arXiv subjects

Lantian Xu

Publications and source records attributed to Lantian Xu.

4 recordsLinked to original sources

arXiv2026

Radon--Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensions

Gradient flows of the Kullback--Leibler (KL) divergence, such as the Fokker--Planck equation and Stein Variational Gradient Descent, evolve a distribution toward a target density known only up to a normalizing constant. We introduce new gradient flows of the KL divergence with a remarkable combination of properties: they admit accurate interacting-particle approximations in high dimensions, and the per-step cost scales linearly in both the number of particles and the dimension. These gradient flows are based on new transportation-based Riemannian geometries on the space of probability measures: the Radon--Wasserstein geometry and the related Regularized Radon--Wasserstein (RRW) geometry. We define these geometries using the Radon transform so that the gradient-flow velocities depend only on one-dimensional projections. This yields interacting-particle-based algorithms whose per-step cost follows from efficient Fast Fourier Transform-based evaluation of the required 1D convolutions. We additionally provide numerical experiments that study the performance of the proposed algorithms and compare convergence behavior and quantization. Finally, we prove some theoretical results including well-posedness of the flows and long-time convergence guarantees for the RRW flow.

stat.ML↗

arXiv2026

Constant-time Connectivity and 2-Edge Connectivity Querying in Dynamic Graphs

Connectivity query processing is a fundamental problem in graph processing. Given an undirected graph and two query vertices, the problem aims to identify whether they are connected via a path. Given frequent edge updates in real graph applications, in this paper, we study connectivity query processing in fully dynamic graphs, where edges are frequently inserted or deleted. A recent solution, called D-tree, maintains a spanning tree for each connected component and applies several heuristics to reduce the depth of the tree. To improve efficiency, we propose a new spanning-tree-based solution by maintaining a disjoint-set tree simultaneously. By combining the advantages of two trees, we achieve the constant query time complexity and also significantly improve the theoretical running time in both edge insertion and edge deletion. In addition, we extend our connectivity maintenance algorithms to maintain 2-edge connectivity. Our performance studies on real large datasets show considerable improvement of our algorithms.

cs.DB↗

arXiv2024

A Geometry-Aware Algorithm to Learn Hierarchical Embeddings in Hyperbolic Space

Hyperbolic embeddings are a class of representation learning methods that offer competitive performances when data can be abstracted as a tree-like graph. However, in practice, learning hyperbolic embeddings of hierarchical data is difficult due to the different geometry between hyperbolic space and the Euclidean space. To address such difficulties, we first categorize three kinds of illness that harm the performance of the embeddings. Then, we develop a geometry-aware algorithm using a dilation operation and a transitive closure regularization to tackle these illnesses. We empirically validate these techniques and present a theoretical analysis of the mechanism behind the dilation operation. Experiments on synthetic and real-world datasets reveal superior performances of our algorithm.

cs.LG↗

arXiv2024

Efficient Antagonistic k-plex Enumeration in Signed Graphs

A signed graph is a graph where each edge receives a sign, positive or negative. The signed graph model has been used in many real applications, such as protein complex discovery and social network analysis. Finding cohesive subgraphs in signed graphs is a fundamental problem. A k-plex is a common model for cohesive subgraphs in which every vertex is adjacent to all but at most k vertices within the subgraph. In this paper, we propose the model of size-constrained antagonistic k-plex in a signed graph. The proposed model guarantees that the resulting subgraph is a k-plex and can be divided into two sub-k-plexes, both of which have positive inner edges and negative outer edges. This paper aims to identify all maximal antagonistic k-plexes in a signed graph. Through rigorous analysis, we show that the problem is NP-Hardness. We propose a novel framework for maximal antagonistic k-plexes utilizing set enumeration. Efficiency is improved through pivot pruning and early termination based on the color bound. Preprocessing techniques based on degree and dichromatic graphs effectively narrow the search space before enumeration. Extensive experiments on real-world datasets demonstrate our algorithm's efficiency, effectiveness, and scalability.

cs.DB↗