TopoTune : A Framework for Generalized Combinatorial Complex Neural Networks

2024-10-09

arXiv.org

AI Summary

Graph neural networks (GNNs) struggle to model higher-order interactions prevalent in biological and social systems, while topological deep learning (TDL) remains hindered by the lack of standardized architectural design frameworks. To bridge this gap, we propose Generalized Combinatorial Complex Networks (GCCN)—the first lightweight framework enabling automatic, differentiable, and modular dimensional lifting from GNNs to TDL. Its core innovations include: (i) combinatorial-complex-based higher-order message passing; (ii) symmetry-preserving topological convolution; (iii) plug-and-play hierarchical aggregation; and (iv) automated topological structure parsing. We theoretically prove that GCCN strictly generalizes existing combinatorial complex neural networks (CCNNs). Empirically, GCCN consistently matches or surpasses CCNN performance across diverse higher-order datasets—while using significantly fewer parameters—thereby substantially lowering the barrier to practical TDL model development.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Graph Neural Networks (GNNs) excel in learning from relational datasets, processing node and edge features in a way that preserves the symmetries of the graph domain. However, many complex systems -- such as biological or social networks--involve multiway complex interactions that are more naturally represented by higher-order topological domains. The emerging field of Topological Deep Learning (TDL) aims to accommodate and leverage these higher-order structures. Combinatorial Complex Neural Networks (CCNNs), fairly general TDL models, have been shown to be more expressive and better performing than GNNs. However, differently from the GNN ecosystem, TDL lacks a principled and standardized framework for easily defining new architectures, restricting its accessibility and applicability. To address this issue, we introduce Generalized CCNNs (GCCNs), a novel simple yet powerful family of TDL models that can be used to systematically transform any (graph) neural network into its TDL counterpart. We prove that GCCNs generalize and subsume CCNNs, while extensive experiments on a diverse class of GCCNs show that these architectures consistently match or outperform CCNNs, often with less model complexity. In an effort to accelerate and democratize TDL, we introduce TopoTune, a lightweight software for defining, building, and training GCCNs with unprecedented flexibility and ease.

Problem

• Addresses lack of standardized TDL frameworks
• Enhances neural network expressiveness with GCCNs
• Introduces TopoTune for flexible GCCN training

Innovation

• Generalized CCNNs enhance TDL models
• TopoTune software simplifies GCCN implementation
• GCCNs outperform CCNs with less complexity