AI-generated videos have achieved near-perfect visual realism (e.g., Sora), urgently necessitating reliable detection mechanisms. However, detecting such videos faces significant challenges in modeling high-dimensional spatiotemporal dynamics and identifying subtle anomalies that violate physical laws. In this paper, we propose a physics-driven AI-generated video detection paradigm based on probability flow conservation principles. Specifically, we propose a statistic called Normalized Spatiotemporal Gradient (NSG), which quantifies the ratio of spatial probability gradients to temporal density changes, explicitly capturing deviations from natural video dynamics. Leveraging pre-trained diffusion models, we develop an NSG estimator through spatial gradients approximation and motion-aware temporal modeling without complex motion decomposition while preserving physical constraints. Building on this, we propose an NSG-based video detection method (NSG-VD) that computes the Maximum Mean Discrepancy (MMD) between NSG features of the test and real videos as a detection metric. Last, we derive an upper bound of NSG feature distances between real and generated videos, proving that generated videos exhibit amplified discrepancies due to distributional shifts. Extensive experiments confirm that NSG-VD outperforms state-of-the-art baselines by 16.00% in Recall and 10.75% in F1-Score, validating the superior performance of NSG-VD. The source code is available at https://github.com/ZSHsh98/NSG-VD.

Online advertising platforms use automated auctions to connect advertisers with potential customers, requiring effective bidding strategies to maximize profits. Accurate ad impact estimation requires considering three key factors: delayed and long-term effects, cumulative ad impacts such as reinforcement or fatigue, and customer heterogeneity. However, these effects are often not jointly addressed in previous studies. To capture these factors, we model ad bidding as a Contextual Markov Decision Process (CMDP) with delayed Poisson rewards. For efficient estimation, we propose a two-stage maximum likelihood estimator combined with data-splitting strategies, ensuring controlled estimation error based on the first-stage estimator's (in)accuracy. Building on this, we design a reinforcement learning algorithm to derive efficient personalized bidding strategies. This approach achieves a near-optimal regret bound of O(dH2 T), where d is the contextual dimension, H is the number of rounds, and T is the number of customers. Our theoretical findings are validated by simulation experiments.

We prove rich algebraic structures of the solution space for 2-layer neural networks with quadratic activation and L2 loss, trained on reasoning tasks in Abelian group (e.g., modular addition). Such a rich structure enables analytical construction of global optimal solutions from partial solutions that only satisfy part of the loss, despite its high nonlinearity.

We introduce Neural Green's Function, a neural solution operator for linear partial dif sitions.

Discrete diffusion models, like continuous diffusion models, generate high-quality samples by gradually undoing noise applied to datapoints with a Markov process. Gradual generation in theory comes with many conceptual benefits; for example, inductive biases can be incorporated into the noising Markov process, and access to improved sampling algorithms. In practice, however, the consistently best performing discrete diffusion model is, surprisingly, masking diffusion, which does not denoise gradually. Here we explain the superior performance of masking diffusion by noting that it makes use of a fundamental difference between continuous and discrete Markov processes: discrete Markov processes evolve by discontinuous jumps at a fixed rate and, unlike other discrete diffusion models, masking diffusion builds in the known distribution of jump times and only learns where to jump to. We show that we can similarly bake in the known distribution of jump times into any discrete diffusion model. The resulting models -- schedule-conditioned diffusion (SCUD) -- generalize classical discrete diffusion and masking diffusion. By applying SCUD to models with noising processes that incorporate inductive biases on images, text, and protein data, we build models that outperform masking.

Contrastive Representation Learning (CRL) has achieved strong empirical success in multiple machine learning disciplines, yet its theoretical sample complexity remains poorly understood. Existing analyses usually assume that input tuples are identically and independently distributed, an assumption violated in most practical settings where contrastive tuples are constructed from a finite pool of labeled data, inducing dependencies among tuples. While one recent work analyzed this learning setting using U-Statistics to estimate the population risk, the techniques used therein require the risk of each class to concentrate uniformly, making excess risk bounds scale in the order of $ρ_{\min}^{-{1}/{2}}$ where $ρ_{\min}$ denotes the probability of the rarest class. Such a dependency can be overly pessimistic in the extreme multiclass settings where there are many tail classes which contribute minimally to the overall population risk. Our contributions are two-fold. Firstly, we improve upon the previous work and prove a bound with a sample complexity of the same order as the number of classes $R$, regardless of the distribution over classes. Furthermore, we formulate a different estimator that captures the concentration of the risk \textit{across classes}, enabling sharper bounds in extreme multi-class learning scenarios, especially where class distributions are long-tailed. Under mild assumptions on the class distributions, the resulting sample complexity is $\mathcal{O}(k)$ where $k$ is the number of samples per tuple.

Gaussian mixture models (GMMs) are fundamental to machine learning due to their flexibility as approximating densities. However, uncertainty quantification of GMMs remains a challenge as differential entropy lacks a closed form. This paper explores polynomial approximations, specifically Taylor and Legendre, to the GMM entropy from a theoretical and practical perspective. We provide new analysis of a widely used approach due to Huber et al. (2008) and show that the series diverges under simple conditions. Motivated by this divergence we provide a novel Taylor series that is provably convergent to the true entropy of any GMM.

We revisit the classical problem of designing Budget-Feasible Mechanisms (BFMs) for submodular valuation functions, which has been extensively studied since the seminal paper of Singer [FOCS'10] due to its wide applications in crowdsourcing and social marketing. We propose TripleEagle, a novel algorithmic framework for designing BFMs, based on which we present several simple yet effective BFMs that achieve better approximation ratios than the state-of-the-art work for both monotone and non-monotone submodular valuation functions. Moreover, our BFMs are the first in the literature to achieve linear complexities while ensuring obvious strategyproofness, making them more practical than the previous BFMs. We conduct extensive experiments to evaluate the empirical performance of our BFMs, and the experimental results strongly demonstrate the efficiency and effectiveness of our approach.

Let's consider a student perceptron with M synaptic populations indexed by m, wm, such that each wmi satisfies its own distributions constraints wmi Qm(wm).