# Learning Subgroup Relations Using Siamese Graph Neural Networks

arXiv: https://arxiv.org/abs/2607.11140 · HTML: https://mlsanity.com/paper/2607.11140/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 15 references that are in the map.
- First posted on arXiv 13 Jul 2026.

## Builds on (most cited first, 8 of 8)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [Graph Neural Networks for Predicting Solvability of Finite Groups](https://mlsanity.com/paper/2606.07619/) (2026)
- [A General Framework for Learning Algebraic Properties from Cayley Graphs using Graph Neural Networks](https://mlsanity.com/paper/2606.26212/) (2026)

## Abstract (arXiv)

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. Each input group is represented by its undirected Cayley graph and encoded by one branch of a Siamese GNN to produce a graph embedding. The resulting graph embeddings are combined with algebraic features derived directly from the input groups to construct a joint feature vector, which is processed by a fully connected classifier to predict subgroup relations between finite groups. By integrating graph-based structural representations with algebraic features, the proposed framework provides a unified approach for learning subgroup relations from finite groups. Experimental results on an expanded and more diverse dataset of 308 finite-group pairs drawn from 11 group families demonstrate the effectiveness of the proposed architecture, achieving a test BA of 91.67% on an independent test set. Additional experiments evaluate generalization to unseen groups, robustness to different Cayley graph generating sets, the contribution of GNN message passing, performance relative to non-neural baselines, and comparison with exact computational methods. These results illustrate the potential of geometric deep learning for subgroup prediction.