January 2026

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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arXiv:2601.21478v1 Announce Type: cross Abstract: Pathophysiolpgical modelling of brain systems from microscale to macroscale remains difficult in group comparisons partly because of the infeasibility of modelling the interactions of thousands of neurons at the scales involved. Here, to address the challenge, we present a novel approach to construct differential causal networks directly from electroencephalogram (EEG) data. The proposed network is based on conditionally coupled neuronal circuits which describe the average behaviour of interacting neuron populations that contribute to […]

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arXiv:2601.21471v1 Announce Type: cross Abstract: We study fixed-confidence best-arm identification (BAI) where a cheap but potentially biased proxy (e.g., LLM judge) is available for every sample, while an expensive ground-truth label can only be acquired selectively when using a human for auditing. Unlike classical multi-fidelity BAI, the proxy is biased (arm- and context-dependent) and ground truth is selectively observed. Consequently, standard multi-fidelity methods can mis-select the best arm, and uniform auditing, though accurate, wastes scarce resources and is […]

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arXiv:2601.21470v1 Announce Type: cross Abstract: We study semi-supervised stochastic optimization when labeled data is scarce but predictions from pre-trained models are available. PPI and SVRG both reduce variance through control variates — PPI uses predictions, SVRG uses reference gradients. We show they are mathematically equivalent and develop PPI-SVRG, which combines both. Our convergence bound decomposes into the standard SVRG rate plus an error floor from prediction uncertainty. The rate depends only on loss geometry; predictions affect only the […]

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arXiv:2601.21301v1 Announce Type: cross Abstract: We present the convergence rates of synchronous and asynchronous Q-learning for average-reward Markov decision processes, where the absence of contraction poses a fundamental challenge. Existing non-asymptotic results overcome this challenge by either imposing strong assumptions to enforce seminorm contraction or relying on discounted or episodic Markov decision processes as successive approximations, which either require unknown parameters or result in suboptimal sample complexity. In this work, under a reachability assumption, we establish optimal $widetilde{O}(varepsilon^{-2})$ […]

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