Tucker Attention: A generalization of approximate attention mechanisms

TL;DR

Tucker Attention introduces a generalized, parameter-efficient self-attention mechanism that encompasses existing methods like GQA, MLA, and MHA, offering comparable performance with fewer parameters.

Contribution

The paper proposes Tucker Attention, a unified framework that generalizes and simplifies existing low-rank attention methods, improving efficiency and interpretability.

Findings

Tucker Attention requires an order of magnitude fewer parameters than GQA and MLA.

It achieves comparable validation metrics in LLM and ViT tests.

Encompasses GQA, MLA, MHA as special cases and is compatible with flash-attention and RoPE.

Abstract

The pursuit of reducing the memory footprint of the self-attention mechanism in multi-headed self attention (MHA) spawned a rich portfolio of methods, e.g., group-query attention (GQA) and multi-head latent attention (MLA). The methods leverage specialized low-rank factorizations across embedding dimensions or attention heads. From the point of view of classical low-rank approximation, these methods are unconventional and raise questions of which objects they really approximate and how to interpret the low-rank behavior of the resulting representations. To answer these questions, this work proposes a generalized view on the weight objects in the self-attention layer and a factorization strategy, which allows us to construct a parameter efficient scheme, called Tucker Attention. Tucker Attention requires an order of magnitude fewer parameters for comparable validation metrics, compared to GQA and MLA, as evaluated in LLM and ViT test cases. Additionally, Tucker Attention~encompasses GQA, MLA, MHA as special cases and is fully compatible with flash-attention and rotary position embeddings (RoPE). This generalization strategy yields insights of the actual ranks achieved by MHA, GQA, and MLA, and further enables simplifications for MLA.