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This talk begins with a brief discussion of the pivotal contributions of John Hopfield and Geoffrey Hinton to the field of neural networks and artificial intelligence (AI), as recognized by this year's Nobel Prize in Physics. We will start with an introduction to Hopfield's associative memory networks, which laid the groundwork for energy-based models and neural computation. From there, the discussion will branch into two transformative directions: the evolution of sequence modeling, driven by advances in backpropagation and recurrent neural networks, and the development of probabilistic generative models, starting with Boltzmann machines and culminating in modern diffusion models. We will trace how these foundational ideas in neural networks led to advances in both sequence modeling, integral to tasks such as natural language processing and time series prediction, and generative modeling, which has revolutionized domains like image and video synthesis. Throughout the talk, I will connect these ideas to ongoing research, including my own work on developing novel machine learning methods to better understand and model complex dynamical systems.
I am an applied mathematician working in machine learning. I also work in mathematical physics and, broadly speaking, probability theory and its applications.
I am an Assistant Professor of Mathematics at KTH Royal Institute of Technology since July 2024. I am also a WINQ Fellow at Nordita, hosted jointly by KTH and Stockholm University, since June 2021. I was a Nordita Fellow from 2018-2021.
I completed my PhD in Applied Mathematics at the University of Arizona in May 2018, under supervision of Jan Wehr. Prior to that, I studied mathematics and physics at the University of Michigan, initially delving into actuarial/financial mathematics.