用量子力学观测量解析图神经网络信号传播，提出更优的路由模型。
Beyond Oversquashing: Understanding Signal Propagation in GNNs Via Observables
- 引入量子力学中的可观测量建模信号位置与集中度
- 证明传统谱图神经网络信号路由能力差
- 提出Schrödinger GNN，提升跨图区域信号传递效率
图神经网络（GNN）通过图移位算子或消息传递机制在图结构中传递信号。但信号传播常导致信息损失，表现为信号在图上过度扩散而非有目的地在感兴趣区域间传递。现有理论中的过平滑与过挤压现象描述了这一问题。本文受量子力学启发，提出用可观测量刻画信号在图中的位置、集中程度及向目标位置的传播量。基于此，我们证明标准谱图神经网络存在信号传播能力不足的问题。进一步提出新型谱图神经网络——Schrödinger GNN，实证其具备更强的跨图区域信号路由能力。
原文摘要 · Abstract (English)
Graph Neural Networks (GNNs) perform computations on graphs by routing the signal between graph regions using a graph shift operator or a message passing scheme. Often, the propagation of the signal leads to a loss of information, where the signal tends to diffuse across the graph instead of being deliberately routed between regions of interest. Two notions that depict this phenomenon are oversmoothing and oversquashing. In this paper, we propose an alternative approach for modeling signal propagation, inspired by quantum mechanics, using the notion of observables. Specifically, we model the place in the graph where the signal lies, how much the signal is concentrated there, and how much of the signal is propagated towards a location of interest when applying a GNN. Using these new concepts, we prove that standard spectral GNNs have poor signal propagation capabilities. We then propose a new type of spectral GNN, termed Schrödinger GNN, which we show has a superior capacity to route the signal across the graph.
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