Mihai Nica

Assistant Professor, Mathematics

Having joined the Department of Mathematics and Statistics in 2020, Prof. Mihai Nica works to improve our theoretical understanding of AI technologies through mathematical analyses. His work focuses on Deep Neural Networks (DNNs), which are a set of algorithms underlying machine learning technology. The algorithms are modelled after the human brain and used to recognize patterns. Nica is exploring the mathematical concepts of probability and stochastic processes, and their applications for DNNs.

“CARE-AI is unique in that it extends from mathematics to engineering to philosophy,” says Nica. “I’m looking forward to collaborations with other CARE-AI members that bridge the gap between purely mathematical results and real-world applications.”

  • Scaling limits of deep neural networks
  • Numerical methods utilising neural networks
  • Phase transitions in high-dimensional learning problems
  • The KPZ universality class

B. Math, University of Waterloo, Canada

PhD, Courant Institute of Mathematical Sciences, New York University

Preprints & Publications

1. Hanin, B. and Nica, M. Finite Depth and Width Corrections to the Neural Tangent Kernel.
Preprint arXiv:1909.05989, 27 pages.
2. Dauvergne, D., Nica, M. and Virág, B. Uniform convergence to the Airy line ensemble. Preprint
arXiv:1907.10160, 48 pages.
3. Nica, M., Quastel, J. and Remenik, D. Solution of the Kolmogorov equation for TASEP.
Preprint arXiv:1906.01692, 12 pages. Submitted.
4. Hanin, B. and Nica, M. Products of Many Large Random Matrices and Gradients in Deep
Neural Networks. Preprint arXiv:1812.05994, 26 pages. Submitted.
5. Ben Arous, G., Mei, S, Montanari, A. and Nica, M. The landscape of the spiked tensor model.
Preprint arXiv:1711.05424, 40 pages. To appear in Communications in Pure and Applied

6. Nica, M. Intermediate disorder limits for multi-layer semi-discrete directed polymers. Preprint
arXiv:1609.00298, 46 pages. Submitted.
7. Corwin, I. and Nica, M. Intermediate disorder directed polymers and the multi-layer extension
of the stochastic heat equation. Electronic Journal of Probability (2017) 22:149 Available
online arXiv:1603.08168 8. Nica, M. Decorated Young tableaux and the Poissonized Robinson-Schensted process. Stochas-
tic Processes and their Applications
, (2017) 127:449474. Available online arXiv:1404.4015 9. Nica, M. Optimal strategy in Guess Who?: Beyond binary search, Probability in the Engi-
neering and Informational Sciences
, (2016) 30: 576592. Available online arXiv:1509.03327 10. Funk, J., Nica, M. and Noyes, M. Stabilization time for a type of evolution on binary strings,
Journal of Theoretical Probability, (2015) 28: 848865. Available online arXiv:1210.0444