Lipschitz Normalization for Self-Attention Layers with Application to Graph Neural Networks
This addresses the problem of training instability in deep graph neural networks for researchers and practitioners, though it is incremental as it builds on existing attention mechanisms.
The authors tackled the performance degradation of deep attention models by enforcing Lipschitz continuity through a normalization method, resulting in state-of-the-art node label prediction and consistent improvements in benchmark tasks for models with 10 to 30 layers.
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.