arXiv:2510. 25354v3 Announce Type: replace Abstract: Hypergraphs provide a natural framework for modeling multiway interactions.
arXiv:2608. 12757v1 Announce Type: cross Abstract: Laplacian-regularized minimization is fundamental in signal processing and machine learning, but is limited by the dense and ill-conditioned nature of the graph Laplacian pseudoinverse.
arXiv:2605. 16836v2 Announce Type: replace-cross Abstract: Hypergraphs provide a principled framework for modeling polyadic interactions, with applications in recommendation systems, social networks, and molecular modeling.
arXiv:2504. 19419v3 Announce Type: replace Abstract: Local clustering aims to identify specific substructures within a large graph without any additional structural information of the graph.
arXiv:2607. 15773v1 Announce Type: new Abstract: Higher-order couplings enhance the expressive power of hypergraph neural networks (HGNNs), but they also intensify representation collapse in deep propagation due to strong multi-way feature mixing.
arXiv:2607. 07330v1 Announce Type: cross Abstract: Hypergraph neural networks have shown powerful capability in modeling higher-order relations, yet their predictive uncertainty remains underexplored.
arXiv:2605. 14981v2 Announce Type: replace Abstract: Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system.
arXiv:2411. 15067v2 Announce Type: replace-cross Abstract: We investigate proximal descent methods, inspired by the minimizing movement scheme introduced by Jordan, Kinderlehrer and Otto, for optimizing entropy-regularized functionals on the Wasserstein space.
arXiv:2606. 02223v1 Announce Type: new Abstract: Estimating the generative mechanism of large-scale networks is a fundamental challenge in statistical machine learning.
arXiv:2607. 07513v1 Announce Type: new Abstract: Self-supervised learning matches supervised accuracy from a fraction of the labels, but the labeled-sample efficiency behind this has lacked a theoretical explanation.
arXiv:2606. 14334v1 Announce Type: new Abstract: High-dimensional datasets often concentrate near low-dimensional structures, but estimating their geometry from samples typically relies on graphs and kernels that scale poorly with dataset size and dimension.
arXiv:2607. 07884v1 Announce Type: new Abstract: In this short note we consider the gradient descent dynamics of deep scalar linear networks, $f(x) = \prod_{l=1}^L w_l x$, which enjoy exact time-course solutions for any integer depth.
arXiv:2607. 05167v1 Announce Type: new Abstract: Many real-world systems are organized as networks where spatio-temporal dynamics unfold along connections and not discretely between nodes.