Abstract: We are rapidly entering an age of machine learning with the potential to revolutionize particle physics. In this talk, I will motivate that deepening the fundamental connections between physics and machine learning will help us solve big problems in both fields. In particular, I will motivate how an emerging area of research, which formulates field theories in terms of neural networks, paves the way for performing numerical, non-perturbative field theory calculations, operating as a distinct alternative to lattice methods. I will show results that motivate a “dynamic” extension to this framework which allows us to explore the space of field theories. Using the Exact Renormalization Group (ERG) as an example, I will go over how training neural networks can be viewed as performing an inverse ERG flow in the dual space of field theories. Underlying these connections is the mathematical framework of optimal transport which also offers rigorous uncertainty estimation.