论文标题
迈向基于神经网络的机器学习的数学理解：我们知道的以及我们不知道什么
Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't
论文作者
论文摘要
本文的目的是回顾过去几年所取得的成就，以理解基于神经网络的机器学习的成功和微妙的原因。在良好的旧应用数学的传统中，我们不仅会注意严格的数学结果，而且还要关注仔细的数值实验以及简化模型的分析所获得的见解。在此过程中，我们还列出了开放问题，我们认为这是进一步研究的最重要主题。这不是对这个快速移动的领域的完整概述，但我们希望提供一种观点，这可能对该地区的新研究人员有帮助。
The purpose of this article is to review the achievements made in the last few years towards the understanding of the reasons behind the success and subtleties of neural network-based machine learning. In the tradition of good old applied mathematics, we will not only give attention to rigorous mathematical results, but also the insight we have gained from careful numerical experiments as well as the analysis of simplified models. Along the way, we also list the open problems which we believe to be the most important topics for further study. This is not a complete overview over this quickly moving field, but we hope to provide a perspective which may be helpful especially to new researchers in the area.
