What Dense Graph Do You Need for Self-Attention?

TL;DR

This paper introduces a theoretical framework and a new sparse Transformer architecture that models token interactions using hypercube graphs, achieving comparable or better performance with significantly reduced complexity.

Contribution

It proposes the Normalized Information Payload (NIP) as a graph scoring function and develops the Hypercube Transformer, a sparse model with $O(N ext{log}N)$ complexity for sequence processing.

Findings

Hypercube Transformer achieves comparable or better results than vanilla Transformer.

The NIP function effectively guides the trade-off between performance and complexity.

The model performs well across tasks with various sequence lengths.

Abstract

Transformers have made progress in miscellaneous tasks, but suffer from quadratic computational and memory complexities. Recent works propose sparse Transformers with attention on sparse graphs to reduce complexity and remain strong performance. While effective, the crucial parts of how dense a graph needs to be to perform well are not fully explored. In this paper, we propose Normalized Information Payload (NIP), a graph scoring function measuring information transfer on graph, which provides an analysis tool for trade-offs between performance and complexity. Guided by this theoretical analysis, we present Hypercube Transformer, a sparse Transformer that models token interactions in a hypercube and shows comparable or even better results with vanilla Transformer while yielding $O(N\log N)$ complexity with sequence length $N$. Experiments on tasks requiring various sequence lengths lay validation for our graph function well.