Boris Hanin


I’m an assistant professor of mathematics at Texas A&M.
I do research in probability, spectral asymptotics, and deep learning. I am currently on leave as a Visiting Scientist at Facebook AI Research NYC.

Office: BLOC 620B
Email: bhanin 'at' math.tamu.edu
CV (June 2019)

Teaching

Papers and preprints

  1. Deep ReLU Networks Have Surprisingly Few Activation Patterns, with D. Rolnick (2019) [arXiv]
  2. Nonlinear Approximation and (Deep) ReLU Networks, with I. Daubechies, R. DeVore, S. Foucart, and G. Petrova (2019) [arXiv]
  3. Interface Asymptotics of Wigner-Weyl Distributions for the Harmonic Oscillator, with S. Zelditch (2019) [arXiv]
  4. Complexity of Linear Regions in Deep Networks, with D. Rolnick, Accepted to ICML 2019 [arXiv]
  5. Interface Asymptotics of Eigenspace Wigner distributions for the Harmonic Oscillator, with S. Zelditch (2019) [arXiv]
  6. Products of Many Large Random Matrices and Gradients in Deep Neural Networks, with M. Nica (2018) [arXiv]
  7. How to Start Training: The Effect of Initialization and Architecture, Accepted to NIPS 2018 [arXiv]
  8. Which Neural Net Architectures Give Rise to Vanishing and Exploding Gradients?, Accepted to NIPS 2018 [arXiv]
  9. Approximating Continuous Functions by ReLU Nets of Minimal Width, with M. Sellke (2017) [arXiv]
  10. Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations (2017) [arXiv]
  11. The Lemniscate Tree of a Random Polynomial, with M. Epstein and E. Lundberg (2018) [arXiv]
  12. Level Spacings and Nodal Sets at Infinity for Radial Perturbations of the Harmonic Oscillator, with T. Beck. International Math Research Notices (in press, 2018) [arXiv]
  13. Local Universality for Zeros and Critical Points of Monochromatic Random Waves, with Y. Canzani (2017) [arXiv]
  14. Nodal Sets of Functions with Finite Vanishing Order, with T. Beck and S. Becker-Khan. Calculus of Variations and PDE (in press, 2018) [arXiv]
  15. Scaling of Harmonic Oscillator Eigenfunctions and Their Nodal Sets Around the Caustic, with S. Zelditch and P. Zhou. Communications in Mathematical Physics. Vol. 350, no. 3, pp. 1147--1183, 2017. [arXiv]
  16. C^∞ Scaling Asymptotics for the Spectral Function of the Laplacian, with Y. Canzani. The Journal of Geometric Analysis. DOI 10.1007/s12220-017-9812-5. [arXiv]
  17. Pairing of Zeros and Critical Points for Random Polynomials. Annales de l'Institut Henri Poincare (B) Probabilites et Statistiques. Volume 53, Number 3 (2017), 1498-1511. [arXiv]
  18. Scaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl Law, with Y. Canzani. Analysis and PDE, Vol. 8 (2015), No. 7, pp. 1707-1731. [arXiv]
  19. High Frequency Eigenfunction Immersions and Supremum Norms of Random Waves, with Y. Canzani. Electronic Research Announcements. MS 22, no. 0, January 2015, pp. 76 - 86. [arXiv]
  20. Pairing of Zeros and Critical Points for Random Meromorphic Functions on Riemann Surfaces. Mathematics Research Letters, Vol. 22 (2015), No. 1, pp. 111-140. [arXiv]
  21. Nodal Sets of Random Eigenfunctions for the Isotropic Harmonic Oscillator, with S. Zelditch and P. Zhou. International Mathematics Research Notices, Vol. 2015, No. 13, pp. 4813 - 4839. [arXiv]
  22. Correlations and Pairing Between Zeros and Critical Points of Gaussian Random Polynomials. International Math Research Notices (2015), Vol. (2), pp. 381-421. [arXiv]
  23. An Intriguing Property of the Center of Mass for Points on Quadradtic Curves and Surfaces, Mathematics Maganize, v. 80, No. 5, pp. 353-362, 2007.