aiqbench analysis
This research introduces $\partial$lift, a novel framework that learns graph lifting operations end-to-end using latent representations to enhance topological neural networks (TNNs). By dynamically identifying higher-order structures like cycles and cliques rather than relying on static methods, the approach achieves significant performance gains in node classification tasks. This advancement addresses a critical bottleneck in TNN scalability by integrating structural learning directly into the model training pipeline.
Differentiable Lifting for Topological Neural Networks
arXiv:2608.01160v1 Announce Type: new 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.
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.
Published as a conference paper at ICLR 2026 (OpenReview: this https URL). 20 pages, 4 figures
Machine Learning (cs.LG); Social and Information Networks (cs.SI)
arXiv:2608.01160 [cs.LG]
(or arXiv:2608.01160v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.01160 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 272 words
Related coverage
Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networks
arXiv · Jul 24, 2026
Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networks
arXiv · Jun 3, 2026
A convergence result of a continuous model of deep learning via a \L{}ojasiewicz--Simon inequality
arXiv · Jul 23, 2026
Batch Before You Lift: Scalable Topological Deep Learning on Large Graphs
arXiv · Oct 10, 2026