February 2026

arXiv:2602.14478v1 Announce Type: new Abstract: We study two log-concave sampling problems: constrained sampling and composite sampling. First, we consider sampling from a target distribution with density proportional to $exp(-f(x))$ supported on a convex set $K subset mathbb{R}^d$, where $f$ is convex. The main challenge is enforcing feasibility without degrading mixing. Using an epigraph transformation, we reduce this task to sampling from a nearly uniform distribution over a lifted convex set in $mathbb{R}^{d+1}$. We then solve the lifted problem […]

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arXiv:2602.14244v1 Announce Type: new Abstract: Federated Learning provides a privacy-preserving paradigm for distributed learning, but suffers from statistical heterogeneity across clients. Personalized Federated Learning (PFL) mitigates this issue by considering client-specific models. A widely adopted approach in PFL decomposes neural networks into a shared feature extractor and client-specific heads. While effective, this design induces a fundamental tradeoff: deep or expressive shared components hinder personalization, whereas large local heads exacerbate overfitting under limited per-client data. Most existing methods rely […]

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arXiv:2602.14029v1 Announce Type: new Abstract: Iterative self-training (self-distillation) repeatedly refits a model on pseudo-labels generated by its own predictions. We study this procedure in overparameterized linear regression: an initial estimator is trained on noisy labels, and each subsequent iterate is trained on fresh covariates with noiseless pseudo-labels from the previous model. In the high-dimensional regime, we derive deterministic-equivalent recursions for the prediction risk and effective noise across iterations, and prove that the empirical quantities concentrate sharply around these […]

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arXiv:2602.14020v1 Announce Type: new Abstract: We study operator-norm covariance estimation from heavy-tailed samples that may include a small fraction of arbitrary outliers. A simple and widely used safeguard is emph{Euclidean norm clipping}, but its accuracy depends critically on an unknown clipping level. We propose a cross-fitted clipped covariance estimator equipped with emph{fully computable} Bernstein-type deviation certificates, enabling principled data-driven tuning via a selector (emph{MinUpper}) that balances certified stochastic error and a robust hold-out proxy for clipping bias. The […]

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arXiv:2602.13942v1 Announce Type: new Abstract: In the era of large language models (LLMs), fine-tuning pretrained models has become ubiquitous. Yet the theoretical underpinning remains an open question. A central question is why only a few epochs of fine-tuning are typically sufficient to achieve strong performance on many different tasks. In this work, we approach this question by developing a statistical framework, combining rigorous early stopping theory with the attention-based Neural Tangent Kernel (NTK) for LLMs, offering new theoretical […]

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arXiv:2602.13906v1 Announce Type: new Abstract: Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise. There is a rich literature establishing the asymptotic normality of rescaled SA iterates under fairly mild conditions. However, these asymptotic results do not quantify the accuracy of the Gaussian approximation in finite time. In this paper, we establish explicit non-asymptotic bounds on the Wasserstein distance between the distribution of the rescaled iterate at time k and the […]

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arXiv:2602.13619v1 Announce Type: new Abstract: We study parametric change-point detection, where the goal is to identify distributional changes in time series, under local differential privacy. In the non-private setting, we derive improved finite-sample accuracy guarantees for a change-point detection algorithm based on the generalized log-likelihood ratio test, via martingale methods. In the private setting, we propose two locally differentially private algorithms based on randomized response and binary mechanisms, and analyze their theoretical performance. We derive bounds on detection […]

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arXiv:2602.13421v1 Announce Type: new Abstract: Computation in biological systems is fundamentally energy-constrained, yet standard theories of computation treat energy as freely available. Here, we argue that variational free energy minimization under a Poisson assumption offers a principled path toward an energy-aware theory of computation. Our key observation is that the Kullback-Leibler (KL) divergence term in the Poisson free energy objective becomes proportional to the prior firing rates of model neurons, yielding an emergent metabolic cost term that penalizes […]

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arXiv:2602.13362v1 Announce Type: new Abstract: A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration, producing narrow but overconfident predictions. However, in safety-critical settings, trustworthy uncertainty estimates are often more valuable than narrow intervals. Realizing the problem, several recent works have focused on post-hoc corrections; however, existing methods either rely on weak notions of calibration (such as PIT uniformity) or […]

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arXiv:2602.13324v1 Announce Type: new Abstract: Deploying autonomous edge robotics in dynamic military environments is constrained by both scarce domain-specific training data and the computational limits of edge hardware. This paper introduces a hierarchical, zero-shot framework that cascades lightweight object detection with compact Vision-Language Models (VLMs) from the Qwen and Gemma families (4B-12B parameters). Grounding DINO serves as a high-recall, text-promptable region proposer, and frames with high detection confidence are passed to edge-class VLMs for semantic verification. We evaluate […]

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