February 2026

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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arXiv:2602.23006v1 Announce Type: new Abstract: Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation, treating the spectral density as a probability distribution for Monte Carlo approximation. Although this probabilistic interpretation works for stationary processes, it is overly restrictive for the nonstationary case, where spectral densities are generally not probability measures. We propose regular Fourier features for harmonizable […]

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arXiv:2602.22985v1 Announce Type: new Abstract: We introduce kernel integrated $R^2$, a new measure of statistical dependence that combines the local normalization principle of the recently introduced integrated $R^2$ with the flexibility of reproducing kernel Hilbert spaces (RKHSs). The proposed measure extends integrated $R^2$ from scalar responses to responses taking values on general spaces equipped with a characteristic kernel, allowing to measure dependence of multivariate, functional, and structured data, while remaining sensitive to tail behaviour and oscillatory dependence structures. […]

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arXiv:2602.22925v1 Announce Type: new Abstract: We study wide Bayesian neural networks focusing on the rare but statistically dominant fluctuations that govern posterior concentration, beyond Gaussian-process limits. Large-deviation theory provides explicit variational objectives-rate functions-on predictors, providing an emerging notion of complexity and feature learning directly at the functional level. We show that the posterior output rate function is obtained by a joint optimization over predictors and internal kernels, in contrast with fixed-kernel (NNGP) theory. Numerical experiments demonstrate that the […]

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