February 2026

arXiv:2602.23023v1 Announce Type: cross Abstract: We study the fundamental problem of clustering $n$ points into $K$ groups drawn from a mixture of isotropic Gaussians in $mathbb{R}^d$. Specifically, we investigate the requisite minimal distance $Delta$ between mean vectors to partially recover the underlying partition. While the minimax-optimal threshold for $Delta$ is well-established, a significant gap exists between this information-theoretic limit and the performance of known polynomial-time procedures. Although this gap was recently characterized in the high-dimensional regime ($n leq […]

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arXiv:2602.22974v1 Announce Type: cross Abstract: Counting immunopositive cells on biological tissues generally requires either manual annotation or (when available) automatic rough systems, for scanning signal surface and intensity in whole slide imaging. In this work, we tackle the problem of counting microglial cells in lumbar spinal cord cross-sections of rats by omitting cell detection and focusing only on the counting task. Manual cell counting is, however, a time-consuming task and additionally entails extensive personnel training. The classic automatic […]

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arXiv:2602.22965v1 Announce Type: cross Abstract: Improper priors are not allowed for the computation of the Bayesian evidence $Z=p({bf y})$ (a.k.a., marginal likelihood), since in this case $Z$ is not completely specified due to an arbitrary constant involved in the computation. However, in this work, we remark that they can be employed in a specific type of model selection problem: when we have several (possibly infinite) models belonging to the same parametric family (i.e., for tuning parameters of a […]

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arXiv:2602.22954v1 Announce Type: cross Abstract: In this work, we analyze alternative effective sample size (ESS) metrics for importance sampling algorithms, and discuss a possible extended range of applications. We show the relationship between the ESS expressions used in the literature and two entropy families, the R’enyi and Tsallis entropy. The R’enyi entropy is connected to the Huggins-Roy’s ESS family introduced in cite{Huggins15}. We prove that that all the ESS functions included in the Huggins-Roy’s family fulfill all the […]

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arXiv:2602.22847v1 Announce Type: cross Abstract: The concept of ranking aggregation plays a central role in preference analysis, and numerous algorithms for calculating median rankings, often originating in social choice theory, have been documented in the literature, offering theoretical guarantees in a centralized setting, i.e., when all the ranking data to be aggregated can be brought together in a single computing unit. For many technologies (e.g. peer-to-peer networks, IoT, multi-agent systems), extending the ability to calculate consensus rankings with […]

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arXiv:2602.22505v1 Announce Type: cross Abstract: Discrete diffusion models have achieved strong empirical performance in text and other symbolic domains, with masked (absorbing-rate) variants emerging as competitive alternatives to autoregressive models. Among existing samplers, the Euler method remains the standard choice in many applications, and more recently, the First-Hitting Sampler (FHS) has shown considerable promise for masked diffusion models. Despite their practical success, the theoretical understanding of these samplers remains limited. Existing analyses are conducted in Kullback-Leibler (KL) divergence, […]

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arXiv:2602.22369v1 Announce Type: cross Abstract: This paper considers a non-standard problem of generating samples from a low-temperature Gibbs distribution with emph{constrained} support, when some of the coordinates of the mode lie on the boundary. These coordinates are referred to as the non-regular part of the model. We show that in a “pre-asymptotic” regime in which the limiting Laplace approximation is not yet valid, the low-temperature Gibbs distribution concentrates on a neighborhood of its mode. Within this region, the […]

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arXiv:2602.22334v1 Announce Type: cross Abstract: Kurtosis-based Independent Component Analysis (ICA) weakens in wide, balanced mixtures. We prove a sharp redundancy law: for a standardized projection with effective width $R_{mathrm{eff}}$ (participation ratio), the population excess kurtosis obeys $|kappa(y)|=O(kappa_{max}/R_{mathrm{eff}})$, yielding the order-tight $O(c_bkappa_{max}/R)$ under balance (typically $c_b=O(log R)$). As an impossibility screen, under standard finite-moment conditions for sample kurtosis estimation, surpassing the $O(1/sqrt{T})$ estimation scale requires $Rlesssim kappa_{max}sqrt{T}$. We also show that emph{purification} — selecting $m!ll!R$ sign-consistent sources — restores […]

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arXiv:2602.22282v1 Announce Type: cross Abstract: Data privacy is important in the AI era, and differential privacy (DP) is one of the golden solutions. However, DP is typically applicable only if data have a bounded underlying distribution. We address this limitation by leveraging second-moment information from a small amount of public data. We propose Public-moment-guided Truncation (PMT), which transforms private data using the public second-moment matrix and applies a principled truncation whose radius depends only on non-private quantities: data […]

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arXiv:2602.21585v1 Announce Type: cross Abstract: Many applications seek to optimize LLM outputs at test time by iteratively proposing, scoring, and refining candidates over a discrete output space. Existing methods use a calibrated scalar evaluator for the target objective to guide search, but for many tasks such scores are unavailable, too sparse, or unreliable. Pairwise comparisons, by contrast, are often easier to elicit, still provide useful signal on improvement directions, and can be obtained from the LLM itself without […]

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