arXiv subjects

Tal Weissblat

Publications and source records attributed to Tal Weissblat.

6 recordsLinked to original sources

arXiv2026

Learning Subgroup Relations Using Siamese Graph Neural Networks

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.

cs.LG↗

arXiv2026

From Finite Cayley Graphs to Growth of Infinite Groups

Graph neural networks (GNNs) have recently been shown to learn algebraic properties of finite groups from their Cayley graphs [1,2]. In this work, we investigate whether such models generalize to infinite finitely generated groups. Motivated by Gromov's theorem [3], a GNN is trained and validated exclusively on finite complete and truncated Cayley graphs, and then evaluated, without retraining, on truncated Cayley graphs of unseen infinite groups. The evaluation includes free abelian groups of various ranks, the discrete Heisenberg group, the infinite dihedral group, free groups, and direct products with both infinite abelian and finite groups. The results show strong generalization across these families, suggesting that finite Cayley graphs encode sufficient local geometric information to transfer to the infinite setting. Overall, this provides evidence that GNNs trained solely on finite groups can capture geometric features related to the growth of infinite finitely generated groups.

math.GR↗

arXiv2026

A General Framework for Learning Algebraic Properties from Cayley Graphs using Graph Neural Networks

In this work, we present a general Graph Neural Network (GNN) framework for learning algebraic properties of finite groups from their Cayley graph representations. The framework provides a unified computational pipeline consisting of a common graph construction procedure, feature representation, training methodology, and GNN architecture, with only the target labeling function varying across classification tasks. To demonstrate the generality of the proposed approach, we consider three representative algebraic properties: abelianity, nilpotency, and solvability. Experiments were conducted on a benchmark of 176 finite groups drawn from several classical families, with all groups included in each classification task. To address class imbalance, class-weighted cross-entropy loss was employed where appropriate during training. Furthermore, the family PSL(2,q) was reserved exclusively for testing, enabling evaluation of the framework's ability to generalize to previously unseen group families. The best-performing models achieved test balanced accuracies of 1.000, 0.856, and 0.875 for abelianity, nilpotency, and solvability, respectively. Although the same computational framework was employed across all tasks, different GNN architectures proved optimal for different algebraic properties, suggesting that the representational complexity required to learn a property depends on its underlying algebraic structure. These results demonstrate that GNNs can effectively learn multiple algebraic properties directly from Cayley graph representations while exhibiting strong generalization to unseen group families. More broadly, the proposed framework establishes a computational methodology for studying algebraic properties of finite groups using graph-based machine learning.

cs.LG↗

arXiv2026

Graph Neural Networks for Predicting Solvability of Finite Groups

We present a Graph Neural Network (GNN) framework for the classification of finite groups according to their solvability. Using undirected Cayley graph representations, the proposed framework learns to distinguish solvable and non-solvable groups directly from structural graph information, without relying on explicit algebraic features. The framework is evaluated on a benchmark dataset of 200 finite groups, comprising 120 solvable and 80 non-solvable groups. The experiments investigate the extent to which GNNs can learn the algebraic property of solvability from Cayley graph representations and generalize to previously unseen finite groups. The selected GNN architecture achieved a balanced accuracy (BA) of 1.000 on the independent test set. Furthermore, repeated experiments using different random seeds and learning rates consistently produced BAs between 0.956 and 1.000, demonstrating the robustness of the proposed framework with respect to the training configuration. To further evaluate generalization, the entire PSL(2,q) family was excluded from the training and validation sets and reserved exclusively for testing. The selected model correctly classified every previously unseen group in this family, demonstrating successful generalization to an entirely unseen family of finite groups.

cs.LG↗

arXiv2021

A characterization of spaces of homogeneous type induced by continuous ellipsoid covers of $\mathbb R^n$

We study the relationship between the concept of a continuous ellipsoid $\Theta$ cover of $\mathbb{R}^n$, which was introduced by Dahmen, Dekel, and Petrushev, and the space of homogeneous type induced by $\Theta$. We characterize the class of quasi-distances on $\mathbb{R}^n$ (up to equivalence) which correspond to continuous ellipsoid covers. This places firmly continuous ellipsoid covers as a subclass of spaces of homogeneous type on $\mathbb{R}^n$ satisfying quasi-convexity and $1$-Ahlfors-regularity.

math.CA↗

arXiv2011

Santalo region of a log-concave function

In this paper we define the Santalo region and the Floating body of a log-concave function. We then study their properties. Our main result is that any relation of Floating body and Santalo region of a convex body is translated to a relation of Floating body and Santalo region of an even log-concave function

math.FA↗