Current Research Interests

Research areas:

• Probability theory, Mathematical foundations of data science, Mathematical physics

Recent keywords:

• High-dimensional learning dynamics, Statistical-computational tradeoffs, spin glasses

People

• Justin Ko (postdoc, current)
• Taj Jones-McCormick (PhD Stats, current)
• Varnan Sarangian (PhD Stats, current)
• Parsa Rangriz (MMath Stat, current)
• Lily Seebach (MMath Data Science, current)
• Aseem Baranwal (PhD CS 2024, now at XTY labs)
• Yiming Xu (postdoc 2024, now Asst. Prof. at U. Kentucky)
• Victor Issa (ENS M2 Intern, 2023, now PhD at ENS Lyons)
• Tingzhou Yu (MMath Stat, 2023, now PhD at U. Alberta)
• Philipp Schroeppel (MMath Stat, 2022, now PhD at Ulm U.)
• Anna Brandenberger (MSc, Perimeter Institute, 2022, now PhD at MIT)

Professional activities

Editorial Work:

• Mathematical Statistics and Learning Associate Editor 2024 -

Conference/Seminar organizing:

• Waterloo probability seminar Fall 2020 -
• Analysis of complex data: Tensors, Networks, and Dynamical Systems Spring 2024
• Harvard CMSA Probability and random matrix theory seminar Fall 17-Spring 19
• Brandeis-Harvard-MIT-Northeastern joint Mathematics colloquium AY1718
• Session on Spin Glasses and Disordered Media at 2017 JMM - Jan. 2017, Atlanta
• Toronto Probability Seminar Fall 16

Publications and preprints

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

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

   arXiv

2. Pseudo-maximum likelihood theory for high-dimensional rank one inference
   with C. Grant and J. Ko
   arXiv
3. Provable Benefits of Unsupervised Pre-training and Transfer Learning via Single-Index Models
   with T. Jones-McCormick and S. Sen
   arXiv

4. Shattering in the Ising pure p-spin model

   with D. Gamarnik and E. Kizildag,

   arXiv

5. Differentially private multivariate medians

   with K. Ramsay and S. Chenouri,

   arXiv

6. Finding planted cliques using Markov Chain Monte Carlo

   with R. Gheissari and Y. Xu,

   SIAM Journal on Mathematics of Data Science (to appear)

7. An elementary concentration bound for Gibbs measures arising in statistical learning theory

   with K. Ramsay and S. Chenouri,

   Transactions of Machine Learning Research (2025)

8. Existence of the free energy for heavy-tailed spin glasses

   with P. Lopatto,

   Communications in Mathematical Physics 405 (2024) no. 226

9. Circuit lower bounds for the p-spin optimization problem,

   with D. Gamarnik and A. S. Wein,

   Markov Processes and Related Fields 30 no. 1 (2024) 81-96 (special issue for IRS 2022)

10. High-dimensional SGD aligns with emerging outlier eigenspaces

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

    International Conference on Learning Representations 12 (ICLR 2024) (spotlight)

11. 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

12. 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

    Extended abstract appeared in NeurIPS 2022 (Outstanding Paper Award)

13. Shattering versus metastability in spin glasses,

    with G. Ben Arous,

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

14. Optimality of Message-Passing Architectures for Sparse Graphs

    with A. Baranwal and K. Fountoulakis,

    Advances in Neural Information Processing Systems 37 (NeurIPS) 2023

15. Graph attention retrospective

    K. Fountoulakis, A. Levi, S. Yang, A. Baranwal and A.J.,

    Journal of Machine Learning Research 24 no. 246 (2023) 1-52

16. Effects of Graph Convolutions in Multi-Layer Networks

    with A. Baranwal and K. Fountoulakis,

    International Conference on Learning Representations 11 (ICLR) 2023 (spotlight)

17. A simple construction of the dynamical Φ⁴₃ model,

    with N. Perkowski,

    Transactions of the American Mathematical Society 376 no. 3 (2023) 1507–1522

18. The overlap gap property in principal submatrix recovery,

    with D. Gamarnik and S. Sen,

    Probability Theory and Related Fields 181 (2021) 757–814

19. Graph Convolution for Semi-Supervised Classification: Improved Linear Separability and Out-of-Distribution Generalization,

    with A. Baranwal and K. Fountoulakis,

    International Conference on Machine Learning 38 (ICML 2021) (spotlight)

    Proceedings of Machine Learning Research 139 (2021) 684-693

20. 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

21. On the unbalanced cut problem and the generalized Sherrington-Kirkpatrick model,

    with S. Sen,

    Annales de l'Instut Henri Poincaré D Comb. Phys. Inter. 8 (2021) 35-88.

22. The overlap gap property and approximate message passing algorithms for p-spin models,

    with D. Gamarnik,

    The Annals of Probability 49 no. 1 (2021) 180-205

23. Low degree hardness of random optimization problems,

    with D. Gamarnik and A. S. Wein

    Foundations of Computer Science (FOCS) (2020) 131-140

24. Statistical thresholds for tensor PCA,

    with P. Lopatto and L. Miolane,

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

25. Algorithmic thresholds for tensor PCA,

    with G. Ben Arous and R. Gheissari,

    The Annals of Probability 48 no. 4 (2020) 2052-2087

26. Bounding flows for spherical spin glass dynamics,

    with G. Ben Arous and R. Gheissari,

    Communications in Mathematical Physics 373 (2020) 1011-1048

27. Dynamics of mean field spin glasses on short and long timescales,

    Journal of Mathematical Physics 60, 083305 (2019)

28. Thouless–Anderson–Palmer equations for generic p-spin glasses,

    with A. Auffinger,

    The Annals of Probabability 47 no. 43 (2019) 2230-2256

29. On the spectral gap of spherical spin glass dynamics,

    with R. Gheissari,

    Annales de l'Institut Henri Poincaré B Probab. et Stat. 55 no. 2 (2019) 756-776

30. On spin distributions for generic p-spin models,

    with A. Auffinger,

    Journal of Statistical Physics (2019) 174-316

31. Spectral gap estimates in mean field spin glasses,

    with G. Ben Arous,

    Communications in Mathematical Physics 361 no. 1 (2018) 1-52

32. MAX κ-CUT and the inhomogeneous Potts spin glass,

    with J. Ko and S. Sen,

    The Annals of Applied Probability 28 no. 3 (2018) 1536–1572

33. Bounding the complexity of replica symmetry breaking for spherical spin glasses,

    with I. Tobasco,

    Proceedings of the American Mathematical Society 146 (2018) 3127-3142

34. Random matrices and the New York City subway system,

    with T. Trogdon,

    Physical Review E 96, 030101(R) (2017)

35. Low temperature asymptotics of spherical mean field spin glasses,

    with I. Tobasco,

    Communications in Mathematical Physics 352 no. 3 (2017) 979-1017

36. Some properties of the phase diagram for mixed p-spin glasses,

    with I. Tobasco,

    Probability Theory and Related Fields 167 (2017) 615-672 (slides)

37. Approximate ultrametricity for random measures with applications to spin glasses,

    Communications on Pure and Applied Mathematics 70 (2017) 611–664 (video)

38. A dynamic programming approach to the Parisi functional,

    with I. Tobasco,

    Proceedings of the American Mathematical Society 144 (2016) 3135-3150

39. On the overlap distribution of branching random walks,

    Electronic Journal of Probability 21 no. 50 (2016) 16 pp.

40. Variational and Structural Methods in Mean Field Spin Glasses,

    Ph.D. Thesis, May 2016

41. Solution of the propeller conjecture in R³,

    with S. Heilman and A. Naor

    Discrete & Compututational Geometry 50 (2013) 263-305 (code)

    Extended abstract appeared at STOC 2012.

42. Charged particle motion in electromagnetic fields varying moderately slowly in space,

    with H. Weitzner,

    Physics of Plasmas 18, 104510 (2011)