aiqbench analysis
This proof-of-concept study demonstrates that Graph Neural Networks can effectively learn abstract algebraic properties of finite groups directly from their geometric Cayley graph representations. By successfully distinguishing solvable from non-solvable groups on out-of-distribution data, the work validates the potential of GNNs to bridge structural graph information with deep theoretical mathematical concepts. The research serves as a foundational exploration for future applications where geometric embeddings might capture complex algebraic invariants in other domains.
Graph Neural Networks for Predicting Solvability of Finite Groups
arXiv:2606.07619v1 Announce Type: new Abstract: We present a Graph Neural Network (GNN) framework for the classification of finite groups according to their solvability. Using graph representations associated with finite groups, including Cayley graphs (CG), the proposed model is trained to distinguish solvable and non-solvable groups using structural graph information alone. The framework is evaluated on groups outside the training dataset in order to investigate the extent to which GNNs can learn algebraic properties arising in group theory. More broadly, the present work explores the relationship between algebraic structure and graph-based geometric representations of finite groups. The present study is intended as a proof-of-concept investigation of whether GNNs can learn algebraic properties of finite groups from graph-based representations
Abstract:We present a Graph Neural Network (GNN) framework for the classification of finite groups according to their solvability. Using graph representations associated with finite groups, including Cayley graphs (CG), the proposed model is trained to distinguish solvable and non-solvable groups using structural graph information alone. The framework is evaluated on groups outside the training dataset in order to investigate the extent to which GNNs can learn algebraic properties arising in group theory. More broadly, the present work explores the relationship between algebraic structure and graph-based geometric representations of finite groups. The present study is intended as a proof-of-concept investigation of whether GNNs can learn algebraic properties of finite groups from graph-based representations
Machine Learning (cs.LG); Group Theory (math.GR)
arXiv:2606.07619 [cs.LG]
(or arXiv:2606.07619v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.07619 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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