skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


This content will become publicly available on January 22, 2026

Title: DEMYSTIFYING TOPOLOGICAL MESSAGE-PASSING WITH RELATIONAL STRUCTURES: A CASE STUDY ON OVERSQUASHING IN SIMPLICIAL MESSAGE-PASSING
Topological deep learning (TDL) has emerged as a powerful tool for modeling higher-order interactions in relational data. However, phenomena such as over- squashing in topological message-passing remain understudied and lack theoreti- cal analysis. We propose a unifying axiomatic framework that bridges graph and topological message-passing by viewing simplicial and cellular complexes and their message-passing schemes through the lens of relational structures. This ap- proach extends graph-theoretic results and algorithms to higher-order structures, facilitating the analysis and mitigation of oversquashing in topological message- passing networks. Through theoretical analysis and empirical studies on simplicial networks, we demonstrate the potential of this framework to advance TDL.  more » « less
Award ID(s):
2145630
PAR ID:
10591216
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
International Conference on Learning Representations 2025
Date Published:
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Predictive tasks on relational databases are critical in real-world applications spanning e-commerce, healthcare, and social media. To address these tasks effectively, Relational Deep Learning (RDL) encodes relational data as graphs, enabling Graph Neural Networks (GNNs) to exploit relational structures for improved predictions. However, existing RDL methods often overlook the intrinsic structural properties of the graphs built from relational databases, leading to modeling inefficiencies, particularly in handling many-tomany relationships. Here we introduce RELGNN, a novel GNN framework specifically designed to leverage the unique structural characteristics of the graphs built from relational databases. At the core of our approach is the introduction of atomic routes, which are simple paths that enable direct single-hop interactions between the source and destination nodes. Building upon these atomic routes, RELGNN designs new composite message passing and graph attention mechanisms that reduce redundancy, highlight key signals, and enhance predictive accuracy. RELGNN is evaluated on 30 diverse real-world tasks from RELBENCH (Fey et al., 2024), and achieves state-of-the-art performance on the vast majority of tasks, with improvements of up to 25%. 
    more » « less
  2. Message passing neural networks have shown a lot of success on graph-structured data. However, there are many instances where message passing can lead to over-smoothing or fail when neighboring nodes belong to different classes. In this work, we introduce a simple yet general framework for improving learning in message passing neural networks. Our approach essentially upsamples edges in the original graph by adding “slow nodes” at each edge that can mediate com- munication between a source and a target node. Our method only modifies the input graph, making it plug-and-play and easy to use with existing models. To understand the benefits of slowing down message passing, we provide theoretical and empirical analyses. We report results on several supervised and self-supervised benchmarks, and show improvements across the board, notably in heterophilic conditions where adjacent nodes are more likely to have different labels. Finally, we show how our approach can be used to generate augmentations for self-supervised learning, where slow nodes are randomly introduced into different edges in the graph to generate multi-scale views with variable path lengths. 
    more » « less
  3. Message passing is a fundamental technique for performing calculations on networks and graphs with applications in physics, computer science, statistics, and machine learning, including Bayesian inference, spin models, satisfiability, graph partitioning, network epidemiology, and the calculation of matrix eigenvalues. Despite its wide use, however, it has long been recognized that the method has a fundamental flaw: It works poorly on networks that contain short loops. Loops introduce correlations that can cause the method to give inaccurate answers or to fail completely in the worst cases. Unfortunately, most real-world networks contain many short loops, which limits the usefulness of the message-passing approach. In this paper we demonstrate how to rectify this shortcoming and create message-passing methods that work on any network. We give 2 example applications, one to the percolation properties of networks and the other to the calculation of the spectra of sparse matrices. 
    more » « less
  4. Networks and network computations have become a primary mathematical tool for analyzing the structure of many kinds of complex systems, ranging from the Internet and transportation networks to biochemical interactions and social networks. A common task in network analysis is the calculation of quantities that reside on the nodes of a network, such as centrality measures, probabilities or model states. In this perspective article we discuss message passing methods, a family of techniques for performing such calculations, based on the propagation of information between the nodes of a network. We introduce the message passing approach with a series of examples, give some illustrative applications and results and discuss the deep connections between message passing and phase transitions in networks. We also point out some limitations of the message passing approach and describe some recently introduced methods that address these limitations. 
    more » « less
  5. This work introduces TopoBench, an open-source library designed to standardize benchmarking and accelerate research in topological deep learning (TDL). TopoBench decomposes TDL into a sequence of independent modules for data generation, loading, transforming and processing, as well as model training, optimization and evaluation. This modular organization provides flexibility for modifications and facilitates the adaptation and optimization of various TDL pipelines. A key feature of TopoBench is its support for transformations and lifting across topological domains. Mapping the topology and features of a graph to higher-order topological domains, such as simplicial and cell complexes, enables richer data representations and more fine-grained analyses. The applicability of TopoBench is demonstrated by benchmarking several TDL architectures across diverse tasks and datasets. 
    more » « less