The Logical Expressiveness of Topological Neural Networks
Graph neural networks (GNNs) are the standard for learning on graphs, yet they have limited expressive power, often expressed in terms of the Weisfeiler-Leman (WL) hierarchy or within the framework of first-order logic. In this context, topological neural networks (TNNs) have recently emerged as a promising alternative for graph representation learning. By incorporating higher-order relational structures into message-passing schemes, TNNs offer higher representational power than traditional GNNs. However, a fundamental question remains open: what is the logical expressiveness of TNNs? Answering this allows us to characterize precisely which binary classifiers TNNs can represent. In this p...
| Authors | Amirreza Akbari, Amauri H. Souza, Vikas Garg |
|---|---|
| Primary category | cs.LG |
| Published | 21 April 2026 |
| Last updated at source | 21 April 2026 |
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