The proliferation of Large Language Models (LLMs) necessitates efficient mechanisms to distinguish machine-generated content from human text. While statistical watermarking has emerged as a promising solution, existing methods suffer from two critical limitations: the lack of a principled approach for selecting sampling distributions and the reliance on fixed-horizon hypothesis testing, which precludes valid early stopping. In this paper, we bridge this gap by developing the first e-value-based watermarking framework, Anchored E-Watermarking, that unifies optimal sampling with anytime-valid inference. Unlike traditional approaches where optional stopping invalidates Type-I error guarantees, our framework enables valid, anytime-inference by constructing a test supermartingale for the detection process. By leveraging an anchor distribution to approximate the target model, we characterize the optimal e-value with respect to the worst-case log-growth rate and derive the optimal expected stopping time. Our theoretical claims are substantiated by simulations and evaluations on established benchmarks, showing that our framework can significantly enhance sample efficiency, reducing the average token budget required for detection by 13-15% relative to state-of-the-art baselines.

Partial Differential Equations (PDEs) is still lacking. This study introduces PIN-Nacle, a benchmarking tool designed to fill this gap.

Recently, data-driven approaches for weather forecasting based on deep learning have shown great promise, achieving accuracies that are competitive with operational systems. However, those methods often employ complex, customized architectures without sufficient ablation analysis, making it difficult to understand what truly contributes to their success.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

In this paper, the solution to the empirical risk minimization problem with $f$-divergence regularization (ERM-$f$DR) is presented and conditions under which the solution also serves as the solution to the minimization of the expected empirical risk subject to an $f$-divergence constraint are established. The proposed approach extends applicability to a broader class of $f$-divergences than previously reported and yields theoretical results that recover previously known results. Additionally, the difference between the expected empirical risk of the ERM-$f$DR solution and that of its reference measure is characterized, providing insights into previously studied cases of $f$-divergences. A central contribution is the introduction of the normalization function, a mathematical object that is critical in both the dual formulation and practical computation of the ERM-$f$DR solution. This work presents an implicit characterization of the normalization function as a nonlinear ordinary differential equation (ODE), establishes its key properties, and subsequently leverages them to construct a numerical algorithm for approximating the normalization factor under mild assumptions. Further analysis demonstrates structural equivalences between ERM-$f$DR problems with different $f$-divergences via transformations of the empirical risk. Finally, the proposed algorithm is used to compute the training and test risks of ERM-$f$DR solutions under different $f$-divergence regularizers. This numerical example highlights the practical implications of choosing different functions $f$ in ERM-$f$DR problems.

The rapid growth of high-dimensional datasets across various scientific domains has created a pressing need for new statistical methods to compare distributions supported on their underlying structures. Assessing similarity between datasets whose samples lie on low-dimensional manifolds requires robust techniques capable of separating meaningful signal from noise. We propose a principled framework for statistical inference of similarity and alignment between distributions supported on manifolds underlying high-dimensional datasets in the presence of heterogeneous noise. The key idea is to link the low-rank structure of observed data matrices to their underlying manifold geometry. By analyzing the spectrum of the sample covariance under a manifold signal-plus-noise model, we develop a scale-invariant distance measure between datasets based on their principal variance structures. We further introduce a consistent estimator for this distance and a statistical test for manifold alignability, and establish their asymptotic properties using random matrix theory. The proposed framework accommodates heterogeneous noise across datasets and offers an efficient, theoretically grounded approach for comparing high-dimensional datasets with low-dimensional manifold structures. Through extensive simulations and analyses of multi-sample single-cell datasets, we demonstrate that our method achieves superior robustness and statistical power compared with existing approaches.

Off-policy model-free deep reinforcement learning methods using previously collected data can improve sample efficiency over on-policy policy gradient techniques. On the other hand, on-policy algorithms are often more stable and easier to use. This paper examines, both theoretically and empirically, approaches to merging on-and off-policy updates for deep reinforcement learning.

Hyperspectral image (HSI) classification typically involves large-scale data and computationally intensive training, which limits the practical deployment of deep learning models in real-world remote sensing tasks. This study introduces SpectralTrain, a universal, architecture-agnostic training framework that enhances learning efficiency by integrating curriculum learning (CL) with principal component analysis (PCA)-based spectral downsampling. By gradually introducing spectral complexity while preserving essential information, SpectralTrain enables efficient learning of spectral -- spatial patterns at significantly reduced computational costs. The framework is independent of specific architectures, optimizers, or loss functions and is compatible with both classical and state-of-the-art (SOTA) models. Extensive experiments on three benchmark datasets -- Indian Pines, Salinas-A, and the newly introduced CloudPatch-7 -- demonstrate strong generalization across spatial scales, spectral characteristics, and application domains. The results indicate consistent reductions in training time by 2-7x speedups with small-to-moderate accuracy deltas depending on backbone. Its application to cloud classification further reveals potential in climate-related remote sensing, emphasizing training strategy optimization as an effective complement to architectural design in HSI models. Code is available at https://github.com/mh-zhou/SpectralTrain.