We introduce a novel framework for optimization based on energy-conserving Hamiltonian dynamics in a strongly mixing (chaotic) regime and establish some of its key properties analytically and numerically. The prototype is a discretization of Born-Infeld dynamics, with a squared relativistic speed limit depending on the objective function. This class of frictionless, energy-conserving optimizers proceeds unobstructed until slowing naturally near vanishing loss (up to a self-tunable hyper-parameter shift), which dominates the phase space volume of the system. Building from studies of chaotic systems such as dynamical billiards, we formulate a specific algorithm with good performance on machine learning and PDE-solving tasks, including generalization (so far studied at small scale). In progress are experiments on applications to computational chemistry, sampling, and larger-scale ML, along with further theoretical study of its impact on representation/feature learning. An application of this ML-inspired method to numerical PDE solving for string compactifications blends three of Mike’s many far-reaching insights.
De Nathan Seiberg
De Vijay Balasubramanian
De Steve Zelditch
De Eva Silverstein
De Eliezer Rabinovici
De Alexander Gorsky
De Rémi Monasson
De David McAllester
De Luca Mazzucato
De Alexander Belavin
De Washington Taylor
De Gérard Ben Arous
De Olivier Benoist
De Viviane Pons
De Viviane Pons
