Spectral Conditioning of Attention Improves Transformer Performance

TL;DR

This paper introduces a spectral conditioning method for attention in transformers, improving their Jacobian properties and overall performance across various architectures and tasks.

Contribution

It provides a theoretical analysis of attention Jacobians and proposes a spectral adjustment technique to enhance transformer training stability and effectiveness.

Findings

Improved Jacobian conditioning leads to better transformer performance.

Spectral conditioning is broadly applicable as a drop-in replacement.

Consistent performance gains across multiple tasks and architectures.

Abstract

We present a theoretical analysis of the Jacobian of an attention block within a transformer, showing that it is governed by the query, key, and value projections that define the attention mechanism. Leveraging this insight, we introduce a method that systematically alters the spectral properties of each attention layer to reduce the Jacobian's condition number, thereby improving the overall conditioning of the attention layers within a transformer network. We empirically show that this improved Jacobian conditioning translates to enhanced performance in practice. Our approach is simple, broadly applicable, and can be easily integrated as a drop-in replacement for a wide range of existing attention mechanisms. We validate its effectiveness across diverse transformer architectures and tasks, demonstrating consistent improvements in performance.