Chain-of-Thought (CoT) prompting and its variants have gained significant attention as effective methods for solving multi-step reasoning tasks with pretrained large language models (LLMs). However, their theoretical underpinnings remain insufficiently explored. We analyze CoT prompting from a statistical perspective, offering insights into why “pretrained LLMs + CoT prompting” performs well. Additionally, we examine the role of the transformer architecture and the inclusion of intermediate reasoning steps in enhancing performance. We introduce a multi-step latent variable model to capture the reasoning process. In this model, we show that the estimator induced by CoT prompting approximates a Bayesian estimator that solves the reasoning task by inferring the posterior distribution from examples in the prompt. We prove that the statistical error of the CoT estimator consists of (i) a prompting error, which is incurred in inferring the desired task from the prompt, and (ii) a pretraining error, which is the statistical error of the pretrained LLM. We further prove that the prompting error decreases exponentially as the number of examples in the prompt increases. For the pretrained LLM, we construct a transformer model class that explicitly approximates the target distribution and establish the generalization error under the Pac-Bayes framework.

Auto-Regressive Video Diffusion Models (AR-VDMs) have shown strong capabilities in generating long, photorealistic videos, but suffer from two key limitations: (i) history forgetting, where the model loses track of previously generated content, and (ii) temporal degradation, where frame quality deteriorates over time. Yet a rigorous theoretical analysis of these phenomena is lacking, and existing empirical understanding remains insufficiently grounded. In this paper, we introduce Meta-ARVDM, a unified analytical framework that studies both errors through the shared autoregressive structure of AR-VDMs. We show that history forgetting is characterized by the conditional mutual information between the generated output and preceding frames, conditioned on inputs, and prove that incorporating more past frames monotonically alleviates history forgetting, thereby theoretically justifying a common belief in existing works. Moreover, our theory reveals that standard metrics fail to capture this effect, motivating a new evaluation protocol based on a “needle-in-a-haystack” task in closed-ended environments (DMLab and Minecraft). We further show that temporal degradation can be quantified by the cumulative sum of per-step errors, enabling prediction of degradation for different schedulers without video rollout. Finally, our evaluation uncovers a strong empirical correlation between history forgetting and temporal degradation, a connection not previously reported.

This paper studies minimax optimization problems defined over infinite-dimensional function classes of over-parameterized two-layer neural networks. In particular, we consider the minimax optimization problem stemming from estimating linear functional equations defined by conditional expectations, where the objective functions are quadratic in the functional spaces. We address (i) the convergence of the stochastic gradient descent-ascent algorithm and (ii) the representation learning of the neural networks. We establish convergence in the mean-field regime by considering the continuous-time, infinite-width limit of the optimization dynamics. Under this regime, stochastic gradient descent-ascent corresponds to a Wasserstein gradient flow over the space of probability measures defined over the space of neural network parameters. We prove that the Wasserstein gradient flow converges globally to a stationary point of the minimax objective at a $\mathcal{O}(T^{-1} + \alpha^{-1} ) $ sublinear rate, and additionally finds the solution to the functional equation when the regularizer of the minimax objective is strongly convex. Here $T$ denotes the time and $\alpha$ is a scaling parameter of the neural networks. In terms of representation learning, our results show that the feature representation induced by the neural networks may deviate from the initial representation by a factor of $\mathcal{O}(\alpha^{-1})$, measured by the Wasserstein distance. Finally, we apply our general results to concrete examples, including policy evaluation, nonparametric instrumental variable regression, and asset pricing.

We study reserve price optimization in multi-phase second price auctions, where the seller's prior actions affect the bidders' later valuations through a Markov Decision Process (MDP). Compared to the bandit setting in existing works, the setting in ours involves three challenges. First, from the seller's perspective, we need to efficiently explore the environment in the presence of potentially untruthful bidders who aim to manipulate the seller's policy. Second, we want to minimize the seller's revenue regret when the market noise distribution is unknown. Third, the seller's per-step revenue is an unknown, nonlinear random variable, and cannot even be directly observed from the environment but realized values. We propose a mechanism addressing all three challenges. To address the first challenge, we use a combination of a new technique named “buffer periods” and inspirations from Reinforcement Learning (RL) with low switching cost to limit bidders' surplus from untruthful bidding, thereby incentivizing approximately truthful bidding. The second one is tackled by a novel algorithm that removes the need for pure exploration when the market noise distribution is unknown. The third challenge is resolved by an extension of LSVI-UCB, where we use the auction's underlying structure to control the uncertainty of the revenue function. The three techniques culminate in the \underline{C}ontextual-\underline{L}SVI-\underline{U}CB-\underline{B}uffer (CLUB) algorithm which achieves $\tilde{\mathcal{O}}(H^{5/2}\sqrt{K})$ revenue regret, where $K$ is the number of episodes and $H$ is the length of each episode, when the market noise is known and $\tilde{\mathcal{O}}(H^{3}\sqrt{K})$ revenue regret when the noise is unknown with no assumptions on bidders' truthfulness.