Research Projects

Convergence Guarantees of Diffusion Models

Joint work with Kexin Fu and Farzan Farnia. Oct. 2023 - Present.

Preprint: On the Mode-Seeking Properties of Langevin Dynamics

• Formulated high-dimensional multi-modal distributions with an inter-mode component
• Theoretically studied the mode-seeking tendencies of Langevin dynamics
• Proposed Chained Langevin Dynamics and provided a provable convergence guarantee
• Validated the theoretical analysis through numerical experiments [github]

Stability and Generalization of Min-Max Optimization

Joint work with Kexin Fu and Farzan Farnia. Sep. 2022 - Oct. 2023.

Paper: Stability and Generalization in Free Adversarial Training

Journal: Transactions on Machine Learning Research (TMLR), 2024.

• Analyzed the algorithmic stability of free, fast, and vanilla adversarial training algorithms
• Provided theoretical comparisons of the generalization properties of the algorithms
• Proposed Free-TRADES with improved generalization performance
• Validated the theoretical analysis through numerical experiments [github]

Learning and Testing Dependent Discrete Distributions

Joint work with Haitong Liu and Siu On Chan. June 2022 - May 2023.

Graduation Project Report: On the Lower Bounds for Learning and Testing Markov Chains

• Analyzed the problem of learning and testing dependent distributions from Markovian trajectories
• Proved a lower bound on the sample complexity of learning Markov chains
• Demonstrated the order-wise optimality of the k-cover-time algorithm

Iterative Methods for Non-Convex Optimization

Joint work with Sijin Chen and Anthony Man-Cho So. June 2021 - Jan. 2022.

Paper: Non-Convex Joint Community Detection and Group Synchronization via Generalized Power Method

Conference: International Conference on Artificial Intelligence and Statistics (AISTATS), 2024.

• Analyzed the non-convex optimization problem of joint group synchronization and community detection
• Proposed a generalized power method (GPM) with spectral initialization
• Established the linear convergence guarantee for GPM and an error bound for spectral initialization
• Demonstrated its significantly lower complexity than the previous semidefinite relaxation methods

Information-Theoretical Analysis of Group Testing

Joint work with Sidharth Jaggi and Qiaoqiao Zhou. June 2020 - March 2022.

Paper: Generalized Group Testing

Conference: International Conference on Artificial Intelligence and Statistics (AISTATS), 2022.

Journal: IEEE Transactions on Information Theory (TIT), March 2023.

• Unified different group testing problem settings including noisy and threshold group testing
• Proposed a non-adaptive probabilistic testing scheme with provable recovery guarantees
• Established novel information-theoretical lower bounds on test complexity
• Proved the order-wise optimality of the proposed scheme under noisy settings