Differentiable Lifting for Topological Neural Networks

2026/08/02 by Jorge Luiz Franco, Gabriel Duarte, Alexander Nikitin +3
Computer Science · #cs.LG #cs.SI

paper · pdf

Published as a conference paper at ICLR 2026 (OpenReview: https://openreview.net/forum?id=eC89CbINIw). 20 pages, 4 figures

arxiv created 2026/08/02 · arxiv updated 2026/08/04

Abstract

Topological neural networks (TNNs) enable leveraging high-order structures on graphs (e.g., cycles and cliques) to boost the expressive power of message-passing neural networks. In turn, however, these structures are typically identified a priori through an unsupervised graph lifting operation. Notwithstanding, this choice is crucial and may have a drastic impact on a TNN's performance on downstream tasks. To circumvent this issue, we propose ∂lift (DiffLift), a general framework for learning graph liftings to hypergraphs and cellular- and simplicial complexes in an end-to-end fashion. In particular, our approach leverages learned vertex-level latent representations to identify and parameterize distributions over candidate higher-order cells for inclusion. This results in a scalable model which can be readily integrated into any TNN. Our experiments show that ∂lift outperforms existing lifting methods on multiple benchmarks for graph and node classification across different TNN architectures. Notably, our approach leads to gains of up to 45% over static liftings, including both connectivity- and feature-based ones.

Citations

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