Batch Before You Lift: Scalable Topological Deep Learning on Large Graphs

David Leko, Luka Benić, Guillermo Bernárdez, Nina Miolane, Olga Fink +1

Topological Deep Learning extends graph-based learning to higher-order domains, such as hypergraphs, cellular, and simplicial complexes. These domains are typically constructed from patterns in an input graph through a process of graph lifting. Full-domain training constructs and stores the complete lifted representation before model execution. On large and dense datasets like Reddit (233k nodes and 57.3M edges), this global materialization becomes a severe computational bottleneck, often rendering training infeasible. To address this limitation, we introduce Cluster-TNN, a domain-agnostic framework that avoids this bottleneck by lifting locally instead. After partitioning the input graph during preprocessing, at runtime Cluster-TNN dynamically samples groups of node clusters, reconstructs their induced subgraphs to form mini-batches, and applies the chosen lifting within each mini-batch. Retaining all edges among sampled nodes preserves the connectivity needed to construct higher-order structures across clusters, producing topological mini-batches that existing Topological Neural Networks can process directly. Across 21 matched comparisons with full-graph execution, Cluster-TNN…