Deep Learning: An Introduction for Applied Mathematicians
Deep Learning: An Introduction for Applied Mathematicians
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DOI：
10.1137/18m1165748
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发表时间：
2019-12-01
期刊：
影响因子：
10.2
通讯作者：
Higham, Desmond J.
中科院分区：
文献类型：
--
作者：
Higham, Catherine F.;Higham, Desmond J.
多层人工神经网络正在成为许多应用领域的普遍工具。这场深度学习革命的核心是来自应用和计算数学的熟悉概念，特别是微积分、逼近论、优化和线性代数。本文从应用数学的角度简要介绍了深度学习的基本思想。我们的目标受众包括热衷于了解该领域的数学研究生和最后一年的本科生。对于希望通过参考深度学习技术的应用来活跃课堂气氛的数学教师来说，本文也可能有用。我们关注三个基本问题：什么是深度神经网络？网络是如何训练的？什么是随机梯度法？我们用一段简短的 MATLAB 代码来说明这些想法，该代码用于设置和训练网络。我们还演示了最先进的软件在大规模图像分类问题上的使用。最后我们引用了当前的文献。
Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics, notably from calculus, approximation theory, optimization, and linear algebra. This article provides a very brief introduction to the basic ideas that underlie deep learning from an applied mathematics perspective. Our target audience includes postgraduate and final year undergraduate students in mathematics who are keen to learn about the area. The article may also be useful for instructors in mathematics who wish to enliven their classes with references to the application of deep learning techniques. We focus on three fundamental questions: What is a deep neural network? How is a network trained? What is the stochastic gradient method? We illustrate the ideas with a short MATLAB code that sets up and trains a network. We also demonstrate the use of state-of-the-art software on a large scale image classification problem. We finish with references to the current literature.