Differentiable Lifting for Topological Neural Networks

• URL: http://arxiv.org/abs/2608.01160v1
• Date: Sun, 02 Aug 2026 11:30:09 GMT
• Title: Differentiable Lifting for Topological Neural Networks
• Abstract summary: Topological neural networks (TNNs) enable leveraging high-order structures on graphs.<n>DiffLift is a framework for learning graph liftings to hypergraphs and cellular- and simplicial complexes.<n>Our approach leads to gains of up to 45% over static liftings, including both connectivity- and feature-based ones.
• Score: 49.208571794040374
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\partial$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 $\partial$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.

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