Related papers: CayleyPy RL: Pathfinding and Reinforcement Learnin…

Convolution operations designed for graph-structured data usually utilize the graph Laplacian, which can be seen as message passing between the adjacent neighbors through a generic random walk. In this paper, we propose PAN, a new graph…

Large language models (LLMs) are typically trained by reinforcement learning (RL) with verifiable rewards (RLVR) and supervised fine-tuning (SFT) on reasoning traces to improve their reasoning abilities. However, how these methods shape…

The potential for machine learning systems to amplify social inequities and unfairness is receiving increasing popular and academic attention. Much recent work has focused on developing algorithmic tools to assess and mitigate such…

Graph Neural Networks (GNNs) offer a principled framework for learning over graph-structured data, yet their expressive capacity is often hindered by over-squashing, wherein information from distant nodes is compressed into fixed-size…

Graph Representation Learning (GRL) methods opened new avenues for addressing complex, real-world problems represented by graphs. However, many graphs used in these applications comprise millions of nodes and billions of edges and are…

We report about the results of the application of modern computer algebra tools for construction of directed strongly regular graphs. The suggested techniques are based on the investigation of non-commutative association schemes and Cayley…

We construct explicit generating sets S_n and \tilde S_n of the for the alternating and the symmetric groups, which turn the Cayley graphs C(Alt(n), S_n) and C(Sym(n), \tilde S_n) into a family of bounded degree expanders for all n. This…

A strict lower bound for the diameter of a symmetric graph is proposed, which is calculable with the order $n$ and other local parameters of the graph such as the degree $k\,(\geq 3)$, even girth $g\,(\geq 4)$, and number of $g$-cycles…

Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…

Advances in tracking technologies have spurred the rapid growth of large-scale trajectory data. Building a compact collection of pathlets, referred to as a trajectory pathlet dictionary, is essential for supporting mobility-related…

We consider the problem of learning the nearest neighbor graph of a dataset of n items. The metric is unknown, but we can query an oracle to obtain a noisy estimate of the distance between any pair of items. This framework applies to…

Given a group $G$, the model $\mathcal{G}(G,p)$ denotes the probability space of all Cayley graphs of $G$ where each element of $G$ is included in the generating set independently at random with probability $p$. In this article, we…

Deep Reinforcement Learning (RL) is a promising approach for adaptive robot control, but its current application to robotics is currently hindered by high sample requirements. To alleviate this issue, we propose to exploit the symmetries…

This document contains supplementary material for the main articles in our Random Cayley Graphs project. We prove refined results about simple random walks on the integers and on the cycle. We are primarily interested in the entropy of…

The pseudo-inverse of a graph Laplacian matrix, denoted as $L^\dagger$, finds extensive application in various graph analysis tasks. Notable examples include the calculation of electrical closeness centrality, determination of Kemeny's…

Very often when studying non-equilibrium systems one is interested in analysing dynamical behaviour that occurs with very low probability, so called rare events. In practice, since rare events are by definition atypical, they are often…

Graph connectivity serves as a fundamental metric for evaluating the reliability and fault tolerance of interconnection networks. To more precisely characterize network robustness, the concept of cyclic connectivity has been introduced,…

Although many algorithms have been designed to construct Bayesian network structures using different approaches and principles, they all employ only two methods: those based on independence criteria, and those based on a scoring function…

Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…

Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…