Boris Hanin


I’m an assistant professor of mathematics at Texas A&M.
I work on deep learning, probability, and spectral asymptotics,.

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

Teaching

  1. In Fall 2019, I am currently teaching two sections of Math 300 Foundations of Mathematics. Here is the [syllabus].
  2. In Fall 2018, I taught a graduate course, Math 689, called Deep Learning: Theory and Applications. Here is the [course website].
  3. In Fall 2017, I taught two sections of Math 221 Multivariable Calculus. Here is the [syllabus].
  4. In Fall and IAP 2015, I taught Math 18.02A and 18.02B Multivariable Calculus (at MIT). Here is the [syllabus].
  5. In Fall 2014, I TAed Math 18.03 Differential Equations (at MIT).
  6. In Winter 2013, I TAed Math 321-1 Honors Real Analysis (at Northwestern).
  7. In Fall 2012, I TAed Math 310-1 Probability Theory (at Northwestern).
  8. In Fall 2012, I TAed Math 300 Foundations of Higher Mathematics (at Northwestern).
  9. In Winter 2011, I TAed Math 310-2 Probability Theory (at Northwestern).
  10. In Winter 2011, I TAed Math 321-2 Honors Real Analysis (at Northwestern).
  11. In Fall 2011, I TAed Math 321-2 Honors Real Analysis (at Northwestern).
  12. In Fall 2011, I TAed Math 310-1 Probability Theory (at Northwestern).
  13. In Fall 2010, I TAed Math 300 Foundations of Higher Mathematics (at Northwestern).
  14. In Fall 2010, I TAed Math 310-1 Probability Theory (at Northwestern).

Papers and preprints ([arXiv])

  1. Finite Depth and Width Corrections to the Neural Tangent Kernel, with M. Nica (2019) [arXiv]
  2. Deep ReLU Networks Have Surprisingly Few Activation Patterns, with D. Rolnick, NeurIPS (2019) [arXiv]
  3. Nonlinear Approximation and (Deep) ReLU Networks, with I. Daubechies, R. DeVore, S. Foucart, and G. Petrova (2019) [arXiv]
  4. Interface Asymptotics of Wigner-Weyl Distributions for the Harmonic Oscillator, with S. Zelditch (2019) [arXiv]
  5. Complexity of Linear Regions in Deep Networks, with D. Rolnick, ICML 2019 [arXiv]
  6. Interface Asymptotics of Eigenspace Wigner distributions for the Harmonic Oscillator, with S. Zelditch (2019) [arXiv]
  7. Products of Many Large Random Matrices and Gradients in Deep Neural Networks, with M. Nica. Communications in Mathematical Physics (in press, 2019) [arXiv]
  8. How to Start Training: The Effect of Initialization and Architecture, with D. Rolnick. NIPS 2018 [arXiv]
  9. Which Neural Net Architectures Give Rise to Vanishing and Exploding Gradients?. NIPS 2018 [arXiv]
  10. Approximating Continuous Functions by ReLU Nets of Minimal Width, with M. Sellke (2017) [arXiv]
  11. Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations (2017) [arXiv]
  12. The Lemniscate Tree of a Random Polynomial, with M. Epstein and E. Lundberg (2018). Annales Institute Henri Poincare (B). [arXiv]
  13. 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]
  14. Local Universality for Zeros and Critical Points of Monochromatic Random Waves, with Y. Canzani (2017) [arXiv]
  15. Nodal Sets of Functions with Finite Vanishing Order, with T. Beck and S. Becker-Khan. Calculus of Variations and PDE (in press, 2018) [arXiv]
  16. 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]
  17. 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]
  18. 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]
  19. 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]
  20. 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]
  21. 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]
  22. 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]
  23. Correlations and Pairing Between Zeros and Critical Points of Gaussian Random Polynomials. International Math Research Notices (2015), Vol. (2), pp. 381-421. [arXiv]
  24. 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.