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:2606. 26873v1 Announce Type: cross Abstract: Graphs provide a natural language for relational data in chemistry, biology and optimisation.
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:2608. 08118v1 Announce Type: new Abstract: There are several methods for searching for graphs with prescribed properties, such as SAT solvers and specialized generators.
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: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: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.
arXiv:2607. 09704v1 Announce Type: new Abstract: We present an exploratory benchmark and quantum-inspired modeling prototype for fraud screening in dynamic financial transaction graphs.
arXiv:2607. 18567v1 Announce Type: new Abstract: A graph foundation model generalizes across graph domains by mapping every input into one shared representation before any task reasoning.
Positional encodings (PEs) enhance the power of graph neural networks (GNNs), both theoretically and empirically. Two of the most popular families of PEs - spectral (e.
arXiv:2608. 11495v1 Announce Type: new Abstract: Graph Neural Networks (GNNs) serve as the backbone for high-stakes applications in Machine-Learning-as-a-Service (MLaaS).
arXiv:2606. 26373v1 Announce Type: cross Abstract: Dense embeddings power semantic search and retrieval-augmented generation, but embedding-inversion attacks can reconstruct source text from a vector: when a vector database leaks, the documents behind it leak too.
arXiv:2602. 14772v2 Announce Type: replace Abstract: The Winner Determination Problem (WDP) in combinatorial auctions is NP-hard, and no existing method reliably predicts which instances will defeat fast greedy heuristics.