Lipschitz Normalization for Self-Attention Layers with Application to Graph Neural Networks

TL;DR

This paper introduces LipschitzNorm, a normalization technique for self-attention layers that enforces Lipschitz continuity, significantly improving the performance of deep graph neural networks by preventing gradient explosion and enabling deeper architectures.

Contribution

The paper proposes LipschitzNorm, a simple, parameter-free normalization method for self-attention modules, enhancing deep graph neural network training and performance.

Findings

LipschitzNorm improves deep GAT and Graph Transformer performance.

Deep GAT with LipschitzNorm achieves state-of-the-art results.

Normalization prevents gradient explosion in deep attention models.

Abstract

Attention based neural networks are state of the art in a large range of applications. However, their performance tends to degrade when the number of layers increases. In this work, we show that enforcing Lipschitz continuity by normalizing the attention scores can significantly improve the performance of deep attention models. First, we show that, for deep graph attention networks (GAT), gradient explosion appears during training, leading to poor performance of gradient-based training algorithms. To address this issue, we derive a theoretical analysis of the Lipschitz continuity of attention modules and introduce LipschitzNorm, a simple and parameter-free normalization for self-attention mechanisms that enforces the model to be Lipschitz continuous. We then apply LipschitzNorm to GAT and Graph Transformers and show that their performance is substantially improved in the deep setting (10 to 30 layers). More specifically, we show that a deep GAT model with LipschitzNorm achieves state of the art results for node label prediction tasks that exhibit long-range dependencies, while showing consistent improvements over their unnormalized counterparts in benchmark node classification tasks.