We show that Polchinski's equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This gives a surprising information-theoretic formulation of the exact renormalization group, expressed in the language of optimal transport. We will provide reviews of both the exact renormalization group, as well as the theory of optimal transportation. Our techniques generalize to other RG flow equations beyond Polchinski's. Moreover, we establish a connection between this more general class of RG flows and stochastic Langevin PDEs, enabling us to construct ML-based adaptive bridge samplers for lattice field theories.

Bio: Jordan Cotler has a Ph.D. in physics from Stanford University and is currently a Junior Fellow at the Harvard Society of Fellows. Using the framework of algorithms, entanglement, and complexity, he addresses fundamental questions in quantum field theory, quantum gravity, and quantum many-body systems. His contributions include developing quantum algorithms for learning properties of natural systems, statistical methods for characterizing quantum many-body chaos, and quantum information techniques for describing black holes and accelerating universes.