Diffusion models, which generate new data instances by learning to reverse a Markov diffusion process from noise, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the theoretical underpinnings remain underdeveloped. Particularly, despite the recent surge of interest in accelerating sampling speed, convergence theory for these acceleration techniques remains limited. In this talk, I will first introduce an acceleration sampling scheme for stochastic samplers that provably improves the iteration complexity under minimal assumptions. The second part focuses on diffusion-based language models, whose ability to generate tokens in parallel significantly accelerates sampling relative to traditional autoregressive methods. Adopting an information-theoretic lens, we establish a sharp convergence theory for diffusion language models, thereby providing the first rigorous justification of both their efficiency and fundamental limits.

Dr.Difan Zou is an assistant professor in computer science department and institute of data science at HKU. He has received his PhD degree in Department of Computer Science, University of California, Los Angeles (UCLA).  His research interests are broadly in machine learning, deep learning theory, graph learning, mechanism interpretation, and interdisciplinary research between AI and other subjects. His research is published in top-tier machine learning conferences (ICML, NeurIPS, COLT, ICLR) and journal papers (IEEE Trans., JMLR, Nature Comm., PNAS, etc.). He serves as an area chair/senior PC member for NeurIPS, ICML and AAAI, and PC members for ICLR, COLT, etc.

While Reinforcement Learning (RL) and Fine-Tuning demonstrably enhance Large Language Model (LLM) capabilities, particularly in reasoning and task adaptation, the underlying mechanisms remain poorly understood. This talk integrates insights from two complementary studies to advance mechanistic interpretability. First, we dissect Reinforcement Learning with Verifiable Rewards (RLVR), revealing its core benefit lies in optimizing the selection of existing high-success-rate reasoning patterns, with theoretical convergence analyses showing distinct dynamics for strong versus weak initial models (mitigated by prior supervised fine-tuning). Second, we employ circuit analysis to interpret fine-tuning mechanisms, uncovering that circuits undergo significant edge changes rather than merely adding components, contrasting prior findings. Leveraging this, we develop a circuit-aware LoRA method, improving performance over standard LoRA by 2.46%. Furthermore, we explore combining circuits for compositional tasks. Together, these studies provide novel theoretical and empirical insights: RL enhances reasoning primarily through pattern selection, while fine-tuning fundamentally rewires circuit connections. This deeper understanding informs the design of more effective and interpretable adaptation strategies for LLMs.