課程資訊
課程名稱
深度學習之數學基礎
Mathematics in Deep Learning 
開課學期
110-2 
授課對象
理學院  數學研究所  
授課教師
黃文良 
課號
MATH5255 
課程識別碼
221 U8940 
班次
 
學分
3.0 
全/半年
半年 
必/選修
選修 
上課時間
星期四7,8,9(14:20~17:20) 
上課地點
天數305 
備註
總人數上限:40人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1102MATH5255_ 
課程簡介影片
 
核心能力關聯
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課程大綱
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課程概述

I will first review some methods for learning, then go to the technique that makes learning DNNs work. Along this line, I will focus on analysis from the perspective of optimization. The goal is to understand why and how a DNN functions. The outline roughly covers:
1. History and models of neural networks.
2. Why deep? Universality theorem for shallow/deep neural networks.
3. Optimization algorithms: back-propagation, block-coordinate descent
algorithms.
4. Classification problem: dimension reduction methods, support vector machines
and kernel methods. Un-supervised learning and auto-encoder.
5. Generative Adversarial Network.
6. ResNet, Mobile Net, U-nets, and RNN.
7. Using DNN to solve problems: the inverse problem, the forward inference
problem, and the generalization. 

課程目標
Students who are interested in analysis learn some analysis tools for DNNs.  
課程要求
Linear algebra and optimization (options) 
預期每週課後學習時數
 
Office Hours
 
參考書目
Given in class notes.
 
指定閱讀
Given in class notes. 
評量方式
(僅供參考)
   
課程進度
週次
日期
單元主題
第2週
2/24  NcCullock-Pitts Model and Rosenblatt's perceptron algorithm 
第3週
3/03  Classification and regression trees 
第4週
3/10  Support vector machine and its implication 
第5週
3/17  Generalization errors 
第6週
3/24  Influential instances 
第7週
3/31  Universality approximation theorems for shallow and Deep NNs  
第8週
4/07  Learning slow down problems  
第9週
4/14  GANs and half plane cutting method 
第10週
4/21  W-GAN (I) and Back-propagation algorithm (II) 
第11週
4/28  The gradient unstable problem (activation functions and non-uniform weight distribution) 
第12週
5/05  Take home and open reference midterm  
第13週
5/12  Capturing global information from non-local mean to transformer and Bert 
第14週
5/19  Dimension reduction and self-supervised learning 
第15週
5/26  Autoencoder, invertible DNNs, and un-rolling algorithms. 
第16週
6/02  Un-rectification(meet.google.com/ztd-bydr-cvy) 
第18週
  Final exam. You need to submit it before June 16th to the department (5th floor)