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.
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.
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.
arXiv:2412. 19419v2 Announce Type: replace-cross Abstract: Graph neural networks are deep neural networks designed for graphs with attributes attached to nodes or edges.
arXiv:2512. 14338v3 Announce Type: replace Abstract: Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data.
arXiv:2607. 02212v1 Announce Type: cross Abstract: Aqueous solubility is a key property in early-stage drug discovery, but most predictive models merge physicochemical descriptors and molecular graph information into a single representation, obscuring whether a prediction is driven by global chemistry, molecular structure, or both.
arXiv:2603. 14846v3 Announce Type: replace Abstract: We define an information-complexity property for aggregation functions, capturing a vast range of practical aggregations, and prove that any Message-Passing Graph Neural Network (MP-GNN) model with such aggregations induces only a polynomial number of equivalence classes on all graphs - while the number of non-isomorphic graphs is super-exponential (in number of vertices).
arXiv:2607. 26241v1 Announce Type: cross Abstract: The Word Problem has been a subject of intensive mathematical study for over a century, initially driving advances in combinatorial group theory and more recently emerging as a foundational hardness assumption in post-quantum cryptography (PQC).
arXiv:2608. 14823v1 Announce Type: new Abstract: Are heterophilic nodes in a graph harder to classify because they are heterophilic or because they are rare?
arXiv:2410. 09737v2 Announce Type: replace Abstract: A popular way to improve the expressive power of graph neural networks (GNNs) is to use Laplacian eigenvectors as additional node features, since they can serve both as structural identifiers and global coordinates of nodes.