I am an Assistant Professor at Princeton ORFE working on **deep learning, probability, and spectral asymptotics.** Prior to Princeton, I was an Assistant Professor in Mathematics at Texas A&M, an NSF Postdoc at MIT Math, and a PhD student in Math at Northwestern, where I was supervised by Steve Zelditch.

**Funding**: I am grateful to be supported by an NSF CAREER grant DMS-2143754 and NSF grants DMS-1855684, DMS-2133806. I am also a consultant for an ONR MURI on Foundations of Deep Learning. See my CV for more information.

**Email**: bhanin ‘at’ princeton.edu

- I am currently looking for grad students and postdocs. If you are a student at Princeton looking to work on deep learning theory, feel free to reach out (see also this somewhat tongue-in-cheek writeup).
- I am organizing the 2023 Princeton Deep Learning Theory Summer School.
- I am giving a mini-course on wide neural networks at the Rome Center on Mathematics for Modeling and Data Sciences. Here are some notes.

I am fortunate to supervise Pierfrancesco Beneventano, Samy Jelassi, and Kaiqi Jiang.

- Bayesian Interpolation with Deep Linear Networks, with A. Zlokapa ArXiv
- Maximal Initial Learning Rates in Deep ReLU Networks, with G. Iyer and D. Rolnick ArXiv
- Deep Architecture Connectivity Matters for Its Convergence: A Fine-Grained Analysis with W. Chen, W. Huang, X. Gong, Z. Wang, NeurIPS 2022 ArXiv
- Random Fully Connected Neural Networks as Perturbatively Solvable Hierarchies (2022) ArXiv
- Ridgeless Interpolation with Shallow ReLU Networks in 1D is Nearest Neighbor Curvature Extrapolation and Provably Generalizes on Lipschitz Functions (2021) ArXiv
- Random Neural Networks in the Infinite Width Limit as Gaussian Processes, Annals of Applied Probability (2023) ArXiv
- Non-asymptotic Results for Singular Values of Gaussian Matrix Products, with G. Paouris. GAFA (2021) ArXiv
- Deep ReLU Networks Preserve Expected Length, with R. Jeong and D. Rolnick, ICLR 2022 ArXiv
- Neural Network Approximation, with R. DeVore and G. Petrova, Acta Numerica (2020) ArXiv
- How Data Augmentation affects Optimization for Linear Regression, with Y. Sun NeurIPS 2021 ArXiv
- Products of Many Large Random Matrices and Gradients in Deep Neural Networks, with M. Nica. Communications in Mathematical Physics (2020) ArXiv
- Finite Depth and Width Corrections to the Neural Tangent Kernel, with M. Nica, Splotlight at ICLR 2020 ArXiv
- Deep ReLU Networks Have Surprisingly Few Activation Patterns, with D. Rolnick, NeurIPS 2019 ArXiv
- Nonlinear Approximation and (Deep) ReLU Networks, with I. Daubechies, R. DeVore, S. Foucart, and G. Petrova. Constructive Approximation (Special Issue on Deep Networks in Approximation Theory) (2019) ArXiv
- Complexity of Linear Regions in Deep Networks, with D. Rolnick, ICML 2019 ArXiv
- How to Start Training: The Effect of Initialization and Architecture, with D. Rolnick. NIPS 2018 ArXiv
- Which Neural Net Architectures Give Rise to Vanishing and Exploding Gradients? NIPS 2018 ArXiv
- Approximating Continuous Functions by ReLU Nets of Minimal Width, with M. Sellke (2017) ArXiv
- Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations. Mathematics 2019, 7(10), 992 (Special Issue on Computational Mathematics, Algorithms, and Data Processing) ArXiv

- Scaling Asymptotics of Spectral Wigner Functions, with S. Zelditch. Journal of Physics A (Special Edition on Claritons and the Asymptotics of Ideas: the Physics of Michael Berry) (2022) ArXiv
- Interface Asymptotics of Wigner-Weyl Distributions for the Harmonic Oscillator, with S. Zelditch. Journal d’Analyse (2022) ArXiv
- Interface Asymptotics of Eigenspace Wigner distributions for the Harmonic Oscillator, with S. Zelditch. Communications in PDE (2020) ArXiv
- Level Spacings and Nodal Sets at Infinity for Radial Perturbations of the Harmonic Oscillator, with T. Beck. International Math Research Notices, 2021. ArXiv
- Local Universality for Zeros and Critical Points of Monochromatic Random Waves, with Y. Canzani. Communication in Mathematical Physics, 2020. ArXiv
- Nodal Sets of Functions with Finite Vanishing Order, with T. Beck and S. Becker-Khan. Calculus of Variations and PDE (2018) ArXiv
- 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
- C^∞ Scaling Asymptotics for the Spectral Function of the Laplacian, with Y. Canzani. The Journal of Geometric Analysis (2018) ArXiv
- 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
- 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
- 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

- The Lemniscate Tree of a Random Polynomial, with M. Epstein and E. Lundberg. Annales Institute Henri Poincare (B), 2018. ArXiv
- 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
- Pairing of Zeros and Critical Points for Random Meromorphic Functions on Riemann Surfaces</b>. Mathematics Research Letters, Vol. 22 (2015), No. 1, pp. 111-140. ArXiv
- Correlations and Pairing Between Zeros and Critical Points of Gaussian Random Polynomials. International Math Research Notices (2015), Vol. (2), pp. 381-421. ArXiv

- Contributed research to Principles of Deep Learning Theory, written by D. Roberts and S. Yaida, Cambridge University Press (2021) ArXiv
- An Intriguing Property of the Center of Mass for Points on Quadradtic Curves and Surfaces, with L. Hanin and R. Fisher. Mathematics Maganize, v. 80, No. 5, pp. 353-362, 2007.