From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module

TL;DR

This paper introduces a differentiable module for learning higher-order cell complex topologies in graph neural networks, enabling better modeling of multi-way data interactions, especially when input graphs are incomplete or noisy.

Contribution

The paper proposes the Differentiable Cell Complex Module (DCM), a novel learnable function for inferring complex topologies in GNNs, integrated with a scalable inference procedure.

Findings

Outperforms state-of-the-art methods on various datasets.

Shows significant improvements when input graphs are missing or noisy.

Effective in both homophilic and heterophilic graph scenarios.

Abstract

Latent Graph Inference (LGI) relaxed the reliance of Graph Neural Networks (GNNs) on a given graph topology by dynamically learning it. However, most of LGI methods assume to have a (noisy, incomplete, improvable, ...) input graph to rewire and can solely learn regular graph topologies. In the wake of the success of Topological Deep Learning (TDL), we study Latent Topology Inference (LTI) for learning higher-order cell complexes (with sparse and not regular topology) describing multi-way interactions between data points. To this aim, we introduce the Differentiable Cell Complex Module (DCM), a novel learnable function that computes cell probabilities in the complex to improve the downstream task. We show how to integrate DCM with cell complex message passing networks layers and train it in a end-to-end fashion, thanks to a two-step inference procedure that avoids an exhaustive search across all possible cells in the input, thus maintaining scalability. Our model is tested on several homophilic and heterophilic graph datasets and it is shown to outperform other state-of-the-art techniques, offering significant improvements especially in cases where an input graph is not provided.