# Yizhe Zhu

I'm a Visiting Assistant Professor at University of California, Irvine. I'm also a Postdoc in the Collaboration on the Theoretical Foundations of Deep Learning. My mentor is Roman Vershynin.

In the fall semester of 2021, I was a Postdoc Fellow at Simons Laufer Mathematical Sciences Institute (formerly MSRI) for the program Universality and Integrability in Random Matrix Theory and Interacting Particle Systems in Berkeley, California. I obtained my Ph.D. in Mathematics from the University of California, San Diego in 2021. My advisor is Ioana Dumitriu. I obtained Bachelor's degree in Mathematics and Applied Mathematics from Shanghai Jiao Tong University. My CV is here.

Email: yizhe.zhu[at]uci.edu

Office: 510V Rowland Hall

Teaching

Spring 2024: MATH 3A (Introduction to Linear Algebra)

Spring 2023: MATH 130A (Probability Theory I) and MATH 130C (Stochastic Process)

Spring 2022: MATH 3A (Introduction to Linear Algebra) and MATH 130C (Stochastic Process)

Math 199 (Supervised Reading and Research) Spring 2022/2023/2024, Autumn 2023, Winter 2023/2024

### Research Interests

I am interested in probability, combinatorics, and their applications in data science. I am working on:

Random matrices, random graphs

Random tensors, random hypergraphs

Community detection, tensor completion, neural networks, differential privacy

I'm co-organizing the Combinatorics and Probability Seminar at UCI.

### Preprints

Online differentially private synthetic data generation, with Yiyun He and Roman Vershynin, submitted, 2024.

Non-backtracking eigenvalues and eigenvectors of random regular graphs and hypergraphs, with Xiangyi Zhu*, submitted, 2023.

Differentially private low-dimensional synthetic data from high-dimensional datasets, with Yiyun He, Thomas Strohmer, and Roman Vershynin, submitted, 2023.

* denotes an undergraduate author

### Papers

A non-backtracking method for long matrix and tensor completion, with Ludovic Stephan, COLT 2024, accepted.

Partial recovery and weak consistency in the non-uniform hypergraph stochastic block model, with Ioana Dumitriu and Haixiao Wang, Combinatorics, Probability and Computing, to appear.

Extreme singular values of inhomogeneous sparse random rectangular matrices, with Ioana Dumitriu, Bernoulli, to appear.

Deformed semicircle law and concentration of nonlinear random matrices for ultra-wide neural networks, with Zhichao Wang, Annals of Applied Probability, 34(2), 1896-1947, 2024. [journal]

Sparse random hypergraphs: Non-backtracking spectra and community detection, with Ludovic Stephan, Information and Inference, 2024. Conference version appeared in FOCS 2022. [journal] [conference proceedings]

The characteristic polynomial of sums of random permutations and regular digraphs, with Simon Coste and Gaultier Lambert, International Mathematics Research Notices, 2024(3), 2461-2510, 2024. [journal]

Robust recovery of low-rank matrices and low-tubal-rank tensors from noisy sketches, with Anna Ma and Dominik Stöger, SIAM Journal on Matrix Analysis and Applications, 44 (4), 1566-1588, 2023. [journal]

Spectral gap-based deterministic tensor completion, with Kameron Decker Harris, Oscar López, and Angus Read, 14th International Conference on Sampling Theory and Applications (SampTA), 2023. [conference proceedings]

Algorithmically effective differentially private synthetic data, with Yiyun He and Roman Vershynin, Proceedings of Thirty Sixth Conference on Learning Theory (COLT), PMLR 195:3941-3968, 2023. [conference proceedings]

Overparameterized random feature regression with nearly orthogonal data, with Zhichao Wang, Proceedings of The 26th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 206:8463-8493, 2023. [conference proceedings]

Global eigenvalue fluctuations of random biregular bipartite graphs, with Ioana Dumitriu, Random Matrices: Theory and Applications, 12(3), 2350004, 2023. [journal]

On the second eigenvalue of random bipartite biregular graphs, Journal of Theoretical Probability, 36, 1269–1303, 2023. [journal]

Sparse recovery properties of discrete random matrices, with Asaf Ferber, Ashwin Sah, and Mehtaab Sawhney, Combinatorics, Probability and Computing, 32(2), 316-325, 2023. [journal]

Deterministic tensor completion with hypergraph expanders, with Kameron Decker Harris, SIAM Journal on Mathematics of Data Science, 3(4), 1117-1140, 2021. [journal]

Spectra of random regular hypergraphs, with Ioana Dumitriu, The Electronic Journal of Combinatorics, 28(3), P3-36, 2021. [journal]

Sparse random tensors: Concentration, regularization and applications, with Zhixin Zhou, Electronic Journal of Statistics, 15(1), 2483-2516, 2021. [journal]

Community detection in the sparse hypergraph stochastic block model, with Soumik Pal, Random Structures and Algorithms, 59(3): 407– 463, 2021. [journal]

Asymptotic behavior of a sequence of conditional probability distributions and the canonical ensemble, with Yu-Chen Cheng and Hong Qian, Annales Henri Poincaré, 22, 1561–1627, 2021. [journal]

Eigenvalues of the non-backtracking operator detached from the bulk, with Simon Coste, Random Matrices: Theory and Applications, 10(3), 2150028, 2021. [journal]

Exact recovery in the hypergraph stochastic block model: A spectral algorithm, with Sam Cole, Linear Algebra and its Applications, 593, 45-73, 2020. [journal]

A graphon approach to limiting spectral distributions of Wigner-type matrices, Random Structures and Algorithms, 56(1), 251– 279, 2020. [journal]

Sparse general Wigner-type matrices: Local law and eigenvector delocalization, with Ioana Dumitriu, Journal of Mathematical Physics, 60(2), 023301, 2019. [journal]

Travel

2024

Nov 4-8, Recent developments beyond classical regimes in statistical learning, Institut de Mathématiques de Toulouse, France

Aug 12-16, Bernoulli-IMS 11th World Congress in Probability and Statistics, Bochum, Germany

Aug 3-8, 2024 Joint Statistical Meetings, Portland

June 17-28, Random Matrix Theory Summer School, University of Michigan

May 20-22, Random Matrices and Applications, ICERM, Brown University

May 16-17, MoDL Collaboration Meeting 2024, UCSD

April 27, Southern California Applied Mathematics Symposium (SOCAMS) 2024, UCSD

April 19-20, Random Matrices and Free Probability, MAA Rocky Mountain Section Meeting

April 17, CMX Lunch Seminar, Caltech

Feb 25-28, The 35th International Conference on Algorithmic Learning Theory (ALT 2024), San Diego

Feb 18-23, Information Theory and Applications Workshop (ITA 2024), San Diego

Jan 21-27, Desert Discrete Math Workshop, Steele/Burnand Anza-Borrego Desert Research Center, Borrego Springs

2023

Nov 16-17, Conference on the Mathematical Theory of Deep Neural Networks (DeepMath 2023), Johns Hopkins University

Oct 10-12, Algorithms for Threat Detection PI Workshop, George Mason University

Sep 28-29, Mathematical and Scientific Foundations of Deep Learning Annual Meeting, New York

Aug 9, Seminar on Statistics, Hong Kong University of Science and Technology

Jul 10-14, Methods for Low Rank Matrices and Tensors, Sampling Theory and Applications Conference (SampTA 2023), Yale University

Jul 6, Oberseminar Stochastik, Institude for Applied Mathematics, University of Bonn, Germany

Jul 3, MIDS Seminar, Mathematical Institute for Machine Learning and Data Science, Katholische Universität Eichstätt - Ingolstadt, Germany

Jun 28-30, 21st INFORMS Applied Probability Society Conference, Nancy, France

May 23-24, Collaboration on the Theoretical Foundations of Deep Learning Meeting, Toyota Technological Institute at Chicago

Apr 25-27, Artificial Intelligence and Statistics (AISTATS) 2023, Valencia, Spain

Apr 22, Southern California Applied Mathematics Symposium, UC Irvine

Apr 13-14, UCLA Synthetic Data workshop

Mar 27-31, Spectra of Random Graphs and Related Combinatorial Problems, Eurandom, Eindhoven, Netherlands

Feb 12-17, Information Theory and Applications Workshop, San Diego

Jan 4-7, AMS Special Session on Tensor Representation, Completion, Modeling and Analytics of Complex Data, JMM 2023, Boston