About Me

I am an assistant professor in the Math & Statistics Department at the University of Guelph working in the area of probability, stochastic processes, and their applications to machine learning. I am also affiliated with the CARE-AI institute and the Vector Institute.

Before Guelph, I was an NSERC postdoctoral fellow at the University of Toronto, with Jeremy Quastel as my supervisor. My old website, http://www.math.toronto.edu/mnica/ has some links to my previous projects.

Before my postdoc at U of T, I was a PhD student at the Courant Institute of Mathematical Sciences in New York under the advisement of Gérard Ben Arous.

Email: nicam@uoguelph.ca


Education

University of Toronto

2017 – 2020

Post-Doctoral Fellowship

New York University

2011 – 2017

PhD

University of Waterloo

2007 – 2011

BMath


Research

Finite Depth & Width Corrections to the Neural Tangent Kernel

(With Boris Hanan)

We prove the precise scaling, at finite depth and width, for the mean and variance of the neural tangent kernel (NTK) in a randomly initialized ReLU network. ICLR Spotlight.

. . . . .

Uniform Convergence to the Airy Line Ensemble

(With Duncan Dauvergne & Bálint Virág)

We prove a general theorem for uniform convergence to the Airy line ensemble that applies to many different last passage percolation settings

. . . . .

Solution of the Kolmogorov Equation for TASEP

(With Jeremy Quastel & Daniel Remenik)

We provide a direct and elementary proof that the transition probability formulas for TASEP solve the Kolmogorov backward equation. Published in Annals of Probability.

Theory of Deep Learning Notes/Videos

Notes on Infinite Depth-and-Width Limits

Notes on Feature Regression and Wide Neural Networks

Expository Math Notes/Videos

Notes on Fibonacci Numbers using Generating Functions and Infinite Sums

Notes on Fibonacci Numbers using Linear Algebra