Adaptive Initial Residual Connections for GNNs with Theoretical Guarantees
This addresses a key bottleneck in deep GNNs for graph learning tasks, offering theoretical guarantees and practical improvements, though it is incremental on existing residual connection research.
The paper tackles the problem of diminished expressiveness in deep graph neural networks by proposing an adaptive residual connection scheme with varying strengths per node, proving it prevents oversmoothing and showing it outperforms standard and state-of-the-art methods, especially on heterophilic graphs.
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.