Current Research Interests

• Probability theory, Mathematics of data science, Mathematical physics

Students

• Aseem Baranwal (PhD, CS, 2020- )
• Tingzhou Yu (MMath Stat, 2021- )
• Philipp Schroeppel (MMath, Stat, 2022)
• Anna Brandenberger (MSc, Perimeter Institute, 2022)

Publications and preprints

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

   with P. Lopatto arXiv

2. Concentration of the exponential mechanism and differentially private multivariate medians

   with K. Ramsay and S. Chenouri arXiv

3. Graph attention retrospective

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

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

   with D. Gamarnik and A. S. Wein, arXiv

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

   with D. Gamarnik and A. S. Wein, Markov Proc. Relat. Fields (special issue for IRS 2022) (to appear)

6. Effects of Graph Convolutions in Multi-Layer Networks

   with A. Baranwal and K. Fountoulakis, International Conference on Learning Representations 11 (ICLR 2023)

7. Shattering versus metastability in spin glasses,

   with G. Ben Arous, Comm. Pure Appl. Math (to appear)

8. A simple construction of the dynamical Φ⁴₃ model,

   with N. Perkowski, Trans. Amer. Math. Soc. Vol. 376, No. 3, pp 1507–1522 (2023)

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

   with G. Ben Arous and R. Gheissari, Advances in Neural Information Processing Systems 36 (NeurIPS 2022), (Outstanding Paper Award) Full version: arXiv

10. The overlap gap property in principal submatrix recovery,

    with D. Gamarnik and S. Sen, Probab. Theo. Relat. Fields 181, pp 757–814 (2021)

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

    with A. Baranwal and K. Fountoulakis, ICML 2021, Proc. Mach. Learn. Res. Vol 139 684-693, 2021

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

    with G. Ben Arous and R. Gheissari, J. Mach. Learn. Res., Vol 22, No.106,1-51(2021)

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

    with S. Sen, Ann. Inst. Henri Poincaré Comb. Phys. Interact. 8 (2021), 35-88.

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

    with D. Gamarnik, Ann. Probab., Vol 49, No. 1 (2021), 180-205.

15. Low degree hardness of random optimization problems,

    with D. Gamarnik and A. S. Wein Foundations of Computer Science (FOCS) 2020 pp. 131-140.

16. Statistical thresholds for tensor PCA,

    with P. Lopatto and L. Miolane, Ann. Appl. Probab. (2020), Vol. 30, No. 4, 1910-1933

17. Algorithmic thresholds for tensor PCA,

    with G. Ben Arous and R. Gheissari, Ann. Probab. (2020), Vol. 48, No. 4, 2052-2087

18. Bounding flows for spherical spin glass dynamics,

    with G. Ben Arous and R. Gheissari, Commun. Math. Phys. 373, 1011-1048 (2020)

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

    J. Math. Phys. 60, 083305 (2019)

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

    with A. Auffinger, Ann. Probab. 47 (2019), no. 4, 2230--2256

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

    with R. Gheissari, Ann. Inst. H. Poincare Probab. Statist., Vol. 55, No. 2 (2019) 756-776

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

    with A. Auffinger, J Stat Phys (2019) 174: 316

23. Spectral gap estimates in mean field spin glasses,

    with G. Ben Arous, Commun. Math. Phys. 361 (1), 1-52 (2018)

24. MAX \kappa-CUT and the inhomogeneous Potts spin glass,

    with J. Ko and S. Sen, Ann. Appl. Probab. (2018), Vol. 28, No. 3, 1536–1572

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

    with I. Tobasco, Proc. Amer. Math. Soc. 146 (2018), 3127-3142

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

    with T. Trogdon, Phys. Rev. E 96, 030101(R) (2017)

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

    with I. Tobasco, Commun. Math. Phys. 352 (3), 979-1017 (2017)

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

    with I. Tobasco, Probab. Theory Relat. Fields (2017) 167:615-672 (slides)

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

    Comm. Pure Appl. Math 70 (2017), 611–664. (video)

30. A dynamic programming approach to the parisi functional,

    with I. Tobasco, Proc. Amer. Math. Soc. 144 (2016), 3135-3150

31. On the overlap distribution of branching random walks,

    Electron. J. Probab., 21 (2016), no. 50, 16 pp.

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

    Ph.D. Thesis, May 2016

33. Solution of the propeller conjecture in R³,

    with S. Heilman and A. Naor, Disc. & Comput. Geom. (2013) 50: 263 (code)

    An extended abstract appeared at STOC 2012.

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

    with H. Weitzner, Physics of Plasmas 18, 104510 (2011)