformer, which replaces the softmax structure with a Gaussian kernel to stabilize the model training and adapts the Nystr\"om method to a non-positive semidefinite matrix to accelerate the computation. We further conduct theoretical analysis by showing that the matrix approximation error of our proposed method is small in the spectral norm. Experiments on Long Range Arena benchmark show that the proposed method is sufficient in getting comparable or even better performance than the full self-attention while requiring fewer computation resources.