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

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. Current methods operate only after this lifting phase, requiring the entire lifted domain to be materialized prior to training. On large and dense datasets like Reddit ($233$k nodes and $57.3$M 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. By retaining all edges among the sampled nodes, Cluster-TNN preserves higher-order structures spanning sampled clusters, producing topological mini-batches that existing Topological Neural Networks can process directly. Across evaluated domains, lifting procedures, and architectures, Cluster-TNN reduces peak GPU memory by an average of $83.2$% while maintaining competitive predictive performance. Notably, such a reduction enables, to our knowledge, the first training of multiple different higher-order Topological Neural Networks on large datasets such as Reddit and OGBN Products. These results establish Cluster-TNN workflow as a general strategy for scaling Topological Deep Learning beyond the limits of global domain construction.