arXiv:2610. 41802v1 Announce Type: cross Abstract: We show that outlier eigenvectors of the Bethe Hessian achieve weak recovery in the stochastic block model down to the Kesten-Stigum threshold, for every fixed common expected degree $d>1$.
arXiv:2411.02835v3 Announce Type: replace-cross Abstract: The Bethe-Hessian matrix, introduced by Saade, Krzakala, and Zdeborov\'a (2014), is a Hermitian matrix designed for applying spectral cluster...
arXiv:2610. 08872v1 Announce Type: cross Abstract: We study community recovery in the sparse symmetric stochastic block model with $q$ communities, average degree $d$ and signal strength $\lambda$ through statistical decision theory and Fisher information, and obtain three characterizations of the Kesten-Stigum threshold $d\lambda^2=1$ and of the information-computation gap below it.
arXiv:2509. 15822v3 Announce Type: replace-cross Abstract: Predictions from statistical physics postulate that recovery of the communities in the Stochastic Block Model (SBM) with a fixed number $K$ of communities is possible in polynomial time above, and only above, the Kesten-Stigum (KS) threshold.
arXiv:2610.27010v1 Announce Type: cross Abstract: We study robust estimation of a Gaussian precision matrix that decomposes as a sparse matrix minus a symmetric, possibly indefinite, low-rank matrix,...
arXiv:2607. 14304v1 Announce Type: cross Abstract: We study sparse random geometric graphs generated by connecting pairs of high-dimensional vectors whose inner product exceeds a threshold.
arXiv:2609.28163v1 Announce Type: cross Abstract: We study the high-dimensional recovery of a signal vector $\mathbf{x}$ in the presence of sparse Wishart-like noise. We define an $N \times N$ matrix...
arXiv:2606. 14335v1 Announce Type: cross Abstract: Recovering structural information from noisy high-dimensional data is a fundamental task in statistical inference.
The paper introduces a Projected Riemannian Gradient Descent (RGD) algorithm for computing the Bures‑Wasserstein barycenter of positive definite matrices, achieving dimension‑independent linear convergence at unit step size. It resolves a previous dichotomy by showing that clipping eigenvalues to a fixed interval yields a closed‑form, non‑expansive projection in the BW metric, allowing the algorithm to match the empirical speed of unit‑step RGD while maintaining theoretical guarantees. The method also extends to the invariant matrix projection problem, providing a unified dimension‑independent analysis.
arXiv:2511. 11927v2 Announce Type: replace-cross Abstract: Principal Component Analysis (PCA) is a standard tool for extracting a low-rank signal from noisy observations.
arXiv:2609. 03762v1 Announce Type: new Abstract: The computation of the Bures-Wasserstein (BW) barycenter of an ensemble of positive definite matrices arises throughout machine learning, optimal transport, and quantum information.
arXiv:2607. 07032v2 Announce Type: replace Abstract: Spectral positional encodings (PEs) for \emph{directed} graphs face two obstacles: magnetic Laplacians require an $O(n^3)$ Hermitian eigendecomposition per potential, and their complex eigenvectors are defined only up to unitary gauge, which prior work handles with basis-invariant architectures.
arXiv:2606. 15581v1 Announce Type: cross Abstract: We study the graph alignment problem for correlated Gaussian Orthogonal Ensemble (GOE) matrices, where the goal is to recover a hidden vertex permutation given two correlated symmetric Gaussian matrices $(A, B)$ with correlation $1/\sqrt{1+\sigma^2}$.