We present an information-theoretic framework for discrete diffusion models that yields principled estimators of log-likelihood using score-matching losses. Inspired by the I-MMSE identity for the Gaussian setup, we derive analogous results for the discrete setting. Specifically, we introduce the Information-Minimum Denoising Score Entropy (I-MDSE) relation, which links mutual information between data and its diffused version to the minimum denoising score entropy (DSE) loss. We extend this theory to masked diffusion and establish the Information-Minimum Denoising Cross-Entropy (I-MDCE) relation, connecting cross-entropy losses to mutual information in discrete masked processes. These results provide a timeintegral decomposition of the log-likelihood of the data in terms of optimal scorebased losses, showing that commonly used losses such as DSE and DCE are not merely variational bounds but tight and principled estimators of log-likelihood. The I-MDCE decomposition further enables practical extensions, including time-free formula, conditional likelihood estimation in prompt-response tasks, and coupled Monte Carlo estimation of likelihood ratios. Experiments on synthetic and realworld data confirm the accuracy, variance stability, and utility of our estimators.

Current document retrieval-augmented generation (DocRAG) Therefore, the number of female respondents who never listened to theradio is: Number of females who never listened = 2,001 * 0.557 = 1,115 methods remain limited by their text-centric approaches, frequently missing "text12": [ "The table provides a

Numerous well-established studies have demonstrated the superhuman capabilities of modern Vision-Language Models (VLMs) across a wide range of tasks. However, growing is the doubt about the continuing availability of reliable high-quality labeling (supervision) from human annotators, leading to stagnation of the model's performance. To address this challenge, "superalignment" employs the so-called weak-to-strong generalization paradigm, where the supervision from a weak model can provide generalizable knowledge for a strong model. While effective in aligning knowledge for clean samples between the strong and weak models, the standard weak-to-strong approach typically fails to capture adversarial robustness, exposing strong VLMs to adversarial attacks. This inability to transfer adversarial robustness is because adversarial samples are normally missing in the superalignment stage. To this end, we are the first to propose the weak-to-strong (adversarial) robustness generalization method to elicit zero-shot robustness in large-scale models by an unsupervised scheme, mitigating the unreliable information source for alignment from two perspectives: alignment re-weighting and source guidance refinement. We analyze settings under which robustness generalization is possible.

Recently, 3DGaussian Splatting (3DGS) has emerged as a powerful alternative to NeRF-based approaches, enabling real-time, high-quality novel view synthesis through explicit, optimizable 3DGaussians. However, 3DGS suffers from significant memory overhead due to its reliance on per-Gaussian parameters to model view-dependent effects and anisotropic shapes. While recent works propose compressing 3DGS with neural fields, these methods struggle to capture high-frequency spatial variations in Gaussian properties, leading to degraded reconstruction of fine details. We present Hybrid Radiance Fields (HyRF), a novel scene representation that combines the strengths of explicit Gaussians and neural fields. HyRF decomposes the scene into (1) a compact set of explicit Gaussians storing only critical high-frequency parameters and (2) grid-based neural fields that predict remaining properties. To enhance representational capacity, we introduce a decoupled neural field architecture, separately modeling geometry (scale, opacity, rotation) and view-dependent color. Additionally, we propose a hybrid rendering scheme that composites Gaussian splatting with a neural field-predicted background, addressing limitations in distant scene representation. Experiments demonstrate that HyRF achieves state-of-the-art rendering quality while reducing model size by over 20 compared to 3DGS and maintaining real-time performance. Our project page is available at https://wzpscott.github.io/hyrf/.

Multi-view clustering aims to enhance clustering performance by leveraging information from diverse sources. However, its practical application is often hindered by a barrier: the lack of correspondences across views. This paper focuses on the understudied problem of fully incomplete multi-view clustering (FIMC), a scenario where existing methods fail due to their reliance on partial alignment. To address this problem, we introduce the Contrastive Prototype Matching Network (CPMN), a novel framework that establishes a new paradigm for cross-view alignment based on matching high-level categorical structures. Instead of aligning individual instances, CPMN performs a more robust cluster prototype alignment. CPMN first employs a correspondence-free graph contrastive learning approach, leveraging mutual k-nearest neighbors (MNN) to uncover intrinsic data structures and establish initial prototypes from entirely unpaired views. Building on the prototypes, we introduce a cross-view prototype graph matching stage to resolve category misalignment and forge a unified clustering structure. Finally, guided by this alignment, we devise a prototype-aware contrastive learning mechanism to promote semantic consistency, replacing the reliance on the initial MNN-based structural similarity. Extensive experiments on benchmark datasets demonstrate that our method significantly outperforms various baselines and ablation variants, validating its effectiveness.

We propose a novel regularization loss that enforces standard Gaussianity, encouraging samples to align with a standard Gaussian distribution.

We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample complexity of replicably testing natural properties of the underlying distributions. On the algorithmic front, we develop new replicable algorithms for testing closeness and independence of discrete distributions. On the lower bound front, we develop a new methodology for proving sample complexity lower bounds for replicable testing that may be of broader interest. As an application of our technique, we establish near-optimal sample complexity lower bounds for replicable uniformity testing--answering an open question from prior work--and closeness testing.

Adam is a popular and widely used adaptive gradient method in deep learning, which has also received tremendous focus in theoretical research. However, most existing theoretical work primarily analyzes its full-batch version, which differs fundamentally from the stochastic variant used in practice. Unlike SGD, stochastic Adam does not converge to its full-batch counterpart even with infinitesimal learning rates. We present the first theoretical characterization of how batch size affects Adam's generalization, analyzing two-layer over-parameterized CNNs on image data. Our results reveal that while both Adam and AdamW with proper weight decay λ converge to poor test error solutions, their mini-batch variants can achieve near-zero test error. We further prove Adam has a strictly smaller effective weight decay bound than AdamW, theoretically explaining why Adam requires more sensitive λtuning.

Fair classification is a critical challenge that has gained increasing importance due to international regulations and its growing use in high-stakes decision-making settings. Existing methods often rely on adversarial learning or distribution matching across sensitive groups; however, adversarial learning can be unstable, and distribution matching can be computationally intensive. To address these limitations, we propose a novel approach based on the characteristic function distance. Our method ensures that the learned representation contains minimal sensitive information while maintaining high effectiveness for downstream tasks. By utilizing characteristic functions, we achieve a more stable and efficient solution compared to traditional methods. Additionally, we introduce a simple relaxation of the objective function that guarantees fairness in common classification models with no performance degradation. Experimental results on benchmark datasets demonstrate that our approach consistently matches or achieves better fairness and predictive accuracy than existing methods. Moreover, our method maintains robustness and computational efficiency, making it a practical solution for real-world applications.

However, existing algorithms either require strict monotonicity or only guarantee the convergence of averaged iterates, as in Fictitious Play in continuous time. We address this gap with the following theoretical result. First, we prove that the last-iterated policy of a proximal-point (PP) update with KL regularization converges to an equilibrium of MFG under non-strict monotonicity. Second, we see that each PP update is equivalent to finding the equilibria of a KL-regularized MFG. We then prove that this equilibrium can be found using Mirror Descent (MD) with an exponential last-iterate convergence rate. Building on these insights, we propose the Approximate Proximal-Point (APP) algorithm, which approximately implements the PP update via a small number of MD steps. Numerical experiments on standard benchmarks confirm that the APP algorithm reliably converges to the unregularized mean-field equilibrium without time-averaging.