: Machine learning tools have started to make an impact in building better tools to analyze physical, chemical and biological systems. In this talk I will briefly review some recent tools such as equivariance and diffusion, and meditate on the connection between optimal transport, diffusion based models, PDEs, optimal control and density functional theory. After this meditation, I will dive a little deeper into equivariant diffusion models for molecule generation, path integral control for transition path sampling, the Navier Stokes equation for weather modeling, and, inspired by traveling waves observed in the brain, using waves as an inductive bias to model the dynamics of latent representations in neural networks. As a cherry on the cake, I will discuss infinitely wide, infinitely deep neural networks and generalize those to quantum field neural networks, resulting in particle-like states, called "hintons".
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