论文标题
出生于AI的污染（BI）：优化能源支持下降（ECD）
Born-Infeld (BI) for AI: Energy-Conserving Descent (ECD) for Optimization
论文作者
论文摘要
我们在强烈混合（混乱）方面引入了一个基于能量持续的哈密顿动力学优化的新型框架，并在分析和数值上建立其关键特性。该原型是对出生式动力学的离散化，根据目标函数的不同，具有平方相对论的速度限制。这类无摩擦，持势的优化器毫不动摇地进行，直到自然放慢速度在最小的损失附近，这主要是系统的相位空间体积。从对动力台球等混乱系统的研究中，我们制定了一种特定的算法，在机器学习和解决PDE解决任务（包括概括）方面具有良好的性能。它不能以较高的局部最小值停止，这是非凸损失功能的优势，并且比浅层山谷中的GD+动量更快。
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.
