January 2026

arXiv:2601.21873v1 Announce Type: cross Abstract: Learning systems often expand their ambient features or latent representations over time, embedding earlier representations into larger spaces with limited new latent structure. We study transfer learning for structured matrix estimation under simultaneous growth of the ambient dimension and the intrinsic representation, where a well-estimated source task is embedded as a subspace of a higher-dimensional target task. We propose a general transfer framework in which the target parameter decomposes into an embedded source […]

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arXiv:2601.21860v1 Announce Type: cross Abstract: The reconstruction and inference of stochastic dynamical systems from data is a fundamental task in inverse problems and statistical learning. While surrogate modeling advances computational methods to approximate these dynamics, standard approaches typically require high-fidelity training data. In many practical settings, the data are indirectly observed through noisy and nonlinear measurement. The challenge lies not only in approximating the coefficients of the SDEs, but in simultaneously inferring the posterior updates given the observations. […]

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arXiv:2601.21856v1 Announce Type: cross Abstract: Ultrasound (US) interpretation is hampered by multiplicative speckle, acquisition blur from the point-spread function (PSF), and scanner- and operator-dependent artifacts. Supervised enhancement methods assume access to clean targets or known degradations; conditions rarely met in practice. We present a blind, self-supervised enhancement framework that jointly deconvolves and denoises B-mode images using a Swin Convolutional U-Net trained with a emph{physics-guided} degradation model. From each training frame, we extract rotated/cropped patches and synthesize inputs by […]

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arXiv:2601.21789v1 Announce Type: cross Abstract: We introduce ECSEL, an explainable classification method that learns formal expressions in the form of signomial equations, motivated by the observation that many symbolic regression benchmarks admit compact signomial structure. ECSEL directly constructs a structural, closed-form expression that serves as both a classifier and an explanation. On standard symbolic regression benchmarks, our method recovers a larger fraction of target equations than competing state-of-the-art approaches while requiring substantially less computation. Leveraging this efficiency, ECSEL […]

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arXiv:2601.21765v1 Announce Type: cross Abstract: We consider Bayesian variable selection for binary outcomes under a probit link with a spike-and-slab prior on the regression coefficients. Motivated by the computational challenges encountered by Markov chain Monte Carlo (MCMC) samplers in high-dimensional regimes, we develop a mean-field variational Bayes approximation in which all variational factors admit closed-form updates, and the evidence lower bound is available in closed form. This, in turn, allows the development of an efficient coordinate ascent variational […]

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arXiv:2601.21739v1 Announce Type: cross Abstract: Adam has been at the core of large-scale training for almost a decade, yet a simple empirical fact remains unaccounted for: both validation scores and the qualitative behaviour of the training runs improve when the momentum parameters satisfy $beta_{1}=beta_{2}$. Some recent studies have reported this pattern, but there is still no explanation for why this choice helps. We show that this choice is closely tied to a structural property that we refer to […]

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arXiv:2601.21719v1 Announce Type: cross Abstract: We introduce the (Wishart) projection mechanism, a randomized map of the form $S mapsto M f(S)$ with $M sim W_d(1/r I_d, r)$ and study its differential privacy properties. For vector-valued queries $f$, we prove non-asymptotic DP guarantees without any additive noise, showing that Wishart randomness alone can suffice. For matrix-valued queries, however, we establish a sharp negative result: in the noise-free setting, the mechanism is not DP, and we demonstrate its vulnerability by […]

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arXiv:2601.21696v1 Announce Type: cross Abstract: Advances in data collection are producing growing volumes of temporal count observations, making adapted modeling increasingly necessary. In this work, we introduce a generative framework for independent component analysis of temporal count data, combining regime-adaptive dynamics with Poisson log-normal emissions. The model identifies disentangled components with regime-dependent contributions, enabling representation learning and perturbations analysis. Notably, we establish the identifiability of the model, supporting principled interpretation. To learn the parameters, we propose an efficient […]

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arXiv:2601.21636v1 Announce Type: cross Abstract: We study privacy amplification for differentially private model training with matrix factorization under random allocation (also known as the balls-in-bins model). Recent work by Choquette-Choo et al. (2025) proposes a sampling-based Monte Carlo approach to compute amplification parameters in this setting. However, their guarantees either only hold with some high probability or require random abstention by the mechanism. Furthermore, the required number of samples for ensuring $(epsilon,delta)$-DP is inversely proportional to $delta$. In […]

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arXiv:2601.21522v1 Announce Type: cross Abstract: The performance of large language models (LLMs) on verifiable tasks is usually measured by pass@k, the probability of answering a question correctly at least once in k trials. At a fixed budget, a more suitable metric is coverage@cost, the average number of unique questions answered as a function of the total number of attempts. We connect the two metrics and show that the empirically-observed power-law behavior in pass@k leads to a sublinear growth […]

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