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

arXiv: https://arxiv.org/abs/2610.12247 · HTML: https://mlsanity.com/paper/2610.12247/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 37 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 11 of 11)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performance](https://mlsanity.com/paper/2304.11127/) (2023)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
- [Convolutional Learning on Simplicial Complexes](https://mlsanity.com/paper/2301.11163/) (2023)
- [Topo-MLP : A Simplicial Network Without Message Passing](https://mlsanity.com/paper/2312.11862/) (2023)
- [HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations](https://mlsanity.com/paper/2505.15405/) (2025)
- [Have Graph -- Will Lift? The Case for Higher-Order Benchmarks](https://mlsanity.com/paper/2605.07397/) (2026)
- [Implicit Regularization of Mini-Batch Training in Graph Neural Networks](https://mlsanity.com/paper/2605.22480/) (2026)

## Abstract (arXiv)

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 reduces peak GPU memory in every configuration, by 83.2% on average 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 as a general strategy for scaling Topological Deep Learning beyond the limitations of global domain construction.