February 2026

arXiv:2602.14642v1 Announce Type: new Abstract: Inverse problems and inverse design in multiphase media, i.e., recovering or engineering microstructures to achieve target macroscopic responses, require operating on discrete-valued material fields, rendering the problem non-differentiable and incompatible with gradient-based methods. Existing approaches either relax to continuous approximations, compromising physical fidelity, or employ separate heavyweight models for forward and inverse tasks. We propose GenPANIS, a unified generative framework that preserves exact discrete microstructures while enabling gradient-based inference through continuous latent embeddings. […]

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arXiv:2602.14520v1 Announce Type: new Abstract: Posterior inference from pulsar observations in the form of light curves is commonly performed using Markov chain Monte Carlo methods, which are accurate but computationally expensive. We introduce a framework that accelerates posterior inference while maintaining accuracy by combining learned latent representations with local simulator-guided optimization. A masked U-Net is first pretrained to reconstruct complete light curves from partial observations and to produce informative latent embeddings. Given a query light curve, we identify […]

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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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