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.