HOPPER: Learnable Hop Extraction for Linearized Graph Sequence Models

2026-08-09

AI Summary

Traditional graph neural networks suffer from over-smoothing, over-squashing, and loss of long-range dependencies due to the coupling of information propagation depth with nonlinear transformations. To address these limitations, this work proposes HOPPER, an end-to-end learnable linearized graph sequence modeling paradigm. HOPPER employs a learnable hop-count sequence extractor to adaptively construct structure-aware, feature-conditioned neighborhood sequences, which are then processed by a state space model. This framework subsumes fixed graph operators—such as adjacency-based and non-backtracking propagation—as special cases, preserves permutation equivariance, and substantially enhances long-range representational capacity. Experiments demonstrate that HOPPER achieves state-of-the-art performance on the ECHO-Synth benchmark and significantly improves accuracy on the LRIM physical reasoning task by dynamically adjusting its structural memory window.

Abstract

Graph neural networks typically propagate information through repeated message-passing layers, coupling the distance over which information travels with the number of nonlinear transformations applied. This coupling can make deep architectures difficult to optimize and can lead to over-smoothing, over-squashing, and the loss of long-range information. Linearized Graph Sequence Models (LGSMs) address this issue by separating information depth from processing depth and treating the 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 they are processed by a modern state-space model. Our framework supports feature-conditioned, structure-aware, graph- and hop-adaptive propagation mechanisms while preserving permutation equivariance. Standard adjacency-based and non-backtracking LGSM sequences arise as special cases of our proposed extractor family. We show that HOPPER is state-of-the-art or competitive across the ECHO-Synth benchmark, and that varying the maximum neighborhood size of message backtracking cancellation (i.e. structural memory window) can optimize accuracy on the LRIM physics-based long-range dependency benchmark. These results demonstrate that learnable sequence extraction provides a flexible and effective approach to long-range graph representation learning.

Problem

• graph neural networks
• long-range dependency
• sequence extraction
• adaptive propagation
• linearized graph sequence models

Innovation

• learnable hop extraction
• Linearized Graph Sequence Models
• state-space models
• long-range graph representation learning
• permutation equivariance