TopoTune: A Framework for Generalized Combinatorial Complex Neural Networks

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.

Many AI models rely on graphs to learn from structured data—like social networks, molecular structures, or computer networks—because graphs naturally capture who connects to whom. These systems are powerful, but they typically focus only on one-on-one relationships—like a friendship between two people—while ignoring the fact that real-world interactions often happen in groups. Think of a group text, a chemical reaction involving multiple molecules, or a scientific collaboration. Ignoring these multi-way patterns means missing critical structure in the data. Our research addresses this gap by introducing TopoTune, a simple yet powerful tool that upgrades any existing graph-based AI model to learn from richer, group-based relationships. With just a few lines of code, users can define and train such advanced models, called topological models, that previously required deep expertise to build. Our models match or outperform prior state-of-the-art methods, often with reduced memory needs. With TopoTune, we turn a previously complex and fragmented area of machine learning into a unified, accessible toolkit that lowers the barrier to using topological models in real-world research.