Arthur Jacot is one of the most powerful and creative mathematicians working on understanding and improving artificial intelligence.  His most influential contribution to the subject is the development of the Neural Tangent Kernel framework. This work, introduced in 2018, provides a rigorous theoretical tool for understanding the behavior of overparameterized or “wide” deep neural networks trained by gradient descent. Jacot and his colleagues proved that as the width of a network approaches infinity, the network’s evolution during training becomes linear and deterministic, governed by a fixed, positive-definite kernel known as the Neural Tangent Kernel . This result shows that in this specific “lazy training” regime, the highly non-convex optimization problem of training a deep neural network can be reduced to a well-understood problem in classical kernel methods, allowing researchers to analytically predict generalization and convergence rates without relying on empirical simulations.

 

Beyond these foundational results,  Jacot’s research explores the deeper theoretical principles governing high-dimensional machine learning. His work investigates the different regimes of training, distinguishing the “lazy” neural tangent kernel limit from the “feature learning” regime where the network’s internal representations genuinely evolve. He also  studies the implicit bias of optimization algorithms like Stochastic Gradient Descent aiming to mathematically explain why overparameterized models successfully generalize rather than simply memorize training data. His efforts focus on the characterization of  the geometric structure of the loss landscape and identifying how optimization dynamics naturally push deep neural networks  towards finding simplified, low-complexity solutions.  He is a clearly a leader in the effort to bridge the gap between the empirical success and the theoretical understanding of modern deep learning.  

 

Jacot is an Assistant Professor at the Courant Institute of Mathematical Sciences, NYU. Previously he was a PhD student at the EPFL under the supervision of Clément Hongle