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1 Computational Photography Si Lu Spring onal_photography.htm 05/29/2018
2 Last Time o 3D Video Stabilization 2
3 Introduction of Neural Networks 3
4 Content Introduction Artificial vs. Biological Neural Nets What are Neural Networks? Neural Network-Basic What is in the black box Gradient Descent Method Speed up training Activation Function Morden Neural Networks 4
5 Content Introduction Artificial vs. Biological Neural Nets What are Neural Networks? Neural Network-Basic What is in the black box Gradient Descent Method Different Optimizors Activation Function Morden Neural Networks 5
6 Artificial vs. Biological Neural Nets
7 7
8 8
9 9
10 10
11 Artificial = Biological? Neuron 90 Billion 11
12 Artificial = Biological?
13 Artificial = Biological?
14 Artificial = Biological?
15 Artificial = Biological?
16 Artificial = Biological?
17 Artificial = Biological?
18 Artificial = Biological?
19 Artificial = Biological?
20 Artificial = Biological?
21 Artificial = Biological?
22 Artificial = Biological?
23 Artificial = Biological? =
24 Content Introduction Artificial vs. Biological Neural Nets What are Neural Networks? Neural Network-Basic What is in the black box Gradient Descent Method Speed up training Activation Function Morden Neural Networks 24
25 What are Neural Networks?
26 What are Neural Networks? Neural network, or artificial neural network, is a computing system inspired by the biological neural networks that constitute animal brains wikipedia
27 What are Neural Networks? wikipedia
28 What are Neural Networks? Input Hidden layer 1 Hidden layer 2 Output wikipedia
29 What are Neural Networks?
30 What are Neural Networks?
31 What are Neural Networks?
32 What are Neural Networks? Trainging dataset Ground truth labels
33 What are Neural Networks?
34 What are Neural Networks?
35 What are Neural Networks?
36 What are Neural Networks? Error
37 What are Neural Networks? Error
38 What are Neural Networks? Repeat millions of times
39 What are Neural Networks?
40 What are Neural Networks?
41 Content Introduction Artificial vs. Biological Neural Nets What are Neural Networks? Neural Network-Basic What is in the black box? Gradient Descent Method Speed up training Activation Function Morden Neural Networks Overfitting-Batch Normalization, Dropout From LeNet to ResNet 41
42 Neural Network Basics
43 Content Introduction Artificial vs. Biological Neural Nets What are Neural Networks? Neural Network-Basic What is in the black box? Gradient Descent Method Speed up training Activation Function Morden Neural Networks 43
44 What is in the black box?
45 What is in the black box?
46 What is in the black box?
47 What is in the black box?
48 What is in the black box?
49 What is in the black box? Neural networks are trained to extract higher and higher levels of abstract features to better represent the dataset via back-propogation
50 What is in the black box? x 1 w 1 x 2 w 2 Σ AF y w 3 x 3 input parameters output Basic Unit: Neuron
51 What is in the black box? x 1 w 1 x 2 w 2 Σ AF y w 3 x 3 input parameters output y = w 1 x 1 +w 2 x 2 +w 3 x 3
52 What is in the black box? x 1 w 1 x 2 w 2 Σ AF y w 3 x 3 input parameters output y = Wx T
53 Content Introduction Artificial vs. Biological Neural Nets What are Neural Networks? Neural Network-Basic What is in the black box? Gradient Descent Method Speed up training Activation Function Morden Neural Networks 53
54 Gradient Descent Method x 1 w 1 x 2 w 2 Σ AF y w 3 x 3 input parameters output y = Wx T
55 Gradient Descent Method y = Wx T Q1. What is the optimal W? Q2. How to obtain the optimal W?
56 Gradient Descent Method W opt = argmin W y-wx T 2 Q1. What is the optimal W? Q2. How to obtain the optimal W?
57 Gradient Descent Method W opt = argmin W y-wx T 2 loss Q1. What is the optimal W? Q2. How to obtain the optimal W?
58 Gradient Descent Method Optimization: Gradient Descent Q1. What is the optimal W? Q2. How to obtain the optimal W?
59 Gradient Descent Method Simplification Original loss function: f= y-wx T 2
60 Gradient Descent Method Simplification Original loss function: f= y-wx T 2 Simplify 1: single w/x/y: f=(y-wx) 2
61 Gradient Descent Method Simplification Original loss function: f= y-wx T 2 Simplify 1: single w/x/y: f=(y-wx) 2 Simplify 2: y=0, x=1: f=w 2
62 Gradient Descent Method f w
63 Gradient Descent Method f w
64 Gradient Descent Method f w
65 Gradient Descent Method
66 Gradient Descent Method
67 Gradient Descent Method f w
68 Content Introduction Artificial vs. Biological Neural Nets What are Neural Networks? Neural Network-Basic What is in the black box? Gradient Descent Method Speed up training Activation Function Morden Neural Networks 68
69 Speed up Training: dataset Large numbe of x, y, w y = Wx T
70 Speed up Training: dataset
71 Speed up Training: dataset Batch
72 Speed up Training: dataset Batch
73 Speed up Training: dataset Batch Stochastic Gradient Descent (SGD)
74 Speed up Training: optimizer Original: W += - LR * dx
75 Speed up Training: optimizer Original: W += - LR * dx Momentum: m += b 1 *m- LR * dx W += m Adding dowhill - inertia
76 Speed up Training: optimizer Original: W += - LR * dx AdaGrad: v += dx^2 W += -LR * dx/sqrt(v) Adding breaking shoes - resistance
77 Speed up Training: optimizer Momentum + AdaGrad RMSProp Adam (Popular)
78 Content Introduction Artificial vs. Biological Neural Nets What are Neural Networks? Neural Network-Basic What is in the black box? Gradient Descent Method Speed up training Activation Function Morden Neural Networks 78
79 Activation Function x 1 w 1 x 2 w 2 Σ AF y w 3 x 3 input parameters output y = Wx T
80
81 Activation Function
82 Activation Function Activate different neurons for different input
83 Activation Function Activate different neurons for different input
84 Activation Function Team Salary Championship Essentially: adding non-linearty
85 Activation Function Team Salary Team Salary Championship Championship Essentially: adding non-linearty
86 Next Time Introduction Artificial vs. Biological Neural Nets What are Neural Networks? Neural Network-Basic What is in the black box? Gradient Descent Method Speed up training Activation Function Morden Neural Networks 86
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