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] [Slides]
- 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, 72(8):6093--6111, 2026.
Conference version in Proceedings of 38th COLT, pages 3580--3581, 2025.
[arXiv] [Conference] [Journal] [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 4th Joint Conference on Statistics and Data Science. Fundamental limits of community detection in contextual multi-layer stochastic block models. July 2026, Guiyang, China.
- 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.