Born-Infeld (BI) for AI: Energy-Conserving Descent (ECD) for Optimization
This provides a novel optimization method for machine learning and PDE-solving tasks, offering advantages in non-convex settings.
The paper tackles optimization in non-convex loss functions by introducing an energy-conserving Hamiltonian framework based on Born-Infeld dynamics, resulting in faster convergence than GD+momentum in shallow valleys and avoidance of high local minima.
We introduce a novel framework for optimization based on energy-conserving Hamiltonian dynamics in a strongly mixing (chaotic) regime and establish 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 the minimal loss, 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. It cannot stop at a high local minimum, an advantage in non-convex loss functions, and proceeds faster than GD+momentum in shallow valleys.