发表机构
Carnegie Mellon University; UC Berkeley; Cornell University（卡内基梅隆大学; 加州大学伯克利分校; 康奈尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
HOPPER是LGSM的可学习扩展，可提取跳序列以实现自适应图传播，在ECHO-Synth基准表现最优或具竞争力，调整结构记忆窗口可优化LRIM基准准确率，为长距离图表示学习提供灵活方法。
AI 中文摘要
图神经网络通常通过重复的消息传递层传播信息，这使得信息传播的距离与应用的非线性变换次数相关联。这种关联会导致深度架构难以优化，还会引发过平滑、过挤压以及长距离信息丢失等问题。线性化图序列模型（LGSM）通过将信息深度与处理深度分离，并将每个节点的连续传播状态视为序列，来解决上述问题。不过，现有的LGSM使用固定图算子构建这些序列，限制了其根据输入图、节点特征和下游任务调整传播的能力。我们提出HOPPER，这是LGSM的端到端可学习扩展，可在现代状态空间模型处理前学习如何提取跳序列。我们的框架支持特征条件化、结构感知、图和跳自适应的传播机制，同时保持置换等变性。标准基于邻接和非回溯的LGSM序列是我们提出的提取器族的特例。我们在ECHO-Synth基准测试中表明，HOPPER达到了当前最优或具有竞争力的性能；改变消息回溯取消的最大邻域大小（即结构记忆窗口）可优化基于物理的长距离依赖基准LRIM的准确率。这些结果证明，可学习序列提取为长距离图表示学习提供了灵活且有效的方法。
英文摘要
Graph neural networks typically propagate information through repeated message-passing layers, coupling propagation distance with the number of nonlinear transformations applied. This coupling can make deep architectures difficult to optimize and lead to over-smoothing, over-squashing, and loss of long-range information. Linearized Graph Sequence Models (LGSMs) address this issue by separating propagation depth from processing depth and representing successive propagation states of each node as a sequence. However, existing LGSMs construct these sequences using fixed graph operators, limiting their ability to adapt propagation to the input graph, node features, and downstream task. We introduce HOPPER, an end-to-end learnable extension of LGSM that learns how hop sequences should be extracted before processing by a modern state-space model. HOPPER supports feature-conditioned, structure-aware, graph and hop-adaptive propagation while preserving permutation equivariance, with standard adjacency-based and non-backtracking LGSM sequences arising as special cases of the extractor family. HOPPER is state-of-the-art or competitive across ECHO-Synth and performs strongly on City-Networks. On the LRIM physics-based long-range dependency benchmark, varying the maximum neighborhood size used for message-backtracking cancellation, corresponding to the structural memory window, substantially affects performance. Ablations further isolate the contributions of the learnable extraction mechanism and its structural and feature-adaptive components, showing that adaptive hop-sequence construction provides gains beyond the downstream sequence model alone. Together, these results demonstrate that learnable sequence extraction is a flexible and effective framework for long-range graph representation learning across synthetic, physics-based and real-world graph benchmarks.
Comments26 pages, 4 figures, 7 tables
