Related papers: CayleyPy RL: Pathfinding and Reinforcement Learnin…

Recent years have seen substantial progress in neural generation of text, images, and audio, supported by mature training pipelines and large-scale optimization. For graphs, however, comparable progress has been more limited. We attribute…

In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…

Logic optimization is an NP-hard problem commonly approached through hand-engineered heuristics. We propose to combine graph convolutional networks with reinforcement learning and a novel, scalable node embedding method to learn which local…

Reinforcement learning has gained traction for active flow control tasks, with initial applications exploring drag mitigation via flow field augmentation around a two-dimensional cylinder. RL has since been extended to more complex…

Graphlets are induced subgraph patterns and have been frequently applied to characterize the local topology structures of graphs across various domains, e.g., online social networks (OSNs) and biological networks. Discovering and computing…

Reeb graphs are simple topological descriptors with applications in many areas like topological data analysis and computational geometry. Despite their prevalence, visualization of Reeb graphs has received less attention. In this paper, we…

We focus on the study of dynamics of two kinds of random walk: generic random walk (GRW) and maximal entropy random walk (MERW) on two model networks: Cayley trees and ladder graphs. The stationary probability distribution for MERW is given…

Diffusion models form an important class of generative models today, accounting for much of the state of the art in cutting edge AI research. While numerous extensions beyond image and video generation exist, few of such approaches address…

We propose a novel entropy flow on weighted graphs, which provides a principled framework that characterizes the evolution of probability distributions over graph structures while sharing geometric intuition with discrete Ricci flow. We…

In the modern age of social media and networks, graph representations of real-world phenomena have become an incredibly useful source to mine insights. Often, we are interested in understanding how entities in a graph are interconnected.…

We introduce a new distributed algorithm for aligning graphs or finding substructures within a given graph. It is based on the cavity method and is used to study the maximum-clique and the graph-alignment problems in random graphs. The…

Learning-based planners leveraging Graph Neural Networks can learn search guidance applicable to large search spaces, yet their potential to address symmetries remains largely unexplored. In this paper, we introduce a graph representation…

In this paper we explore methods to exploit symmetries for ensuring sample efficiency in reinforcement learning (RL), this problem deserves ever increasing attention with the recent advances in the use of deep networks for complex RL tasks…

We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular…

Strongly regular graphs (SRGs) are highly symmetric combinatorial objects, with connections to many areas of mathematics including finite fields, finite geometries, and number theory. One can construct an SRG via the Cayley Graph of a…

Deep graph clustering, which aims to group nodes into disjoint clusters by neural networks in an unsupervised manner, has attracted great attention in recent years. Although the performance has been largely improved, the excellent…

Reasoning over structured graphs remains a fundamental challenge for Large Language Models (LLMs), particularly when scaling to large graphs. Existing approaches typically follow the retrieval-augmented generation (RAG) paradigm: first…

In the graph stream model of computation, an algorithm processes the edges of an input graph in one or more sequential passes while using a memory sublinear in the input size. This model poses significant challenges for constructing long…

We consider the random walk in an independent and identically distributed (i.i.d.) random environment on a Cayley graph of a finite free product of copies of $\mathbb{Z}$ and $\mathbb{Z}_2$. Such a Cayley graph is readily seen to be a…

Graph neural networks (GNNs) extends the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we…