[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86149-en":3,"doc-seo-86149-105":30,"detail-sidebar-cat-0-en-105":83},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86149,962075114101,"Seraphina","https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165",8,"Research & Report","Learning Subgroup Relations Using Siamese Graph Neural Networks","Subgroup prediction in computational group theory is addressed through a Siamese Graph Neural Network that learns isomorphism-to-subgroup relations between pairs of finite groups. Each group is converted into an undirected Cayley graph and encoded by a shared GNN branch to obtain graph embeddings. Algebraic features derived from the input groups are combined with the embeddings to form a joint representation, classified by a fully connected network. Experiments report 95.9% test accuracy (47/49) and highlight geometric deep learning for subgroup prediction.","Learning Subgroup Relations Using Siamese Graph Neural Networks  \nTal Weissblat  \n[Email: tal.weisblat@gmail.com](Email: tal.weisblat@gmail.com)  \nAbstract  \nDetermining 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 demonstrate the effectiveness of the proposed architecture, achieving a test accuracy of 95.9%(47/49) on an independent test set and illustrating the potential of geometric deep learning for subgroup prediction.  \nKeywords: Computational Group Theory, Finite Groups, Subgroup Prediction, Cayley Graphs, Graph Neural Networks, Siamese Graph Neural Networks, Geometric Deep Learning.  \n1 Introduction  \nDetermining whether one finite group is isomorphic to a subgroup of another is a fundamental problem in computational group theory. Subgroup structure plays a central role in the study and classification of finite groups, with applications in computational algebra, symmetry analysis, and many other areas of mathematics. Classical approaches rely on exact algebraic algorithms that exploit the structural properties of finite groups to compute and analyze subgroup structures and determine subgroup relations. Although these methods are mathematically rigorous and highly effective, recent advances in machine learning have introduced new opportunities for learning algebraic relationships directly from suitable representations of groups, complementing traditional symbolic techniques.  \nOne particularly natural representation of a finite group is its Cayley graph, which encodes the multiplication structure of the group with respect to a generating set [1] . Cayley graphs provide  \na graph-theoretic representation of algebraic objects while preserving important structural information, making them a natural bridge between computational group theory and graphbased machine learning. At the same time, Graph Neural Networks (GNNs) have emerged as a successful deep learning frameworks for learning from graph-structured data. By iteratively aggregating information from neighboring nodes, GNNs can learn expressive graph representations and have achieved remarkable success across a wide range of applications [2,3] .  \nMotivated by these developments, recent studies have explored the use of GNNs for learning algebraic properties directly from Cayley graph representations. In particular, previous studies demonstrated that GNNs can successfully predict important algebraic properties of finite groups directly from their Cayley graphs [4,5] . More recently, the theoretical expressive power of finite Cayley graphs has also been investigated, establishing connections between their local structure and properties of infinite groups [6] . Taken together, these studies suggest that Cayley graphs constitute an informative representation for combining computational group theory with geometric deep learning.  \nBuilding on these previous studies, the present work considers a different but closely related learning problem. Whereas previous studies focused on predicting properties of individual groups, we investigate whether one finite group is isomorphic to a subgroup of another. 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