通过通用层方程统一图神经网络
Unifying Graph Neural Networks Through a Common Layer Equation
浏览论文内容
中文总结 AI 辅助
该研究提出通用层方程统一图神经网络，分解其组件以实现架构组织、比较与生成，关联传播特性与图神经网络问题，并揭示经验逆问题。
中文摘要 AI 辅助
图神经网络通常通过特定家族的方程来描述，其符号掩盖了共享计算和结构差异。我们提出一种通用层方程，它通过七个组件表示所覆盖的架构：更新域、通道集、传播库、逐通道消息映射、通道融合算子、自/残差映射和更新映射。核心分解将信息移动的位置（由传播库编码）与移动的内容（由消息映射编码）分开。函数值填充将同一方程扩展到局部消息传递、注意力、谱滤波、全局通信、特定关系通道、高阶域和几何消息。我们通过对七个非互斥架构家族的经典层和组件分配进行简化，明确并可验证地实现了这种统一。固定的槽位规范按计算角色分配操作，并定义了框架的覆盖边界。该分解还产生了组件级理论见解：在端点局部消息和节点局部更新下，算子支持界定了单层依赖关系，且在给定假设下，单层全局混合需要完整的有效算子行。所得框架在通用设计空间中组织了200多种架构，支持组件级比较和结构一致架构的生成，并将传播选择与过平滑、过压缩、异质性和表达能力联系起来。它还揭示了将可测量的图和任务属性映射到已验证组件选择的经验逆问题。
英文摘要
Graph neural networks are commonly described through family-specific equations whose notation obscures shared computations and structural differences. We introduce a common layer equation that represents covered architectures through seven components: an update domain, channel set, propagation bank, per-channel message maps, channel-fusion operator, ego/residual map, and update map. The central factorization separates where information moves, encoded by the propagation bank, from what moves, encoded by the message maps. Function-valued fillings extend the same equation across local message passing, attention, spectral filtering, global communication, relation-specific channels, higher-order domains, and geometric messages. We make this unification explicit and checkable through worked reductions of canonical layers and component assignments spanning seven nonexclusive architectural families. A fixed slot discipline assigns operations by computational role and defines the framework's coverage boundary. The decomposition also yields component-level theoretical insights: under endpoint-local messages and node-local updates, operator support bounds one-layer dependencies, and one-layer global mixing requires a full effective operator row under the stated hypotheses. The resulting framework organizes more than 200 architectures in a common design space, enables component-wise comparison and generation of structurally consistent architectures, and connects propagation choices to oversmoothing, oversquashing, heterophily, and expressivity. It further exposes the empirical inverse problem of mapping measurable graph and task properties to validated component choices.
