February 2026

arXiv:2410.03919v2 Announce Type: replace-cross Abstract: Posterior sampling in contextual bandits with a Gaussian prior can be implemented exactly or approximately using the Laplace approximation. The Gaussian prior is computationally efficient but it cannot describe complex distributions. In this work, we propose approximate posterior sampling algorithms for contextual bandits with a diffusion model prior. The key idea is to sample from a chain of approximate conditional posteriors, one for each stage of the reverse diffusion process, which are obtained […]

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arXiv:2402.02644v4 Announce Type: replace-cross Abstract: Estimating the structure of Bayesian networks as directed acyclic graphs (DAGs) from observational data is a fundamental challenge, particularly in causal discovery. Bayesian approaches excel by quantifying uncertainty and addressing identifiability, but key obstacles remain: (i) representing distributions over DAGs and (ii) estimating a posterior in the underlying combinatorial space. We introduce PIVID, a method that jointly infers a distribution over permutations and DAGs using variational inference and continuous relaxations of discrete distributions. […]

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arXiv:2310.11736v4 Announce Type: replace-cross Abstract: We study feature learning in a compositional variant of kernel ridge regression in which the predictor is applied to a learnable linear transformation of the input. When the response depends on the input only through a low-dimensional predictive subspace, we show that all global minimizers of the population objective for the linear transformation annihilate directions orthogonal to this subspace, and in certain regimes, exactly identify the subspace. Moreover, we show that global minimizers […]

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arXiv:2112.06251v4 Announce Type: replace-cross Abstract: We propose a new regression algorithm that learns from a set of input-output pairs. Our algorithm is designed for populations where the relation between the input variables and the output variable exhibits a heterogeneous behavior across the predictor space. The algorithm starts with generating subsets that are concentrated around random points in the input space. This is followed by training a local predictor for each subset. Those predictors are then combined in a […]

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arXiv:2602.07132v2 Announce Type: replace Abstract: Computation methods for solving entropy-regularized reward optimization — a class of problems widely used for fine-tuning generative models — have advanced rapidly. Among those, Adjoint Matching (AM, Domingo-Enrich et al., 2025) has proven highly effective in continuous state spaces with differentiable rewards. Transferring these practical successes to discrete generative modeling, however, remains particularly challenging and largely unexplored, mainly due to the drastic shift in generative model classes to discrete state spaces, which are […]

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arXiv:2602.06797v2 Announce Type: replace Abstract: We study optimal learning-rate schedules (LRSs) under the functional scaling law (FSL) framework introduced in Li et al. (2025), which accurately models the loss dynamics of both linear regression and large language model (LLM) pre-training. Within FSL, loss dynamics are governed by two exponents: a source exponent $s>0$ controlling the rate of signal learning, and a capacity exponent $beta>1$ determining the rate of noise forgetting. Focusing on a fixed training horizon $N$, we […]

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arXiv:2602.06320v2 Announce Type: replace Abstract: Modern machine learning models are typically trained via multi-pass stochastic gradient descent (SGD) with small batch sizes, and understanding their dynamics in high dimensions is of great interest. However, an analytical framework for describing the high-dimensional asymptotic behavior of multi-pass SGD with small batch sizes for nonlinear models is currently missing. In this study, we address this gap by analyzing the high-dimensional dynamics of a stochastic differential equation called a emph{stochastic gradient flow} […]

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arXiv:2602.01427v2 Announce Type: replace Abstract: Few-shot learning requires models to generalize under limited supervision while remaining robust to distribution shifts. Existing Sinkhorn Distributionally Robust Optimization (DRO) methods provide theoretical guarantees but rely on a fixed reference distribution, which limits their adaptability. We propose a Prototype-Guided Distributionally Robust Optimization (PG-DRO) framework that learns class-adaptive priors from abundant base data via hierarchical optimal transport and embeds them into the Sinkhorn DRO formulation. This design enables few-shot information to be organically […]

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arXiv:2601.21812v2 Announce Type: replace Abstract: We introduce a model-agnostic forward diffusion process for time-series forecasting that decomposes signals into spectral components, preserving structured temporal patterns such as seasonality more effectively than standard diffusion. Unlike prior work that modifies the network architecture or diffuses directly in the frequency domain, our proposed method alters only the diffusion process itself, making it compatible with existing diffusion backbones (e.g., DiffWave, TimeGrad, CSDI). By staging noise injection according to component energy, it maintains […]

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arXiv:2511.19628v2 Announce Type: replace Abstract: This study investigates the limitations of applying Markov Chain Monte Carlo (MCMC) methods to arbitrary objective functions, focusing on a two-block MCMC framework which alternates between Metropolis-Hastings and Gibbs sampling. While such approaches are often considered advantageous for enabling data-driven regularization, we show that their performance critically depends on the sharpness of the employed likelihood form. By introducing a sharpness parameter and exploring alternative likelihood formulations proportional to the target objective function, we […]

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