Adaptive Initial Residual Connections for GNNs with Theoretical Guarantees

TL;DR

This paper introduces an adaptive residual connection scheme for GNNs that maintains embedding quality in deep networks, backed by theoretical guarantees and superior empirical performance, especially on heterophilic graphs.

Contribution

It provides the first theoretical analysis of adaptive residuals in GNNs, demonstrating their effectiveness in preventing oversmoothing and improving performance.

Findings

Adaptive residuals prevent oversmoothing in deep GNNs.

Theoretical guarantees for both adaptive and static residuals.

Heuristic residual strengths perform comparably to learned ones.

Abstract

Message passing is the core operation in graph neural networks, where each node updates its embeddings by aggregating information from its neighbors. However, in deep architectures, this process often leads to diminished expressiveness. A popular solution is to use residual connections, where the input from the current (or initial) layer is added to aggregated neighbor information to preserve embeddings across layers. Following a recent line of research, we investigate an adaptive residual scheme in which different nodes have varying residual strengths. We prove that this approach prevents oversmoothing; particularly, we show that the Dirichlet energy of the embeddings remains bounded away from zero. This is the first theoretical guarantee not only for the adaptive setting, but also for static residual connections (where residual strengths are shared across nodes) with activation functions. Furthermore, extensive experiments show that this adaptive approach outperforms standard and state-of-the-art message passing mechanisms, especially on heterophilic graphs. To improve the time complexity of our approach, we introduce a variant in which residual strengths are not learned but instead set heuristically, a choice that performs as well as the learnable version.