Jiaoyang Huang

Research Interests

I am interested in probability theory and its applications to problems from statistics, combinatorics, statistical physics and computer science. So far I have done research on

sparse random graphs, studying the spectral properties of random regular graphs and Erdős–Rényi graphs.
interacting particle systems, e.g. discrete log gas, nonintersecting random walks and tilings, proving the universality of their asymptotic behaviors.
statistical learning, investigating optimization and generalization properties.
posterior sampling for Bayesian inference and uncertainty quantification of large-scale inverse problems.

Research Papers

Random Matrices and Random Graphs

Edge universality of random regular graphs of growing degrees
with Horng-Tzer Yau.
Preprint, 2023.
Edge Universality of Sparse Random Matrices
with Horng-Tzer Yau.
Preprint, 2022.
Large Deviation Principles via Spherical Integrals
with Serban Belinschi and Alice Guionnet.
Probability and Mathematical Physics 3, no.3, p:543-625, 2022.
Eigenvalues for the Minors of Wigner Matrices
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 58(4), 2201-2215, 2022.
Large Deviations Asymptotics of Rectangular Spherical Integral
with Alice Guionnet.
Accepted by Journal of Functional Analysis, 2023.
Spectrum of Random d-regular Graphs Up to the Edge
with Horng-Tzer Yau.
Accepted by Communications on Pure and Applied Mathematics, 2023.
Invertibility of adjacency matrices for random d-regular graphs
Duke Mathematical Journal 170(18): 3977-4032, 2021.
Edge rigidity and universality of random regular graphs of intermediate degree
with Roland Bauerschmidt, Antti Knowles and Horng-Tzer Yau.
Geometric and Functional Analysis, 30(3):693--769, 2020.
Transition from Tracy-Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős–Rényi graphs.
with Benjamin Landon and Horng-Tzer Yau.
Annals of Probability, 48(2):916--962, 2020.
Spectral Statistics of Sparse Erdős–Rényi Graph Laplacians
with Benjamin Landon.
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, volume 56, pages 120--154, 2020.
Local Kesten--McKay Law for Random Regular Graphs
with Roland Bauerschmidt and Horng-Tzer Yau.
Communications in Mathematical Physics, 369(2):523--636, 2019.
Invertibility of adjacency matrices for random d-regular directed graphs,
Permanent draft, 2018.
Eigenvector Statistics of Sparse Random Matrices
with Paul Bourgade and Horng-Tzer Yau.
Electron. J. Probab. Volume 22 (2017), paper no. 64, 38 pp.
Bulk Eigenvalue Statistics for Random Regular Graphs
with Roland Bauerschmidt, Antti Knowles and Horng-Tzer Yau.
Ann. Probab., Volume 45, no. 6A (2017), 3626-3663.
Bulk Universality of Sparse Random Matrices
with Benjamin Landon and Horng-Tzer Yau.
J. Math. Phys. 56 (2015), no. 12, 123301, 19pp.

Interacting Particle Systems and Random Tilings

Strong Characterization for the Airy Line Ensemble
with Amol Aggarwal.
Preprint, 2023.
Local Statistics and Concentration for Non-intersecting Brownian Bridges With Smooth Boundary Data
with Amol Aggarwal.
Preprint, 2023.
Edge Rigidity of Dyson Brownian Motion with General Initial Data
with Amol Aggarwal.
Preprint, 2023.
Pearcey universality at cusps of polygonal lozenge tiling
with Fan Yang and Lingfu Zhang.
Preprint, 2023.
Asymptotics of Generalized Bessel Functions and Weight Multiplicities via Large Deviations of Radial Dunkl Processes
with Colin McSwiggen.
Preprint, 2023.
Dynamical Loop Equation
with Vadim Gorin.
Preprint, 2022.
Edge Statistics for Lozenge Tilings of Polygons, II: Airy Line Ensemble
with Amol Aggarwal.
Preprint, 2021.
Edge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains
Preprint, 2021.
Law of Large Numbers and Central Limit Theorems by Jack Generating Functions
Advances in Mathematics 380, 107545, 2021.
β-Nonintersecting Poisson Random Walks: Law of Large Numbers and Central Limit Theorems
International Mathematics Research Notices, 2021(8), 5898-5942.
Edge Universality for Nonintersecting Brownian Bridges
Preprint, 2020.
Height Fluctuations of Random Lozenge Tilings Through Nonintersecting Random Walks
Preprint, 2020.
Dyson Brownian Motion for General β and Potential at the Edge
with Arka Adhikari.
Probability Theory and Related Fields, 178, 893–950, 2020.
Rigidity and Edge Universality of Discrete β-Ensembles
with Alice Guionnet.
Communications on Pure and Applied Mathematics, 72(9):1875--1982, 2019.
Local Law and Mesoscopic Fluctuations of Dyson Brownian Motion for General β and Potentials
with Benjamin Landon.
Probability Theory and Related Fields, 175(1-2):209--253, 2019.

Statistical Learning

How Does Information Bottleneck Help Deep Learning?
with Kenji Kawaguchi, Zhun Deng and Xu Ji.
International Conference on Machine Learning (ICML), 2023.
PatchGT: Transformer over Non-trainable Clusters for Learning Graph Representations
with Han Gao, Xu Han, Jian-Xun Wang and Liping Liu.
In Learning on Graphs Conference, pp. 27-1. PMLR, 2022.
Long Random Matrices and Tensor Unfolding
with Gerard Ben Arous and Daniel Z Huang.
Accepted by Annals of Applied Probability, 2022.
Robustness Implies Generalization via Data-Dependent Generalization Bounds
Kenji Kawaguchi, Zhun Deng and Kyle Luh.
International Conference on Machine Learning (ICML), 2022.
Power Iteration for Tensor PCA
with Guang Cheng, Daniel Z. Huang and Qing Yang.
Journal of Machine Learning Research 23 (128), 1-47,2022.
Understanding End-to-End Model-Based Reinforcement Learning Methods as Implicit Parameterization
with with Clement Gehring, Kenji Kawaguchi, and Leslie Pack Kaelbling.
Advances in Neural Information Processing Systems (NeurIPS), 2021.
How Shrinking Gradient Noise Helps the Performance of Neural Networks
with Zhun Deng, and Kenji Kawaguchi.
IEEE International Conference on Big Data (Big Data), 1002-1007, 2021.
Towards Understanding the Dynamics of the First-Order Adversaries
with Zhun Deng, Hangfeng He and Weijie Su.
In Proceedings of the 37th International Conference on Machine Learning(ICML), 2020.
Dynamics of deep neural networks and neural tangent hierarchy
with Horng-Tzer Yau.
In Proceedings of the 37th International Conference on Machine Learning(ICML), 2020.
Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes
with Kenji Kawaguchi.
In Proceedings of the 57th Allerton Conference on Communication, Control, and Computing (Allerton), IEEE, 2019.
Every Local Minimum Value is the Global Minimum Value of Induced Model in Non-convex Machine Learning
with Kenji Kawaguchi and Leslie Pack Kaelbling.
Neural Computation, 31(12), 2293-2323, MIT press, 2019.
Effect of Depth and Width on Local Minima in Deep Learning
with Kenji Kawaguchi and Leslie Pack Kaelbling.
Neural Computation, 31(7), 1462-1498, MIT press, 2019.

Posterior Sampling

Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance
with Yifan Chen, Daniel Z Huang, Sebastian Reich and Andrew M Stuart.
Preprint, 2023.
Efficient derivative-free Bayesian inference for large-scale inverse problems
with Daniel Z Huang, Sebastian Reich and Andrew M Stuart.
Inverse Problems 38 no.12 p: 125006, 2022.

Undergraduate Research

Mesoscopic Perturbations of Large Random Matrices
Random Matrices Theory Appl., Volume 07, no. 02, 1850004 (2018).
Asymptotic Expansion of Spherical Integral
J. Theor. Probab., (2018).
Laurent Phenomenon Sequences
with Joshua Alman and Cesar Cuenca.
J. Algebraic Combin. 43 (2016), no. 3 589-633.