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Learning Subgroup Relations Using Siamese Graph Neural Networks

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Determining whether one finite group is isomorphic to a subgroup of another is a fundamental problem in computational group theory. In this work, we propose a Siamese Graph Neural Network (Siamese GNN) for subgroup prediction using Cayley graph representations of finite groups.

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arXiv Machine Learning
Jul 15

Learning the Graphical Nature of Symmetries

arXiv:2607. 12026v1 Announce Type: cross Abstract: Finite groups are rigid algebraic objects, whose Cayley graphs expose a rich network geometry through which group-theoretic structure can be measured, compared, and learned.

By Rashid Barket, Enrico Grimaldi, Yacoub Hendi, Edward Hirst, Adam Onus, Harmeet Singh
arXiv Machine Learning
Aug 28

Aitchison Embeddings for Learning Compositional Graph Representations

The paper introduces a compositional graph embedding framework based on Aitchison geometry, where nodes are represented as simplex-valued mixtures over latent archetypal factors. By embedding these mixtures using isometric log-ratio coordinates, the method preserves Aitchison distances while allowing unconstrained optimization in Euclidean space, yielding intrinsically interpretable embeddings. The approach achieves competitive performance on node classification and link prediction tasks and enables principled component restriction through subcompositional coherence, allowing analysis of how archetype groups influence representations and predictions.

By Nikolaos Nakis, Chrysoula Kosma, Panagiotis Promponas, Michail Chatzianastasis, Giannis Nikolentzos