Zhangsong Li
Hello! I am a third-year Ph.D student in School of Mathematical Sciences at Peking University, where I am fortunate to be advised by Jian Ding. Previously, I obtained my B.S. degree in mathematics from Peking University.
My research interest lies in the intersection of probability, statistical inference and theoretical computer science.
Links: CV (last update: April 2026), arXiv preprint, Google Scholar.
Email: ramblerlzs at pku dot edu dot cn.
Research
- Algorithmic Contiguity from Low-Degree Heuristic II: Predicting Detection-Recovery Gaps
Zhangsong Li
[arXiv]
- Fundamental Limits of Community Detection in Contextual Multi-Layer Stochastic Block Models
Shuyang Gong, Dong Huang, Zhangsong Li
[arXiv]
- The Algorithmic Phase Transition in Correlated Spiked Models
Zhangsong Li
[arXiv] [Slides]
- Detecting Correlation Efficiently in Stochastic Block Models: Breaking Otter’s Threshold in the Entire Supercritical Regime
Guanyi Chen, Jian Ding, Shuyang Gong, Zhangsong Li
[arXiv]
- A Smooth Computational Transition in Tensor PCA
Zhangsong Li
[arXiv] [Slides]
- Detection and Reconstruction of a Random Hypergraph from Noisy Graph Projection
Shuyang Gong, Zhangsong Li, Qiheng Xu
Conference version to appear in ISIT 2026.
[arXiv] [Slides]
- Asymptotic Diameter of Preferential Attachment Model
Hang Du, Shuyang Gong, Zhangsong Li, Haodong Zhu
Electronic Communications in Probability, 31:1--12, 2026.
[arXiv] [Journal] [Slides]
- A Computational Transition for Detecting Multivariate Shuffled Linear Regression by Low-Degree Polynomials
Zhangsong Li
IEEE Transactions on Information Theory, 72(4):2444--2456, 2026.
[arXiv] [Journal]
- Detecting Correlation Efficiently in Very Supercritical Stochastic Block Models: Breaking the Otter's Threshold Barrier
Guanyi Chen, Jian Ding, Shuyang Gong, Zhangsong Li
Conference version in Proceedings of 37th SODA, pages 2743--2759, 2026.
[Conference] [Full version]
- Algorithmic Contiguity from Low-Degree Conjecture and Applications in Correlated Random Graphs
Zhangsong Li
Conference version in Proceedings of 29th APPROX/RANDOM, pages 30:1--30:18, 2025.
[arXiv] [Conference] [Slides]
- Robust Random Graph Matching in Dense Graphs via an Approximate Message Passing Type Algorithm
Zhangsong Li
IEEE Transactions on Information Theory, to appear.
Conference version in Proceedings of 38th COLT, pages 3580--3581, 2025.
[arXiv] [Conference] [Slides]
- A Computational Transition for Detecting Correlated Stochastic Block Models by Low-Degree Polynomials
Guanyi Chen, Jian Ding, Shuyang Gong, Zhangsong Li
Annals of Statistics, 54(1):226--251, 2026.
[arXiv] [Journal] [Slides by Jian Ding]
- The Umeyama Algorithm for Matching Correlated Gaussian Geometric Models in the Low-Dimensional Regime
Shuyang Gong, Zhangsong Li
[arXiv] [Slides by Shuyang Gong]
- Low-Degree Hardness of Detection for Correlated Erdős-Rényi Graphs
Jian Ding, Hang Du, Zhangsong Li
Annals of Statistics, 53(5):1833--1856, 2025.
[arXiv] [Journal] [Slides]
- A Polynomial-Time Iterative Algorithm for Random Graph Matching with Non-vanishing Correlation
Jian Ding, Zhangsong Li
Mathematics of Operations Research, online 2025.
[arXiv] [Journal] [Poster]
- A Polynomial Time Iterative Algorithm for Matching Gaussian Matrices with Non-vanishing Correlation
Jian Ding, Zhangsong Li
Foundations of Computational Mathematics, 25(4):1287--1344, 2025.
[arXiv] [Journal] [Slides]
Miscellaneous
- On Injectivity of Phase Retrieval
Zhangsong Li
[arXiv]
- Improved Computational Lower Bound of Estimation for Multi-Frequency Group Synchronization
Zhangsong Li
[arXiv]
Talks
- The 59th IEEE International Symposium on Information Theory. Detection and reconstruction of a random hypergraph from noisy graph projection. July 2026, Guangzhou, China.
- AMSS Stochastic Analysis Seminar (Chinese Academy of Sciences). Recent progress on tensor PCA: From Kikuchi spectral algorithm to tensor networks. June 2026, Beijing, China.
- Peking University Sino-Russian Student Mathematical Seminar. The algorithmic phase transition for correlated spiked models. December 2025, Beijing, China.
- The 29th International Conference on Randomization and Computation. Algorithmic contiguity from low-degree conjecture and applications in correlated random graphs. August 2025, Berkeley, United States.
- The 38th Annual Conference on Learning Theory. Robust random graph matching in Gaussian models via vector approximate message passing. July 2025, Lyon, France.
- International Conference on Applied Probability. Robust random graph matching in Gaussian models via vector approximate message passing. June 2025, Beijing, China.
- YMSC Probability Seminar. Asymptotic diameter of preferential attachment model (joint with Shuyang Gong). May 2025, Beijing, China.
- Tsinghua University Statistics Seminar. Recent progress on random graph matching problems. March 2025, Beijing, China.
- Tsinghua Sanya International Mathematics Forum. Low-degree hardness of detection for correlated Erdős-Rényi graphs. January 2024, Sanya, China.
- Peking University Elite Training Program. A polynomial-time iterative algorithm for random graph matching with non-vanishing correlation. June 2023, Beijing, China.
Teaching Assistant
Advanced Calculus (I), Fall 2026.
Probability Theory, Spring 2025.
Advanced Probability Theory, Fall 2024.
Applied Stochastic Process (Honor), Fall 2023.