Aukosh Jagannath

Research

My recent work focuses on high-dimensional pheneomena in the mathematical foundations of data science, including the dynamics of learning algorithms, statistical-computational tradeoffs, and the hardness of random optimization problems. The tools and techniques I use come from probability, PDEs, variational calculus, and statistical physics, specifically the mean field theory of spin glasses.

Selected publications

1. Local geometry of high-dimensional mixture models: Effective spectral theory and dynamical transitions

   with G. Ben Arous, R. Gheissari, and J. Huang

   Annals of Statistics (to appear)

2. High-dimensional limit theorems for SGD: Effective dynamics and critical scaling

   with G. Ben Arous and R. Gheissari

   Communications on Pure and Applied Mathematics 77 no. 3 (2024) 2030–2080

   Conference version appeared in NeurIPS 2022 (Outstanding Paper Award)

3. Hardness of random optimization problems for boolean circuits, low-degree polynomials, and Langevin dynamics

   with D. Gamarnik and A. S. Wein

   SIAM Journal on Computing 53 no. 1 (2024) 1–46

4. Shattering versus metastability in spin glasses

   with G. Ben Arous

   Communications on Pure and Applied Mathematics 77 no. 1 (2024) 139–176

5. Online stochastic gradient descent on non-convex losses from high-dimensional inference

   with G. Ben Arous and R. Gheissari

   Journal of Machine Learning Research 22 no. 106 (2021) 1–51

6. Statistical thresholds for tensor PCA

   with P. Lopatto and L. Miolane

   Annals of Applied Probability 30 no. 4 (2020) 1910–1933

Full publication list and professional activities