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.
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arXiv:2606. 26212v1 Announce Type: new Abstract: A Graph Neural Network (GNN) framework for predicting the solvability of finite groups from their Cayley graph representations was introduced in [1].
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.
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.
arXiv:2607. 11140v1 Announce Type: new Abstract: Determining whether one finite group is isomorphic to a subgroup of another is a fundamental problem in computational group theory.
The paper introduces a new mathematical framework for polynomial group convolutional neural networks (PGCNNs) using graded group algebras. It presents two natural parametrizations of the architecture—based on Hadamard and Kronecker products—that are related by a linear map. The authors compute the dimension of the resulting neuromanifold, show it depends only on the number of layers and group size, and describe the general fiber of the Kronecker parametrization, conjecturing a similar description for the Hadamard case, supported by explicit computations for small groups and shallow networks.
arXiv:2602. 10031v2 Announce Type: replace Abstract: Graph neural networks (GNNs) are commonly divided into message-passing neural networks (MPNNs) and spectral GNNs, reflecting two largely separate research traditions in machine learning and signal processing.