HOPPER: Learnable Hop Extraction for Linearized Graph Sequence Models

• URL: http://arxiv.org/abs/2608.09031v1
• Date: Mon, 10 Aug 2026 02:31:46 GMT
• Title: HOPPER: Learnable Hop Extraction for Linearized Graph Sequence Models
• Abstract summary: We introduce HOPPER, an end-to-end learnable extension of Linearized Graph Sequence Models.<n>HOPPER learns how hop sequences should be extracted before they are processed by a modern state-space model.<n>We show that HOPPER is state-of-the-art or competitive across the ECHO- Synth benchmark.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Generative Diffusion Models of Stochastic Graph Signals [74.4097723209053]
  This paper tackles problems of conditional graph signal generative modeling and tackles them with a single denoising diffusion framework.<n>We learn a reverse diffusion process, parametrized by graph neural networks (GNNs), that draws graph signals conditioned directly on the graph topology and on node-feature side information.<n>We demonstrate our method on two generative tasks: stock price forecasting and optimal wireless resource allocation, with extensive numerical results in both domains.
  arXiv  Detail & Related papers  (2026-07-07T22:02:13Z)
• Semi-supervised Instruction Tuning for Large Language Models on Text-Attributed Graphs [62.544129365882014]
  We propose a novel Semi-supervised Instruction Tuning pipeline for Graph Learning, named SIT-Graph.<n> SIT-Graph is model-agnostic and can be seamlessly integrated into any graph instruction tuning method that utilizes LLMs as the predictor.<n>Extensive experiments demonstrate that when incorporated into state-of-the-art graph instruction tuning methods, SIT-Graph significantly enhances their performance on text-attributed graph benchmarks.
  arXiv  Detail & Related papers  (2026-01-19T08:10:53Z)
• From Mice to Trains: Amortized Bayesian Inference on Graph Data [2.809401516758154]
  Inference on graph-structured data requires methods that are permutation-invariant, scalable across varying sizes and sparsities, and capable of capturing complex long-range dependencies.<n>ABI is a simulation-based framework that employs generative neural networks to enable fast, likelihood-free posterior inference.
  arXiv  Detail & Related papers  (2026-01-05T16:16:28Z)
• Scalable Graph Generative Modeling via Substructure Sequences [50.32639806800683]
  We introduce Generative Graph Pattern Machine (G$2$PM), a generative Transformer pre-training framework for graphs.<n>G$2$PM represents graph instances (nodes, edges, or entire graphs) as sequences of substructures.<n>It employs generative pre-training over the sequences to learn generalizable and transferable representations.
  arXiv  Detail & Related papers  (2025-05-22T02:16:34Z)
• Lightweight yet Efficient: An External Attentive Graph Convolutional Network with Positional Prompts for Sequential Recommendation [8.49353541052153]
  We propose an External Attentive Graph convolutional network with Positional prompts for Sequential recommendation, namely EA-GPS.<n>We show that the proposed EA-GPS outperforms the state-of-the-art methods.
  arXiv  Detail & Related papers  (2025-02-21T09:34:31Z)
• Beyond Message Passing: Neural Graph Pattern Machine [50.78679002846741]
  We introduce the Neural Graph Pattern Machine (GPM), a novel framework that bypasses message passing by learning directly from graph substructures.<n>GPM efficiently extracts, encodes, and prioritizes task-relevant graph patterns, offering greater expressivity and improved ability to capture long-range dependencies.
  arXiv  Detail & Related papers  (2025-01-30T20:37:47Z)
• LASE: Learned Adjacency Spectral Embeddings [9.227991604045416]
  We learn nodal Adjacency Spectral Embeddings (ASE) from graph inputs.<n>LASE is interpretable, parameter efficient, robust to inputs with unobserved edges.<n>LASE layers combine Graph Convolutional Network (GCN) and fully-connected Graph Attention Network (GAT) modules.
  arXiv  Detail & Related papers  (2024-12-23T17:35:19Z)
• Range-aware Positional Encoding via High-order Pretraining: Theory and Practice [14.521929085104441]
  Unsupervised pre-training on vast amounts of graph data is critical in real-world applications wherein labeled data is limited. We propose a novel pre-training strategy on graphs that focuses on modeling their multi-resolution structural information. Our approach relies solely on the graph structure, it is also domain-agnostic and adaptable to datasets from various domains.
  arXiv  Detail & Related papers  (2024-09-27T19:53:10Z)
• A Pure Transformer Pretraining Framework on Text-attributed Graphs [50.833130854272774]
  We introduce a feature-centric pretraining perspective by treating graph structure as a prior. Our framework, Graph Sequence Pretraining with Transformer (GSPT), samples node contexts through random walks. GSPT can be easily adapted to both node classification and link prediction, demonstrating promising empirical success on various datasets.
  arXiv  Detail & Related papers  (2024-06-19T22:30:08Z)
• Long Range Graph Benchmark [32.317725340138104]
  MP-GNNs that simply rely on 1-hop message passing often fare better in several existing graph benchmarks. We benchmark both baseline GNNs and Graph Transformer networks to verify that the models which capture long-range dependencies perform significantly better on these tasks.
  arXiv  Detail & Related papers  (2022-06-16T13:33:22Z)
• Spectral Graph Convolutional Networks With Lifting-based Adaptive Graph Wavelets [81.63035727821145]
  Spectral graph convolutional networks (SGCNs) have been attracting increasing attention in graph representation learning. We propose a novel class of spectral graph convolutional networks that implement graph convolutions with adaptive graph wavelets.
  arXiv  Detail & Related papers  (2021-08-03T17:57:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.