标题： 从连续观点看机器学习 显示英文标题

标题： Machine Learning from a Continuous Viewpoint

摘要： 我们提出了一种机器学习的连续公式，作为变分法和微分积分方程的问题，非常类似于经典数值分析和统计物理的精神。 我们证明了传统的机器学习模型和算法，如随机特征模型、浅层神经网络模型和残差神经网络模型，都可以作为不同连续公式的特定离散化来恢复。 我们还展示了从这种连续公式中自然产生的新模型，如基于流的随机特征模型，以及新算法，如平滑粒子方法和谱方法。 我们讨论了如何在该框架下研究泛化误差和隐式正则化等问题。 显示英文摘要

摘要： We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, very much in the spirit of classical numerical analysis and statistical physics. We demonstrate that conventional machine learning models and algorithms, such as the random feature model, the shallow neural network model and the residual neural network model, can all be recovered as particular discretizations of different continuous formulations. We also present examples of new models, such as the flow-based random feature model, and new algorithms, such as the smoothed particle method and spectral method, that arise naturally from this continuous formulation. We discuss how the issues of generalization error and implicit regularization can be studied under this framework.