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: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: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: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.
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:2505.11298v2 Announce Type: replace Abstract: Graph Neural Networks (GNNs) are powerful tools for learning on structured data, yet the relationship between their expressivity and predictive per...
The survey titled "When Vision Meets Graphs: A Survey on Graph Reasoning and Learning" reviews how visual depictions of graphs can be used as inputs for graph reasoning and learning. It highlights that while Graph Neural Networks dominate graph machine learning, most pipelines ignore the visual form of graphs, despite scientists routinely interpreting graphs visually. The paper organizes existing work into three threads—vision for graph reasoning, vision for graph learning, and scientific graphs—aiming to clarify current capabilities and chart a path toward foundation models that perceive and reason about graphs like scientists do.
arXiv:2502. 16533v3 Announce Type: replace-cross Abstract: Graph Transformers (GTs) have demonstrated a strong capability in modeling graph structures by addressing the intrinsic limitations of graph neural networks (GNNs), such as over-smoothing and over-squashing.
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. 08996v1 Announce Type: cross Abstract: Graph Neural Networks have emerged as a powerful tool for the fast and accurate prediction of various crystal properties.