Limiting Over-Smoothing and Over-Squashing of Graph Message Passing by Deep Scattering Transforms

TL;DR

This paper introduces a Deep Scattering Message Passing neural network that uses spectral transformation to mitigate over-smoothing and over-squashing in graph neural networks, improving stability and accuracy.

Contribution

The paper presents a novel multi-layer DSMP model that leverages spectral transformation to address key issues in GNNs, with theoretical and empirical validation.

Findings

The DSMP model effectively reduces over-smoothing and over-squashing.

Spectral transformation enhances the stability and accuracy of graph signal processing.

Empirical results demonstrate superior performance over traditional GNNs.

Abstract

Graph neural networks (GNNs) have become pivotal tools for processing graph-structured data, leveraging the message passing scheme as their core mechanism. However, traditional GNNs often grapple with issues such as instability, over-smoothing, and over-squashing, which can degrade performance and create a trade-off dilemma. In this paper, we introduce a discriminatively trained, multi-layer Deep Scattering Message Passing (DSMP) neural network designed to overcome these challenges. By harnessing spectral transformation, the DSMP model aggregates neighboring nodes with global information, thereby enhancing the precision and accuracy of graph signal processing. We provide theoretical proofs demonstrating the DSMP's effectiveness in mitigating these issues under specific conditions. Additionally, we support our claims with empirical evidence and thorough frequency analysis, showcasing the DSMP's superior ability to address instability, over-smoothing, and over-squashing.