arXiv:2606. 05266v1 Announce Type: new Abstract: We establish the first sharp thresholds for low-degree polynomial tests in planted-vs-planted settings, where the goal is to determine with vanishing error which of two structured planted mechanisms generated the observed data.
arXiv:2508. 02158v2 Announce Type: replace-cross Abstract: Detection of planted subgraphs in Erd\"os-R\'enyi random graphs has been extensively studied, leading to a rich body of results characterizing both statistical and computational thresholds.
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:2608. 13171v1 Announce Type: cross Abstract: To avoid missing important variables and their connections in networks, more and more variables are included in network analysis.
arXiv:2602. 17104v2 Announce Type: replace-cross Abstract: We propose a streamlined spectral algorithm for community detection in the two-community stochastic block model (SBM) under constant edge density assumptions.
arXiv:2606. 01400v1 Announce Type: cross Abstract: Evaluating large language models (LLMs) across comprehensive benchmarks is expensive and time-consuming.
arXiv:2606. 24421v1 Announce Type: new Abstract: Spectral filtering recently delivered substantial pruning for \emph{static} subgraph matching: Laplacian interlacing rejects candidates whose neighborhoods cannot host the query.
arXiv:2606. 07623v1 Announce Type: new Abstract: This paper develops a model-theoretic framework for verifying context-conditioned language-model behavior by replacing benchmark labels with finite semantic certificates.
arXiv:2601. 03946v3 Announce Type: replace-cross Abstract: We consider the densest submatrix problem, which seeks the submatrix of fixed size of a given binary matrix that contains the most nonzero entries.
arXiv:2608. 16315v1 Announce Type: cross Abstract: Correlation clustering is a fundamental unsupervised learning problem.
arXiv:2606. 18001v1 Announce Type: new Abstract: Knowledge graph (KG) foundation models (KGFMs) are zero-shot generalizers: trained once, they can predict links on unseen graphs without retraining.
arXiv:2607. 05898v1 Announce Type: new Abstract: Evaluating whether unlearning algorithms truly remove training data influence remains an open challenge.
arXiv:2607. 20286v1 Announce Type: cross Abstract: We propose a novel framework for computing rigorous bounds on the probability that a large language model (LLM) generates harmful output to a given prompt.