TopoTune : A Framework for Generalized Combinatorial Complex Neural Networks

TL;DR

TopoTune introduces a flexible framework for transforming graph neural networks into higher-order topological models, enabling better capture of complex multi-way interactions in relational data with improved performance and accessibility.

Contribution

The paper presents Generalized CCNNs (GCCNs), a unified framework that generalizes and subsumes existing CCNNs, along with TopoTune, a software tool for easy development and training of these models.

Findings

GCCNs outperform traditional CCNNs in various experiments.

TopoTune simplifies the creation and training of TDL models.

GCCNs often achieve comparable or better results with less complexity.

Abstract

Graph Neural Networks (GNNs) effectively learn from relational data by leveraging graph symmetries. However, many real-world systems -- such as biological or social networks -- feature multi-way interactions that GNNs fail to capture. Topological Deep Learning (TDL) addresses this by modeling and leveraging higher-order structures, with Combinatorial Complex Neural Networks (CCNNs) offering a general and expressive approach that has been shown to outperform GNNs. However, TDL lacks the principled and standardized frameworks that underpin GNN development, restricting its accessibility and applicability. To address this issue, we introduce Generalized CCNNs (GCCNs), a 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.