Differentiable Lifting for Topological Neural Networks

2026-08-02

AI Summary

This work addresses the limited adaptability of conventional topological neural networks, which rely on predefined graph lifting operations to construct higher-order structures and thus fail to tailor these structures to downstream tasks. To overcome this limitation, the authors propose DiffLift, a novel framework that enables end-to-end differentiable graph lifting for the first time. DiffLift parameterizes the distribution of higher-order topological units—such as hyperedges, cells, or simplices—via vertex-level latent representations and employs differentiable sampling to dynamically assemble task-adaptive topological structures. The approach is compatible with a broad range of topological neural network architectures and achieves substantial performance gains over existing static lifting strategies across multiple graph and node classification benchmarks, with improvements of up to 45%.

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.

Problem

• topological neural networks
• graph lifting
• higher-order structures
• end-to-end learning
• hypergraphs

Innovation

• Differentiable Lifting
• Topological Neural Networks
• Hypergraphs
• Simplicial Complexes
• End-to-End Learning