heterogeneous graph message passing

Message Passing Neural Networks (MPNNs) suffer from limited effective receptive fields (ERFs) due to the locality of message passing, hindering long-range dependency modeling and causing “over-squashing.” This work provides the first systematic theoretical analysis of this limitation. We propose IM-MPNN, a novel architecture that constructs hierarchical, multi-scale graph structures via graph coarsening and employs an interleaved multi-scale message passing mechanism—extending ERF without significantly increasing depth or parameter count. Crucially, we introduce a theory-driven ERF analytical framework to guide efficient long-range interaction modeling. On long-range graph benchmarks—including LRGB—IM-MPNN achieves an average accuracy gain of 8.2% over baseline MPNNs, while maintaining faster inference than deeper MPNN variants. These results demonstrate IM-MPNN’s synergistic advantages in modeling capacity, computational efficiency, and scalability.

This work addresses the fundamental challenge of implementing biologically plausible distributed Bayesian inference in spiking neural networks (SNNs). We propose the first unified framework—within the leaky integrate-and-fire (LIF) neuron model—that neurally realizes the three canonical linear message operations (equality, addition, and multiplication) required for Gaussian belief propagation on factor graphs. By mapping Gaussian message passing onto spike-based encoding, propagation, and decoding processes, our model achieves biologically interpretable approximate inference. The method matches the accuracy of the standard sum-product algorithm in message updates and demonstrates empirical efficacy on both Kalman filtering (dynamic inference) and Bayesian linear regression (static inference). These results validate its applicability across diverse probabilistic inference tasks and bridge a critical theoretical gap between probabilistic reasoning and spiking neuromorphic computation.

This study addresses the slow global error convergence of Gaussian Belief Propagation (GBP) on large-scale graphs by proposing the H-GBP framework. Grounded in spectral radius analysis and matrix operator derivations, this method introduces a novel two-level acceleration mechanism based on iterative graph abstraction and recovery. Furthermore, the convergence of the proposed algorithm toward the optimal solution is rigorously proven. Experimental results demonstrate that H-GBP achieves substantial speedups on linear sparse graphs and attains state-of-the-art computational efficiency in pose graph optimization and bundle adjustment tasks.

We address node classification on sparse graphs—where expected node degree is $O(1)$—with fixed feature dimension and a large number of nodes. Under an asymptotic regime where the number of nodes tends to infinity, we propose and implement, for the first time, the **asymptotically locally Bayes-optimal classifier**. This classifier is exactly realizable by a message-passing GNN whose architecture continuously interpolates between an MLP (in the low graph signal-to-noise ratio regime) and a GCN (in the high-SNR regime), revealing their fundamental unification. Theoretically, we derive the first non-asymptotic generalization error upper bound; rigorously prove that the proposed GNN achieves the Bayes-optimal error rate; and demonstrate strict improvement over existing methods on analytically tractable SNR models. Our approach integrates statistical-physics-inspired message passing, local tree-expansion analysis, sparse random graph modeling (e.g., degree-corrected stochastic block model), and Bayesian inference—providing both a unified theoretical foundation and practical architectural guidance for learning on sparse graphs.

This paper addresses three critical challenges in hypergraph learning: (i) the ambiguity of homophily definitions, (ii) architectural neglect of higher-order structural properties, and (iii) structural biases in prevailing benchmark datasets. To tackle these, we propose the first theoretical framework for higher-order homophily, formally defining and empirically validating it as a key determinant of hypergraph neural network (HNN) performance. We introduce a unified MultiSet message-passing paradigm and a novel architecture—MultiSetMixer—featuring hyperedge-aware node representations and joint node-hyperedge random sampling. Furthermore, we systematically expose fundamental structural distributional biases across mainstream benchmarks. Extensive experiments demonstrate that our approach achieves significant improvements over state-of-the-art methods across multiple benchmarks. The work establishes a theoretically grounded, interpretable, and scalable paradigm for hypergraph learning.

This work addresses the challenge of adaptively determining the optimal neighborhood aggregation range (i.e., hop count) in graph neural networks (GNNs). To this end, the authors propose a Bayesian nonparametric approach that models the message-passing process as a stochastic process and, for the first time, employs a Beta process to infer the neighborhood hop distribution. This formulation yields a unified Bayesian framework that simultaneously optimizes model parameters and automatically infers the most appropriate neighborhood scope. By jointly optimizing neighborhood selection and model learning, the method significantly enhances both the representational capacity and predictive calibration of GNNs. Experimental results demonstrate that the approach is compatible with mainstream GNN architectures and achieves competitive or superior node classification performance across multiple benchmark datasets, including both homophilic and heterophilic graphs.

本文提出基于位置编码的可变形图神经网络模块PEBDSAM，解决传统GNN过平滑、长依赖压缩等问题，适用于异质图和大规模数据集。

This study addresses the lack of theoretical guarantees for belief propagation (BP) in sparse, loopy factor graphs under non-Gaussian settings. By leveraging the central limit theorem, the authors analyze the statistical properties of BP message passing and prove that, under four reasonable assumptions, the marginal beliefs over variables converge to a Gaussian distribution as iterations proceed. This work provides the first theoretical convergence guarantee for Gaussian belief propagation (GBP) in non-Gaussian, sparse graphical models, uncovering an intrinsic “Gaussianization” mechanism inherent to BP. Experimental validation on stereo vision depth estimation demonstrates that variable beliefs become markedly Gaussian after only a few iterations, thereby substantiating the empirical success and broad applicability of GBP in spatial AI and related domains.

Graph Neural Networks (GNNs) often underperform on heterophilous graphs, where adjacent nodes exhibit significantly different labels or features. While existing approaches primarily focus on architectural modifications, they fail to fundamentally alleviate the underlying heterophily issue. This work proposes GRAPHITE, a novel framework that explicitly enhances graph homophily through direct graph transformation. Specifically, GRAPHITE introduces auxiliary feature nodes and reconstructs the graph structure based on a homophily-aware criterion, thereby optimizing message passing. Theoretical analysis and extensive experiments demonstrate that GRAPHITE substantially outperforms state-of-the-art GNN methods across multiple heterophilous graph benchmarks, while maintaining competitive performance on homophilous graphs.

This work addresses rank collapse in message-passing neural networks (MPNNs), a generalization of the over-smoothing phenomenon, by identifying two underlying mechanisms: shared component amplification (SCA) and component dominance (CD). For the first time, the paper decomposes over-smoothing into these distinct factors and establishes a theoretical connection between MPNNs and personalized PageRank. To mitigate rank collapse without altering the backbone architecture, the authors propose a multi-relational splitting (MRS) framework and introduce multi-input multi-output graph convolution (MIMO-GC) along with its local variant, LMGC, which inject multi-relational structure into standard MPNNs. Furthermore, they design an infinitely deep MPNN variant grounded in personalized PageRank. The proposed methods effectively alleviate rank collapse, enable infinite-depth propagation, preserve initial features, and significantly enhance model expressiveness and stability.