1. Towards Deep Understanding on Convolutional Neural Networks
Lingxi Xie
The Johns Hopkins University
Slides available on my homepage (search “Lingxi Xie”)

2. Towards Deep Understanding on CNN
Outline
Introduction
Towards Deep Understanding on CNN
Neuron-level: the Max-Conv Operator
Mid-level: the GNPP Algorithm
Regularization: the DisturbLabel Algorithm
Feature Visualization: the InterActive Algorithm
Conclusions and Future Work
8/9/2019
Towards Deep Understanding on CNN

3. Towards Deep Understanding on CNN
Outline
Introduction
Towards Deep Understanding on CNN
Neuron-level: the Max-Conv Operator
Mid-level: the GNPP Algorithm
Regularization: the DisturbLabel Algorithm
Feature Visualization: the InterActive Algorithm
Conclusions and Future Work
8/9/2019
Towards Deep Understanding on CNN

4. Towards Deep Understanding on CNN
Lingxi Xie (谢凌曦)
Education Background
Bachelor in Engineering, Tsinghua University, 2010
Ph.D. in Engineering, Tsinghua University, 2015
Working Experience
Visiting Student, the University of Texas at San Antonio, 2014 (supervisor: Prof. Qi Tian)
Research Intern, Microsoft Research Asia, 2013 – 2015 (supervisor: Dr. Jingdong Wang)
Postdoc Researcher, University of California, Los Angeles, 2015 – 2016 (supervisor: Prof. Alan Yuille)
8/9/2019
Towards Deep Understanding on CNN

5. Towards Deep Understanding on CNN
Lingxi Xie (谢凌曦)
Research interests
Computer Vision
Large-scale image classification
Fine-grained object recognition
Multimedia Information Retrieval
Near-duplicate object retrieval
Large-scale image search
Deep Learning
The Convolutional Neural Networks (CNN)
8/9/2019
Towards Deep Understanding on CNN

6. Contributors in Alphabetical Order
Dr. John Flynn, Univ. of California, Los Angeles
Prof. Weiyao Lin, Shanghai Jiao Tong University
Prof. Qi Tian, Univ. of Texas at San Antonio
Dr. Jingdong Wang, Microsoft Research Asia
Prof. Meng Wang, Hefei Univ. of Technology
Zhen Wei, Shanghai Jiao Tong University
Prof. Alan Yuille, the Johns Hopkins University
Prof. Bo Zhang, Tsinghua University
Dr. Liang Zheng, Univ. of Texas at San Antonio
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Towards Deep Understanding on CNN

7. Towards Deep Understanding on CNN
Introduction
Computer vision and image processing
An important direction of artificial intelligence
Teaching computers to understand images
A wide range of real-world applications
Image classification
Image retrieval or search
Object detection
Semantic segmentation
......
8/9/2019
Towards Deep Understanding on CNN

8. Talk: Deep Learning and CNN
Image Classification
BIRD
DOG
DOG
FLOWER
FLOWER
Image
Dataset
Black-foot. Albatross
Chihuahua
daffodil
Groove-billed Ani
Siberian Husky
snowdrop
Bird-200
Dog-120
Flwr-102
Rhinoceros Auklet
Golden Retriever
Colts’ foot
Test
FLOWER ? ?
DOG
Colts’ foot
Siberian Husky
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Talk: Deep Learning and CNN

9. Talk: Deep Learning and CNN
Image Retrieval
Image
Dataset
Holiday
QUERY TP TP TP TP
Test TP
True-
Positive FP TP FP TP FP
False-Positive
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Talk: Deep Learning and CNN

10. Fast Development and Challenges
Computer vision is promising
The performance on almost every benchmark is largely boosted in the recent 5 years
The industry has applied many state-of-the-art techniques to real-world systems
Computer vision is very difficult
Many fundamental problems remain unsolved
Deep learning: a double-edged sword
8/9/2019
Towards Deep Understanding on CNN

11. A Machine Learning Perspective
Problem settings
Dataset: 𝒟= 𝐱 𝑛 , 𝐲 𝑛 𝑛=1 𝑁
𝐱 𝑛 : 𝐷-dimensional input vector (𝐷 is often large)
𝐲 𝑛 : 𝐶-dimensional output vector (𝐶 is # of classes)
Classification vs. regression: different encoding schemes
Model: 𝐟 𝐱 ∈ 𝕄 𝐶
For image processing, the function 𝐟 𝐱 is often very complicated, and thus difficult to be manually designed
Learning: supervised vs. unsupervised
8/9/2019
Talk: Deep Learning and CNN

12. Towards Deep Understanding on CNN
Deep Learning
Deep Learning
The state-of-the-art machine learning theory
Using a cascade of many layers of non-linear neurons for feature extraction and transformation
Learning multiple levels of feature representation
Higher-level features are derived from lower-level features to form a hierarchical architecture
Multiple levels of representation correspond to different levels of abstraction
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Towards Deep Understanding on CNN

13. Towards Deep Understanding on CNN
Deep Learning (cont.)
The prerequisites of deep learning
A large-scale dataset (e.g., ImageNet)
Powerful computational resources (e.g., GPU)
A side note: designing an effective image processing framework
From global to local: the BoVW model
From shallow to deep: the CNN model
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Towards Deep Understanding on CNN

14. Talk: Deep Learning and CNN
Blooming Development!
Conference publications
CVPR 2012: <10 Deep Learning papers.
CVPR 2016: >200 Deep Learning papers!
Competitions
ILSVRC 2011: no CNNs in top-10
ILSVRC 2012: only AlexNet in top-10 (No. 1)
ILSVRC 2015: all CNNs in top-10
8/9/2019
Talk: Deep Learning and CNN

15. Applications in Computer Vision
Basic networks for image classification
AlexNet, GoogLeNet, VGGNet, ResNet, etc.
Fine-tuning for other computer vision tasks
Object detection: R-CNN, Faster R-CNN, etc.
Semantic segmentation: FCN, DeepLab, etc.
Deep features for transfer learning
Image classification on small datasets, image retrieval, person re-identification, etc.
8/9/2019
Talk: Deep Learning and CNN

16. Applications in Other Fields
Which problems to solve?
Given a problem, if we can define a differentiable loss function, then it is possible to construct a deep network to formulate this problem
What are the advantages?
Deep learning is good at learning complicated data distribution, it shows advantages especially when we are not aware of the exact distribution, but we can “let data speak themselves”
8/9/2019
Talk: Deep Learning and CNN

17. Convolutional Neural Networks
The Convolutional Neural Networks
A fundamental machine learning tool
Good performance in a wide range of problems in computer vision as well as other research areas
Evolutions in many real-world applications
Theory: a multi-layer, hierarchical network often has a larger capacity, also requires a larger amount of data to get trained
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Towards Deep Understanding on CNN

18. Designing CNN Structures
History
From linear to non-linear
From shallow to deep
From fully-connected to convolutional
Today
A cascade of various types of non-linear units
Typical units: convolution, pooling, activation, etc.
8/9/2019
CVPR 2017 – In submission

19. Convolutional Neural Networks
The Convolutional Neural Networks
Example 1: the LeNet [LeCun, 1998]
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Towards Deep Understanding on CNN

20. Convolutional Neural Networks
The Convolutional Neural Networks
Example 2: the AlexNet [Krizhevsky, 2012]
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Towards Deep Understanding on CNN

21. Towards Deep Understanding on CNN
Basic Notations
CNN is trained on a dataset 𝒮= 𝐱 𝑛 , 𝐲 𝑛 𝑛=1 𝑁 , where 𝑁 is the dataset size, 𝐱 𝑛 ∈ ℝ 𝐷 is a data point, and 𝐲 𝑛 = 0,⋯,0,1,0,⋯,0 Τ ∈ ℝ 𝐶
Let CNN be a model 𝕄: 𝐡 𝐗 0 ;𝜽 ∈ ℝ 𝐶 , in which 𝐗 0 is the input image, and 𝜽 is the set of weights (neuron connections)
𝐗 𝑙 is the neuron responses on the 𝑙-th layer, which is a 𝑊 𝑙 × 𝐻 𝑙 × 𝐷 𝑙 cube
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Towards Deep Understanding on CNN

22. Towards Deep Understanding on CNN
CNN Training Process
In each iteration 𝑡, a mini-batch ℬ 𝑡 is sampled from 𝒮, and the current model parameters 𝜽 𝑡−1 are updated via Stochastic Gradient Descent (SGD):
𝜽 𝑡 = 𝜽 𝑡−1 + 𝛾 𝑡−1 ∙ 1 ℬ 𝑡 ∙ 𝐱,𝐲 ∈ ℬ 𝑡 𝛻 𝜽 𝑡−1 𝐿 𝐱,𝐲
𝛾 𝑡−1 : the current learning rate
𝐿 𝐱,𝐲 : the loss function of 𝐱,𝐲
Computed via gradient back-propagation
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Towards Deep Understanding on CNN

23. Towards Deep Understanding on CNN
Our Goal
Many basic properties of CNN remain unclear
The main reason may lie in the deep structure and the high-dimensional space, which make it very difficult to analyze the behavior of the network
CNN should not be considered as a black box
We aim at exploring the properties in different ways, including going deep into the framework, and performing some fine-scaled visual recognition tasks (part detection, etc.)
8/9/2019
Towards Deep Understanding on CNN

24. Towards Deep Understanding on CNN
Outline
Introduction
Towards Deep Understanding on CNN
Neuron-level: the Max-Conv Operator
Mid-level: the GNPP Algorithm
Regularization: the DisturbLabel Algorithm
Feature Visualization: the InterActive Algorithm
Conclusions and Future Work
8/9/2019
Towards Deep Understanding on CNN

25. Towards Deep Understanding on CNN
Outline
Introduction
Towards Deep Understanding on CNN
Neuron-level: the Max-Conv Operator
Mid-level: the GNPP Algorithm
Regularization: the DisturbLabel Algorithm
Feature Visualization: the InterActive Algorithm
Conclusions and Future Work
8/9/2019
Towards Deep Understanding on CNN

26. Towards Deep Understanding on CNN
Motivation
CNN feature is not reversal-invariant
Reversal-invariant: given an image 𝐗 0 and its reversed (left-right flipped) copy, the intermediate output of a model 𝕄 should be identical on them
A convolutional filter (kernel) can only capture visual contents in one direction
Given that the number of filters on each layer is limited, this property largely constrains the model capacity
8/9/2019
Towards Deep Understanding on CNN

27. Deep Features on Small Datasets
Six (6) datasets used
Generic classification: Caltech256
Scene classification: MIT Indoor-67, SUN-397
Fine-grained object recognition: Oxford Pet-37, Oxford Flower-102, Caltech-UCSD Bird-200
We evaluate the original deep features and InterActive features on different layers individually, and then combine them together
8/9/2019
Towards Deep Understanding on CNN

28. Reversal Invariance: Deep Features
Model
C-256
I-67
S-397
P-37
F-102
B-200
AlexNet (w/o AUGM), ORIG
67.69
53.91
41.01
76.95
84.56
43.43
AlexNet (w/o AUGM), AVG
70.39
58.10
44.47
79.60
87.17
47.98
AlexNet (w/o AUGM), MAX
70.17
57.77
44.19
79.40
86.88
47.82
AlexNet (w/ AUGM), ORIG
70.48
57.78
44.77
80.85
87.27
47.17
AlexNet (w/ AUGM), AVG
71.75
59.76
46.42
81.79
88.34
49.28
AlexNet (w/ AUGM), MAX
71.57
59.45
46.24
81.55
88.26
49.15
VGGNet-16 (w/ AUGM), ORIG
82.69
75.78
60.43
93.09
93.69
71.62
VGGNet-16 (w/ AUGM), AVG
83.09
76.06
61.50
93.31
94.01
72.66
VGGNet-16 (w/ AUGM), MAX
83.12
75.93
61.39
93.25
93.97
72.73
VGGNet-19 (w/ AUGM), ORIG
83.51
75.49
61.30
93.10
93.57
71.70
VGGNet-19 (w/ AUGM), AVG
83.90
75.93
62.40
93.17
93.83
72.55
VGGNet-19 (w/ AUGM), MAX
83.90
75.83
62.25
93.12
93.84
72.59
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Towards Deep Understanding on CNN

29. Towards Deep Understanding on CNN
Original Convolution
Original convolution
𝑓 𝑎,𝑏,𝑘 𝑙 𝐈;𝕄 = 𝐟 𝑎,𝑏 𝑙−1 , 𝜽 𝑘 𝑙 + 𝑏 𝑘 𝑙
When the kernel 𝜽 𝑘 𝑙 is not symmetric, 𝑓 𝑎,𝑏,𝑘 𝑙 is not reversal-invariant
Solution: using reversal-invariant operators!
8/9/2019
Towards Deep Understanding on CNN

30. Reversal-Invariant Convolution
Average convolution (Avg-Conv)
𝑓 𝑎,𝑏,𝑘 𝑙 𝐈;𝕄 = 𝐟 𝑎,𝑏 𝑙−1 , 𝜽 𝑘 𝑙 + 𝐟 𝑎,𝑏 𝑙−1 ,R , 𝜽 𝑘 𝑙 + 𝑏 𝑘 𝑙
Max convolution (Max-Conv)
𝑓 𝑎,𝑏,𝑘 𝑙 𝐈;𝕄 = max 𝐟 𝑎,𝑏 𝑙−1 , 𝜽 𝑘 𝑙 , 𝐟 𝑎,𝑏 𝑙−1 ,R , 𝜽 𝑘 𝑙 𝑏 𝑘 𝑙
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Towards Deep Understanding on CNN

31. Towards Deep Understanding on CNN
Explanation
Convolution is a template matching process
𝐟 𝑎,𝑏 𝑙−1 , 𝜽 𝑘 𝑙 : the matching score between the input patch 𝐟 𝑎,𝑏 𝑙−1 and the template 𝜽 𝑘 𝑙
An input patch gets a high score if it is similar to the template
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Towards Deep Understanding on CNN

32. Towards Deep Understanding on CNN
Explanation (cont.)
Reversal-invariant convolution: computing the matching scores of a patch and its reversed copy, and performing average or max operator
Avg-Conv: a patch gets a high score if it is similar to both the template and its reversed copy
Max-Conv: a patch gets a high score if it is similar to either the template or its reversed copy
Max-Conv is more reasonable, and it enlarges the model capacity by having more templates
8/9/2019
Towards Deep Understanding on CNN

33. Reversal-Invariant CNN
Replacing all the convolution layers (including fully-connected layers) of the original network with reversal-invariant convolution operators
Such a network produces identical features for an image and its reversed copy
This property can be proved with mathematical induction
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Towards Deep Understanding on CNN

34. Towards Deep Understanding on CNN
CIFAR Experiments
The CIFAR10/CIFAR100 datasets
Low-resolution natural images (10 or 100 classes)
50,000 training and 10,000 testing images
Uniformly distributed over 10/100 classes
The network structure
A 3-layer LeNet (input size: 32×32)
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Towards Deep Understanding on CNN

35. Towards Deep Understanding on CNN
CIFAR10 Results
CIFAR10
w/o AUGM
w/ AUGM
LeNet
18.11±.20
16.99±.22
LeNet, AVG
21.01±.35
20.99±.26
LeNet, MAX
16.93±.18
𝟏𝟔.𝟔𝟒±.17
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Towards Deep Understanding on CNN

36. Towards Deep Understanding on CNN
CIFAR100 Results
CIFAR100
w/o AUGM
w/ AUGM
LeNet
46.08±.26
44.55±.10
LeNet, AVG
47.79±.41
47.55±.31
LeNet, MAX
43.90±.19
𝟒𝟑.𝟔5±.16
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Towards Deep Understanding on CNN

37. Towards Deep Understanding on CNN
ILSVRC2012 Experiments
The ILSVRC2012 dataset
High-resolution natural images (1,000 classes)
1.3M training and 50K validation images
Almost uniformly distributed over all classes
The network structure
The AlexNet
5 convolution layers, 3 pooling layers, and 3 fully-connected layers
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Towards Deep Understanding on CNN

38. Towards Deep Understanding on CNN
ILSVRC2012 Results
ILSVRC2012, top-1
w/o AUGM
w/ AUGM
AlexNet
43.05±.19
42.52±.07
AlexNet, MAX
42.16±.05
𝟒𝟐.𝟏𝟎±.07
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39. Towards Deep Understanding on CNN
ILSVRC2012 Results
ILSVRC2012, top-5
w/o AUGM
w/ AUGM
AlexNet
20.62±.08
19.52±.05
AlexNet, MAX
19.42±.03
𝟏𝟗.𝟏𝟐±.07
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Towards Deep Understanding on CNN

40. Towards Deep Understanding on CNN
Back to Deep Features
Model
C-256
I-67
S-397
P-37
F-102
B-200
AlexNet (w/ AUGM), ORIG
70.75
58.04
45.12
81.02
87.39
47.53
AlexNet (w/ AUGM), AVG
71.97
60.01
46.64
81.98
88.40
.49.53
AlexNet (w/ AUGM), MAX
71.81
59.77
46.47
81.93
88.29
49.42
AlexNet-MAX (w/ AUGM), ORIG
71.78
59.91
46.47
81.92
88.17
49.55
8/9/2019
Towards Deep Understanding on CNN

41. Towards Deep Understanding on CNN
Summary
Reversal-invariant is important in extracting deep features and training a CNN model
Cancelling out the reversal transform in natural images
Max-Conv is an efficient solution
Considering the reversed copy of a filter (kernel)
Equivalently increasing the model capacity
Achieving reversal-invariance in deep features
8/9/2019
Towards Deep Understanding on CNN

42. Towards Deep Understanding on CNN
Outline
Introduction
Towards Deep Understanding on CNN
Neuron-level: the Max-Conv Operator
Mid-level: the GNPP Algorithm
Regularization: the DisturbLabel Algorithm
Feature Visualization: the InterActive Algorithm
Conclusions and Future Work
8/9/2019
Towards Deep Understanding on CNN

43. Towards Deep Understanding on CNN
Motivation
The basic units in a CNN are neurons
CNN considers each neuron individually, while we argue that it is important to model the co-occurrence of neuron responses
In the BoVW model, visual words are grouped as visual phrases, but it remains unclear if the same idea works well in neural networks
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Towards Deep Understanding on CNN

44. Towards Deep Understanding on CNN
Neural Words
Defined on a hidden layer 𝐗 𝑙 of the CNN, for simplicity, denote 𝐗 𝑙 as 𝐗
𝐗 is a 3D cube with 𝑊×𝐻×𝐷 neurons
We naturally consider the data as a set of 𝐷-dimensional neural words: 𝒳= 𝐱 𝑤,ℎ 𝑤=1,ℎ=1 𝑊,𝐻
The spatial position of each word is closely related to its receptive field on the input image
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Towards Deep Understanding on CNN

45. Geometric Neural Phrase
A geometric neural phrase is a group of neighboring neurons: 𝒢 𝑤,ℎ = 𝐱 𝑤,ℎ 𝑘 𝑘=0 𝐾
𝐱 𝑤,ℎ 0 = 𝐱 𝑤,ℎ : the central word
𝐱 𝑤,ℎ 𝑘 (𝑘>0): the side words, which are located in a small neighborhood of 𝐱 𝑤,ℎ
For each neural word, there is a neural phrase
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Towards Deep Understanding on CNN

46. Geometric Neural Phrase (cont.)
side words
Neural Phrase: Type 1
Neural Phrase: Type 2
central word
Convolutional Neural Network
neuron
map
conv
pool
fully-
connect
classifier
input image
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Towards Deep Understanding on CNN

47. Geometric Neural Phrase Pooling
Computing a 𝐷-dimensional vector for each geometric neural phrase individually
𝐳 𝑤,ℎ = 𝐱 𝑤,ℎ + max 𝑘>0 𝑠 𝑤,ℎ 𝑘 × 𝐱 𝑤,ℎ 𝑘
max 𝑘>0 : dimension-wise maximization
𝑠 𝑤,ℎ 𝑘 =σ or 𝑠 𝑤,ℎ 𝑘 = σ 2 , according to the relative position to the central word
σ∈ 0,1 : the smoothing parameter
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Towards Deep Understanding on CNN

48. Towards Deep Understanding on CNN
GNPP: an Illustration
Isolated neuron responses are punished
We argue that an isolated neuron response often corresponds to unexpected random noise, thus it is less reliable than clustered neuron responses
0.0
0.2
0.4
0.8
1.0
0.1
0.3
0.7
0.6
0.5
0.9
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49. Towards Deep Understanding on CNN
GNPP as a Network Layer
GNPP does not change the dimension of data, thus it can be inserted as an intermediate layer anywhere into a network
In practice, we only insert the GNPP layer between a convolutional layer and a pooling layer, since GNPP punishes isolated responses, and pooling after GNPP is an efficient way of aggregating these rectified neuron responses
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Towards Deep Understanding on CNN

50. Towards Deep Understanding on CNN
MNIST Experiments
The MNIST dataset
Handwritten digit recognition (10 classes)
60,000 training and 10,000 testing images
The network structure
A 2-layer LeNet (input size: 28×28)
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51. Towards Deep Understanding on CNN
MNIST Results L1 L2 D
T1 (1.0)
T1 (0.9)
T1 (0.8)
T2 (1.0)
T2 (0.9)
T2 (0.8)
0.87±.02
0.87±.02
0.87±.02
0.87±.02
0.87±.02
0.87±.02 √
0.72±.04
0.73±.03
0.70±.05
0.71±.06
0.71±.06
0.72±.04 √
0.75±.03
0.79±.02
0.77±.05
0.73±.04
0.75±.04
0.73±.05 √ √
𝟎.𝟕𝟐±.03
𝟎.𝟔𝟕±.04
𝟎.𝟔𝟗±.04
𝟎.𝟔𝟑±.03
𝟎.𝟔𝟒±.03
𝟎.𝟔𝟕±.03 √
0.72±.03
0.72±.03
0.72±.03
0.72±.03
0.72±.03
0.72±.03 √ √
0.59±.02
0.61±.05
0.62±.03
0.59±.03
0.59±.02
0.63±.03 √ √
0.63±.03
0.62±.07
0.64±.03
0.62±.05
0.60±.03
0.65±.03 √ √ √
𝟎.𝟓𝟖±.05
𝟎.𝟓𝟓±.05
𝟎.𝟓𝟕±.02
𝟎.𝟓𝟒±.05
𝟎.𝟓𝟔±.04
𝟎.𝟔𝟏±.05
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Towards Deep Understanding on CNN

52. Towards Deep Understanding on CNN
SVHN Experiments
The SVHN dataset
Street view digit recognition (10 classes)
73,257 training, 26,032 testing and 531,131 extra images (after pre-proc., 598,388 training images)
The network structure
A 3-layer LeNet (input size: 32×32)
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53. Towards Deep Understanding on CNN
SVHN Results L1 L2 L3
T1 (1.0)
T1 (0.9)
T1 (0.8)
T2 (1.0)
T2 (0.9)
T2 (0.8)
4.63±.06
4.63±.06
4.63±.06
4.63±.06
4.63±.06
4.63±.06 √
4.46±.06
4.47±.05
4.42±.09
4.42±.08
4.42±.07
4.43±.09 √
4.15±.08
4.18±.01
4.17±.07
4.08±.10
4.19±.07
4.20±.05 √ √
3.76±.03
3.72±.05
3.77±.06
3.53±.07
3.64±.07
3.65±.10 √
4.10±.05
4.07±.03
4.10±.05
4.10±.07
4.10±.03
4.14±.07 √ √
3.55±.10
3.60±.03
3.67±.06
3.47±.05
3.47±.02
3.55±.09 √ √
𝟑.𝟒𝟑±.06
3.52±.07
𝟑.𝟓𝟓±.04
𝟑.𝟒𝟏±.03
3.42±.04
3.51±.05 √ √ √
3.46±.07
𝟑.𝟒𝟕±.06
3.55±.06
3.43±.05
𝟑.𝟑𝟗±.01
𝟑.𝟒𝟔±.03
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Towards Deep Understanding on CNN

54. Towards Deep Understanding on CNN
CIFAR Experiments
The CIFAR10/CIFAR100 datasets
Low-resolution natural images (10 or 100 classes)
50,000 training and 10,000 testing images
Uniformly distributed over 10/100 classes
The network structure
A 3-layer LeNet (input size: 32×32)
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Towards Deep Understanding on CNN

55. Towards Deep Understanding on CNN
CIFAR10 Results L1 L2 L3
T1 (1.0)
T1 (0.9)
T1 (0.8)
T2 (1.0)
T2 (0.9)
T2 (0.8)
17.07±.15
17.07±.15
17.07±.15
17.07±.15
17.07±.15
17.07±.15 √
16.67±.22
16.80±.25
16.84±.12
16.65±.19
17.03±.15
17.04±.17 √
15.79±.22
16.09±.17
15.95±.31
15.69±.11
16.07±.27
15.90±.09 √ √
15.49±.15
15.31±.20
15.51±.25
15.27±.10
15.29±.14
15.28±.16 √
15.82±.23
15.76±.18
15.98±.14
16.05±.29
15.90±.25
15.94±.09 √ √
15.15±.20
15.29±.12
15.44±.19
15.29±.32
15.19±.35
15.20±.35 √ √
𝟏𝟒.𝟗𝟐±.18
15.00±.18
15.15±.15
𝟏𝟒.𝟖𝟑±.25
14.93±.20
14.92±.16 √ √ √
14.97±.17
𝟏𝟒.𝟖𝟑±.23
𝟏𝟒.𝟕𝟖±.17
15.22±.16
𝟏𝟒.𝟕𝟗±.26
𝟏𝟒.𝟖𝟓±.26
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56. Towards Deep Understanding on CNN
CIFAR100 Results L1 L2 L3
T1 (1.0)
T1 (0.9)
T1 (0.8)
T2 (1.0)
T2 (0.9)
T2 (0.8)
44.99±.19
44.99±.19
44.99±.19
44.99±.19
44.99±.19
44.99±.19 √
44.62±.17
44.53±.45
44.78±.06
44.43±.29
44.58±.36
44.58±.52 √
43.34±.23
43.71±.19
43.37±.26
43.21±.23
43.03±.27
43.37±.30 √ √
43.11±.24
42.77±.37
42.99±.24
42.96±.32
42.81±.38
43.08±.39 √
43.99±.07
43.63±.11
43.50±.26
43.38±.37
43.34±.27
43.46±.25 √ √
42.85±.38
42.81±.27
42.82±.29
43.08±.27
42.79±.34
42.93±.22 √ √
𝟒𝟐.𝟑𝟓±.30
𝟒𝟐.𝟑𝟒±.31
𝟒𝟐.𝟎𝟒±.20
𝟒𝟐.𝟗𝟐±.33
𝟒𝟐.𝟕𝟐±.25
𝟒𝟐.𝟓𝟒±.29 √ √ √
42.97±.29
42.77±.36
42.36±.18
43.31±.34
42.85±.18
42.60±.36
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Towards Deep Understanding on CNN

57. Analysis on Small Experiments
GNPP produces consistent accuracy gain when it is inserted anywhere into the network
However, larger improvement is observed when it is inserted after a high-level convolutional layer, which verifies the hypothesis that high-level layers better satisfy the assumption of GNPP
The parameter 𝐾 and 𝜎 do not impact a lot on the accuracy
In the following experiments, 𝐾=4 and 𝜎=0.8
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Towards Deep Understanding on CNN

58. Towards Deep Understanding on CNN
Larger Experiments
Experiments with a big network (BigNet) on the four small datasets
BigNet: an 11-layer network with 3×3 filters with 3 pooling layers, GNPP is inserted before the second and the third pooling layers
Experiments on the ImageNet (ILSVRC2012) with the AlexNet
GNPP is only inserted before the pool-5 layer
8/9/2019
Towards Deep Understanding on CNN

59. Results with a Big Network
MNIST
SVHN
CIFAR10
CIFAR100
Wan, ICML’13
𝟎.𝟐𝟏
1.94
9.32 −
Zeiler, ICLR’13
0.47
2.80
15.13
42.51
Goodfellow, ICML’14
0.45
2.47
9.38
38.57
Lin, ICLR’14
2.35
8.81
35.68
Lee, AISTATS’15
0.39
1.92
7.97
34.57
Liang, CVPR’15
0.31
1.77
7.09
𝟑𝟏.𝟕𝟓
BigNet, w/o GNPP
0.36
2.14
7.80
31.03
BigNet, w/ GNPP
𝟎.𝟑𝟐
𝟏.𝟖𝟕
𝟕.𝟏𝟒
𝟐𝟗.𝟕𝟒
Lee, AISTATS’16
𝟏.𝟔𝟗
𝟔.𝟎𝟓
32.37
8/9/2019
Towards Deep Understanding on CNN

60. Towards Deep Understanding on CNN
ILSVRC2012 Results
ILSVRC2012
top-1
top-5
AlexNet, w/o GNPP
43.19
19.87
AlexNet, w/ GNPP
𝟒𝟐.𝟏𝟔
𝟏𝟗.𝟐𝟒
8/9/2019
Towards Deep Understanding on CNN

61. GNPP Helps Image Representation
When GNPP is inserted after the conv-5 layer, the neuron response becomes smoother
Interestingly, since the roles of fully-connected layers do not change, the conv-5 layer adjusts itself to be more concentrated
As a result, the conv-5 layer in a GNPP-Net produces better image representation
On Caltech256, classification accuracy +1.20%
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Towards Deep Understanding on CNN

62. GNPP Helps Image Representation
The heatmap of neuron responses
Original
Image
AlexNet
Heatmap on
conv-5 layer
GNPPNet
GNPP-5 layer
eagle
snake
pig
boat
monkey
sleigh
crab
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63. GNPP Increases Model Capacity
GNPP adds more fixed neuron connections between a layer and its previous layer
Example: the GNPP layer after the conv-5 layer of the AlexNet increases the number of connections of each neuron to the previous layer from 9 to 21, and the total number of connections between conv-4 and conv-5 from 149.5M to 348.9M
Meanwhile, the number of parameters does not change, which prevents the net from over-fitting
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Towards Deep Understanding on CNN

64. GNPP Increases Model Capacity
Comparison: AlexNet with GNPP vs. AlexNet with 512 channels on conv-5
Number of connections between conv-4 and conv-5: 348.9M vs M
Extra time cost: 1.29% vs. 9.97%
Extra memory cost: 2.52% vs. 5.58%
Top-1 error rate: 42.16% vs %
Top-5 error rate: 19.24% vs %
8/9/2019
Towards Deep Understanding on CNN

65. GNPP Accelerates Network Training
GNPP allows a neuron has a larger receptive field, thus visual information is propagated faster throughout the network, consequently, the training process converges faster
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Towards Deep Understanding on CNN

66. GNPP Accelerates Network Training
GNPP allows a neuron has a larger receptive field, thus visual information is propagated faster throughout the network, consequently, the training process converges faster
8/9/2019
Towards Deep Understanding on CNN

67. Towards Deep Understanding on CNN
Summary
The co-occurrence of neuron responses needs to be considered explicitly
GNPP is a possible solution to this purpose
Effective: consistently improves the accuracy
Efficient: only requires 1.29% extra time and 2.52% extra memory costs
Can be explained in many different ways, including improving image representation, increasing model capacity, and accelerating network training
8/9/2019
Towards Deep Understanding on CNN

68. Towards Deep Understanding on CNN
Outline
Introduction
Towards Deep Understanding on CNN
Neuron-level: the Max-Conv Operator
Mid-level: the GNPP Algorithm
Regularization: the DisturbLabel Algorithm
Feature Visualization: the InterActive Algorithm
Conclusions and Future Work
8/9/2019
Towards Deep Understanding on CNN

69. The CNN Training Process
In each iteration 𝑡, a mini-batch ℬ 𝑡 is sampled from 𝒮, and the current model parameters 𝜽 𝑡−1 are updated via Stochastic Gradient Descent (SGD):
𝜽 𝑡 = 𝜽 𝑡−1 + 𝛾 𝑡−1 ∙ 1 ℬ 𝑡 ∙ 𝐱,𝐲 ∈ ℬ 𝑡 𝛻 𝜽 𝑡−1 𝐿 𝐱,𝐲
𝛾 𝑡−1 : the current learning rate
𝐿 𝐱,𝐲 : the loss function of 𝐱,𝐲
Computed via gradient back-propagation
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Towards Deep Understanding on CNN

70. A Review of CNN Regularization
A way of preventing over-fitting
Typical CNN regularization methods
Weight decay: constraining the parameters with ℓ 2 -regularization
Data augmentation: generating more training data by randomly transforming input images
Dropout: randomly discarding a part of neuron responses in training
Introducing stochastic operation in training
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Towards Deep Understanding on CNN

71. A Summary of CNN Regularization
Regularization Method
Regularization Units
Weight decay
Neuron connections (weights)
Data augmentation
Input layer (neurons)
Dropout
Hidden layer (neurons)
DropConnect
Stochastic Pooling
Pooling layer (neurons)
DisturbLabel
Loss layer (neurons)
DisturbLabel is the first work to regularize CNN on the loss layer!
8/9/2019
Towards Deep Understanding on CNN

72. The DisturbLabel Algorithm
Working on each mini-batch independently
An extra sampling process for each data point
Each data is disturbed with probability 𝛼
𝛼 is named the noise rate of the algorithm
For a disturbed datum 𝐱 𝑛 , 𝐲 𝑛 , it is assigned with a new class label 𝑐 , which is distributed uniformly among 1,2,⋯,𝐶 , regardless of the true label 𝑐.
This datum is changed to 𝐱 𝑛 , 𝐲 𝑛 , in which 𝐲 𝑛 depends on 𝑐 , and sent into the network training process.
8/9/2019
Towards Deep Understanding on CNN

73. A Toy Example of DisturbLabel
Each mini-batch is disturbed indepently
The disturbed label may remain unchanged 5
Batch 1 2
Batch 2
Batch 4 3
Batch 3 1
Batch 5 7
Batch 𝑇 ……
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Towards Deep Understanding on CNN

74. The Effect of Noise Rate 𝛼
A proper noise rate helps to improve the accuracy, but introducing too much noise harms recognition
Just like the drop-ratio in Dropout
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Towards Deep Understanding on CNN

75. DisturbLabel as Regularizer
DisturbLabel acts as a regularizer, which improves the recognition accuracy by preventing over-fitting
Training error increases while testing error decreases
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76. DisturbLabel as Model Ensemble
Given the original dataset 𝒮= 𝐱 𝑛 , 𝐲 𝑛 𝑛=1 𝑁 and the way of disturbing labels, we generate a family of noisy datasets 𝒰= 𝒮 𝑢 , 𝜆 𝑢 𝑢=1 𝑈 , where 𝒮 𝑢 is the 𝑢-th noisy set, and 𝜆 𝑢 is the probability of its presence
Note that the total number 𝑈 of possible datasets is exponentially large, thus it is impossible to train an individual model for each of these sets, nor to combine them at the testing stage
8/9/2019
Towards Deep Understanding on CNN

77. DisturbLabel as Model Ensemble (cont.)
An equivalent solution is to use mini-batches. The family of all possible mini-batches is 𝒱= ℬ 𝑣 , 𝜏 𝑣 𝑣=1 𝑉 , where 𝜏 𝑣 is the probability of the presence of the 𝑣-th mini-batch ℬ 𝑣
A mini-batch can be sampled from different 𝒮 𝑢 ’s
DisturbLabel samples one mini-batch following the probability distribution over the family 𝒱, and serves as an alternative way of training the same model with different data
8/9/2019
Towards Deep Understanding on CNN

78. Cooperation with Dropout
Both Dropout and DisturbLabel ensembles models
Dropout: different structures trained on same data
DisturbLabel: same structures trained on different data
8/9/2019
Towards Deep Understanding on CNN

79. DisturbLabel as Data Augmentation
Given a disturbed data point 𝐱 𝑛 , 𝐲 𝑛 , its loss function value is 𝐿 𝐱 𝑛 , 𝐲 𝑛 . We can generate a data point 𝐱 𝑛 , 𝐲 𝑛 with the original class label preserved, and 𝐿 𝐱 𝑛 , 𝐲 𝑛 ≈𝐿 𝐱 𝑛 , 𝐲 𝑛 , so that the effect of 𝐱 𝑛 , 𝐲 𝑛 is approximately equivalent to that of 𝐱 𝑛 , 𝐲 𝑛
𝐱 𝑛 , 𝐲 𝑛 can be considered an augmented datum
𝐱 𝑛 can be computed by iterative back-propagation
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Towards Deep Understanding on CNN

80. Visualizing Augmented Data
Ep. 1
1.77%
Ep. 2
1.08%
Ep. 5
0.97%
Ep. 10
0.90%
Ep. 20
0.86%
Ep. 10
28.97%
Ep. 20
25.61%
Ep. 30
24.82%
Ep. 40
24.68%
Ep. 60
23.33%
Ep. 80
22.74%
Ep. 100
22.50% 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9

81. Application: Few Training Data
The MNIST and CIFAR10 datasets
In all the classes, only 1% or 10% training data are preserved
MNIST
CIFAR10
1% data, w/o DisturbLabel
10.92
43.29
1% data, w/ DisturbLabel
6.38
37.83
10% data, w/o DisturbLabel
2.83
27.21
10% data, w/ DisturbLabel
1.89
24.37
100% data, w/o DisturbLabel
0.86
22.50
100% data, w/ DisturbLabel
0.66
20.26
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Towards Deep Understanding on CNN

82. Application: Imbalanced Training Data
The MNIST and CIFAR10 datasets
Except for the first class, only 1% or 10% training data are preserved
MNIST
CIFAR10
overall
first class
overall
first class
1% data, w/o DisturbLabel
9.31
0.28
42.01
11.48
1% data, w/ DisturbLabel
6.29
2.35
36.92
24.30
10% data, w/o DisturbLabel
2.78
0.47
26.50
13.09
10% data, w/ DisturbLabel
1.76
1.46
24.03
18.19
100% data, w/o DisturbLabel
0.86
0.89
22.50
22.41
100% data, w/ DisturbLabel
0.66
0.71
20.26
20.29
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Towards Deep Understanding on CNN

83. Towards Deep Understanding on CNN
MNIST Experiments
The MNIST dataset
Handwritten digit recognition (10 classes)
60,000 training and 10,000 testing images
The network structure
A 2-layer LeNet (input size: 28×28)
A 5-layer BigNet (input size: 24×24)
DisturbLabel with 𝛼=10%
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Towards Deep Understanding on CNN

84. Towards Deep Understanding on CNN
SVHN Experiments
The SVHN dataset
Street view digit recognition (10 classes)
73,257 training, 26,032 testing and 531,131 extra images (after pre-proc., 598,388 training images)
The network structure
A 3-layer LeNet (input size: 32×32)
A 5-layer BigNet (input size: 24×24)
DisturbLabel with 𝛼=10%
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Towards Deep Understanding on CNN

85. Towards Deep Understanding on CNN
MNIST and SVHN Results
MNIST
w/o DA
w/ DA
SVHN
w/o DA
w/ DA
Wan, ICML’13
0.52
0.21
Wan, ICML’13 −
1.94
Zeiler, ICLR’13
0.47 −
Zeiler, ICLR’13
2.80 −
Goodfellow, ICML’14
0.45 −
Goodfellow, ICML’14
2.47 −
Lin, ICLR’14
0.47 −
Lin, ICLR’14
2.35 −
Lee, AISTATS’15
0.39 −
Lee, AISTATS’15
1.92 −
Liang, CVPR’15
0.31 −
Liang, CVPR’15
1.77 −
LeNet, no regul.
0.86
0.48
LeNet, no regul.
3.93
3.48
LeNet, + Dropout
0.68
0.43
LeNet, + Dropout
3.65
3.25
LeNet, + DisturbLabel
0.66
0.45
LeNet, + DisturbLabel
3.69
3.27
LeNet, + both regul.
0.63
0.41
LeNet, + both regul.
3.61
3.21
BigNet, no regul.
0.69
0.39
BigNet, no regul.
2.87
2.35
BigNet, + Dropout
0.36
0.29
BigNet, + Dropout
2.23
2.08
BigNet, + DisturbLabel
0.38
0.32
BigNet, + DisturbLabel
2.28
2.21
BigNet, + both regul.
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Towards Deep Understanding on CNN
0.28
BigNet, + both regul.
2.19
2.02

86. Towards Deep Understanding on CNN
CIFAR Experiments
The CIFAR10/CIFAR100 datasets
Low-resolution natural images (10 or 100 classes)
50,000 training and 10,000 testing images
Uniformly distributed over 10/100 classes
The network structure
A 3-layer LeNet (input size: 32×32)
A 5-layer BigNet (input size: 24×24)
DisturbLabel with 𝛼=10%
8/9/2019
Towards Deep Understanding on CNN

87. Towards Deep Understanding on CNN
CIFAR Results
CIFAR10
w/o DA
w/ DA
CIFAR100
w/o DA
w/ DA
Wan, ICML’13 −
9.32
Wan, ICML’13 − −
Zeiler, ICLR’13
15.13 −
Zeiler, ICLR’13
42.51 −
Goodfellow, ICML’14
11.68
9.38
Goodfellow, ICML’14
38.57 −
Lin, ICLR’14
10.41
8.81
Lin, ICLR’14
35.68 −
Lee, AISTATS’15
9.69
7.97
Lee, AISTATS’15
34.57 −
Liang, CVPR’15
8.69
7.09
Liang, CVPR’15
31.75 −
LeNet, no regul.
22.50
15.76
LeNet, no regul.
56.72
43.31
LeNet, + Dropout
19.42
14.24
LeNet, + Dropout
49.08
41.28
LeNet, + DisturbLabel
20.26
14.48
LeNet, + DisturbLabel
51.83
41.84
LeNet, + both regul.
19.18
13.98
LeNet, + both regul.
48.72
40.98
BigNet, no regul.
11.23
9.29
BigNet, no regul.
39.54
33.59
BigNet, + Dropout
9.69
7.08
BigNet, + Dropout
33.30
27.05
BigNet, + DisturbLabel
9.82
7.93
BigNet, + DisturbLabel
34.81
28.39
BigNet, + both regul.
8/9/2019
9.45
Towards Deep Understanding on CNN
6.98
BigNet, + both regul.
32.99
26.63

88. Towards Deep Understanding on CNN
ILSVRC2012 Experiments
The ILSVRC2012 dataset
High-resolution natural images (1,000 classes)
1.3M training and 50K validation images
Almost uniformly distributed over all classes
The network structure
The AlexNet
5 convolution layers, 3 pooling layers, and 3 fully-connected layers
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89. Towards Deep Understanding on CNN
ILSVRC2012 Results
ILSVRC2012
top-1
top-5
AlexNet, + Dropout
43.1
19.9
AlexNet, + both regul.
42.8
19.7
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Towards Deep Understanding on CNN

90. Towards Deep Understanding on CNN
Summary
Regularization is an important technique to prevent over-fitting in network training
DisturbLabel regularizes CNN on the loss layer
DisturbLabel is very simple to implement
DisturbLabel works well in a wide range of tasks
DisturbLabel can be interpreted as an implicit way of model ensemble and/or data augmentation
8/9/2019
Towards Deep Understanding on CNN

91. Towards Deep Understanding on CNN
Outline
Introduction
Towards Deep Understanding on CNN
Neuron-level: the Max-Conv Operator
Mid-level: the GNPP Algorithm
Regularization: the DisturbLabel Algorithm
Feature Visualization: the InterActive Algorithm
Conclusions and Future Work
8/9/2019
Towards Deep Understanding on CNN

92. The State-of-the-Art Method
Extracting deep feature from a single image
Given an image, passing it through a pre-trained network (e.g., AlexNet or VGGNet)
Since VGGNet produces better results, we take it as the default network in the following experiments
Extracting the intermediate output on a specified layer (e.g., pool-5 or fc-6)
Sending the feature vectors into machine learning tools (e.g., SVM or KNN classifiers)
8/9/2019
Towards Deep Understanding on CNN

93. Improving Deep Features
For an input image, we resize it so that:
The aspect ratio is maximally preserved
The area (number of pixels) is approximately
The width and height are multipliers of 32 (the down-sampling rate of VGGNet)
On each layer (e.g., pool-4, pool-5, fc-6, etc.), we average the neuron responses on different spatial positions into a vector (e.g., on the pool-5 and fc-6 layers, the vectors are of 512 and 4096 dimensions, respectively)
8/9/2019
Towards Deep Understanding on CNN

94. Improving Deep Features (cont.)
This algorithm significantly improves classification accuracy, compared to the original image resizing method (resizing an image to 224×224 directly, where 224×224 is the input size of VGGNet)
Examples (using the pool-5 features):
On Caltech256: improved from 77.46% to 81.40%
On SUN-397: improved from 48.19% to 55.22%
On Flower-102: improved from 86.87% to 94.70%
We use it as the default way of feature extraction
8/9/2019
Towards Deep Understanding on CNN

95. Towards Deep Understanding on CNN
Problems Encountered
In the improved deep feature extraction
The input image size is relatively large (≈ )
The receptive field of a neuron is relatively small
On the pool-4, pool-5 and fc-6 layer, a neuron can “see” , and input pixels, respectively
Two problems occurs
A low-level neuron may not see enough visual context to make prediction (the “small” problem)
There may be some irrelevant low-level neurons which contaminate image representation (the “big” problem)
8/9/2019
Towards Deep Understanding on CNN

96. Problems Encountered (cont.)
Result: low-level features are less reliable
However, we need low-level features to represent some local visual attributes (e.g., object parts)
SMALL problem
sky
water
BIG problem
dog

97. Towards Deep Understanding on CNN
Solution?
How to deal with these problems?
For the “small” problem: low-level neurons must receive information from high-level neurons
For the “big” problem: a weight (activeness) must be computed for each low-level neuron
In short, we need to back-propagate high-level information throughout the network to assist the representative ability of low-level features
This process should be unsupervised!
8/9/2019
Towards Deep Understanding on CNN

98. The InterActive Algorithm
Main goal: in extracting deep features, adding a back-propagation process, so that low-level neurons can receive high-level information
Flowchart:
Defining a score function in the top level
Back-propagating gradients to get the activeness of neuron connections
Collecting the activeness of network connections as the activeness of neurons
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Towards Deep Understanding on CNN

99. InterActive: an Illustration
Output Layer
Hidden Layer 3
Hidden Layer 2
Hidden Layer 1
Input Layer
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Towards Deep Understanding on CNN

100. InterActive: an Illustration
Score Function
Activeness of Connections
Activeness of Hidden Layer 3
Activeness of Hidden Layer 2
Activeness of Hidden Layer 1
Activeness of Input Layer
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Towards Deep Understanding on CNN

101. Towards Deep Understanding on CNN
Related Algorithms
The back-propagation process looks like some other algorithms, such as:
Gradient back-propagation in network training
Visualizing the CNN [Zeiler, CVPR’14]
Object detectors in object CNNs [Zhou, ICLR’15]
Top-down visual attention [Cao, ICCV’15]
8/9/2019
Towards Deep Understanding on CNN

102. Related Algorithms (cont.)
InterActive differs from the algorithms:
We focus on generating descriptive image features, while they focus on network visualization
We can visualize back-propagated neuron activeness, while they visualize neuron responses
We perform back-propagation in an unsupervised way, while all the others are supervised
Being unsupervised, we can generalize to many more problems with a different set of image classes
8/9/2019
Towards Deep Understanding on CNN

103. Mathematical Notations
Let the CNN be a model 𝕄: 𝐡 𝐗 0 ;𝜽 , where 𝐗 0 is the input image, and 𝜽 is the weights of neuron connections
𝐗 𝑙 is the neuron responses on the 𝑡-th layer, which is a 𝑊 𝑙 × 𝐻 𝑙 × 𝐷 𝑙 cube
𝐱 𝑙 is the average over all spatial positions of 𝐗 𝑙 , i.e., a 𝐷 𝑙 -dimensional vector:
𝑥 𝑑 𝑙 = 1 𝑊 𝑙 × 𝐻 𝑙 𝑤=0 𝑊 𝑙 −1 ℎ=0 𝐻 𝑙 −1 𝑋 𝑤,ℎ,𝑑 𝑙
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Towards Deep Understanding on CNN

104. The Statistics of Neuron Responses
We send each image in Caltech256 to VGGNet, and perform statistics on different layers
Higher levels have better feature sparsity

105. The PDF of Neuron Responses
We study the PDF of neuron responses on the 𝑇-th layer, which is the starting point of back-propagation. We assume the following PDF:
𝑓 𝐱 𝑇 = 𝐶 𝑝 ×exp − 𝐱 𝑇 𝑝 𝑝
𝑝: norm (1 or 2 in this work)
𝐶 𝑝 : normalization coefficient
8/9/2019
Towards Deep Understanding on CNN

106. Towards Deep Understanding on CNN
The Score Function
A popular method to produce discriminative features from generative models
Computing the gradient of the log-likelihood with respect to the model parameters
Given input 𝐗 0 , we compute 𝐗 𝑇 and define a PDF 𝑓 𝑇 ≝𝑓 𝐗 𝑇 , then score function w.r.t. the parameter of the 𝑡-th layer, 𝜽 𝑙 :
𝜕 ln 𝑓 𝑇 𝜕 𝜽 𝑙 = 𝜕 ln 𝑓 𝑇 𝜕 𝐗 𝑙+1 × 𝜕 𝐗 𝑙+1 𝜕 𝜽 𝑙
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Towards Deep Understanding on CNN

107. The Activeness of Connections
The score function defines the activeness over each individual neuron connections
𝜕 ln 𝑓 𝑇 𝜕 𝜽 𝑙 = 𝜕 ln 𝑓 𝑇 𝜕 𝐗 𝑙+1 × 𝜕 𝐗 𝑙+1 𝜕 𝜽 𝑙
𝜕 ln 𝑓 𝑇 𝜕 𝐗 𝑙+1 : the layer score, computed by back-propagating gradients through the network
𝜕 𝐗 𝑙+1 𝜕 𝜽 𝑙 : the inter-layer activeness, computed by definition ( 𝐗 𝑙+1 involves simple operation of 𝜽 𝑙 )
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Towards Deep Understanding on CNN

108. The Importance of Neurons
We rewrite each neuron activeness term as:
𝜕 ln 𝑓 𝑇 𝜕 𝜃 𝑤,ℎ,𝑑, 𝑤 ′ , ℎ ′ , 𝑑 ′ 𝑙 = 𝑥 𝑤,ℎ,𝑑 𝑙 × 𝛼 𝑤,ℎ,𝑑, 𝑤 ′ , ℎ ′ , 𝑑 ′ 𝑙
𝛼 𝑤,ℎ,𝑑, 𝑤 ′ , ℎ ′ , 𝑑 ′ 𝑙 : the importance of the neuron 𝑥 𝑤,ℎ,𝑑 𝑙 to the connection (weight) between 𝑥 𝑤,ℎ,𝑑 𝑙 and 𝑥 𝑤 ′ , ℎ ′ , 𝑑 ′ 𝑙+1 , i.e., 𝜃 𝑤,ℎ,𝑑, 𝑤 ′ , ℎ ′ , 𝑑 ′ 𝑙
8/9/2019
Towards Deep Understanding on CNN

109. The Importance of Neurons (cont.)
We rewrite the entire neuron activeness as:
𝑥 𝑤,ℎ,𝑑 𝑙 = 𝑥 𝑤,ℎ,𝑑 𝑙 × 𝛾 𝑤,ℎ,𝑑 𝑙
𝛾 𝑤,ℎ,𝑑 𝑙 = 𝑤 ′ , ℎ ′ , 𝑑 ′ 𝛼 𝑤,ℎ,𝑑, 𝑤 ′ , ℎ ′ , 𝑑 ′ 𝑙
𝛾 𝑤,ℎ,𝑑 𝑙 is the importance of each neuron 𝑥 𝑤,ℎ,𝑑 𝑙
To visualize 𝛾 𝑤,ℎ,𝑑 𝑙 , we sum up it as a 2D heatmap: 𝛾 𝑤,ℎ 𝑙 = 𝑑 𝛾 𝑤,ℎ,𝑑 𝑙
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Towards Deep Understanding on CNN

110. Different Configurations
The norm 𝑝: larger 𝑝 indicates higher sparsity
The relationship between the start layer 𝑇 and the end layer 𝑙
The last configuration: 𝑇=𝐿−1 (𝐿 is the total number of layers), the 𝑙-th layer receives the information from the highest level of the network
The next configuration: 𝑇=𝑙+1, the 𝑙-th layer receives information only from the next layer
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Towards Deep Understanding on CNN

111. Towards Deep Understanding on CNN
Visualization (cont.)
Original Image
layer
pool-1
layer
pool-2
layer
conv-3-3
layer
pool-3
layer
conv-4-3
layer
pool-4
layer
conv-5-3
layer
pool-5
last config.
𝑝=1
last config.
𝑝=2
next config.
𝑝=1
bird
next config.
𝑝=2
last config.
𝑝=1
last config.
𝑝=2
next config.
𝑝=1
flower
next config.
𝑝=2
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Towards Deep Understanding on CNN

112. Towards Deep Understanding on CNN
Visualization (cont.)
Original Image
layer
pool-1
layer
pool-2
layer
conv-3-3
layer
pool-3
layer
conv-4-3
layer
pool-4
layer
conv-5-3
layer
pool-5
last config.
𝑝=1
last config.
𝑝=2
next config.
𝑝=1
cat
next config.
𝑝=2
last config.
𝑝=1
last config.
𝑝=2
next config.
𝑝=1
scene
next config.
𝑝=2
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Towards Deep Understanding on CNN

113. Towards Deep Understanding on CNN
Discussions
Gradient carries image weighting information
Back-propagation is useful on the testing stage
The next and last configurations
Using the last configuration is often better
Richer information is considered when we propagate deeper information through the network
The power parameter 𝑝
A larger 𝑝 makes the spatial weighting more concentrated (higher sparsity)
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Towards Deep Understanding on CNN

114. Experiments on Small Datasets
Six (6) datasets used
Generic classification: Caltech256
Scene classification: MIT Indoor-67, SUN-397
Fine-grained object recognition: Oxford Pet-37, Oxford Flower-102, Caltech-UCSD Bird-200
We evaluate the original deep features and InterActive features on different layers individually, and then combine them together
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Towards Deep Understanding on CNN

115. Results: Separate Layers
Model
Dims
C-256
I-67
S-397
P-37
F-102
B-200
pool-1
ORIG, AVG-p 64
11.12
19.96
8.52
12.09
29.36
5.10
pool-1
ORIG, MAX-p 64
8.77
16.82
7.27
14.83
27.95
7.81
pool-1
next, 𝑝=1 64
11.01
19.97
8.62
11.60
29.11
4.95
pool-1
next, 𝑝=2 64
11.26
19.71
8.92
12.38
31.07
5.30
pool-1
last, 𝑝=1 64
12.93
20.83
9.83
20.64
32.93
8.55
pool-1
last, 𝑝=2 64
𝟏𝟑.𝟏𝟒
𝟐𝟏.𝟏𝟎
𝟏𝟎.𝟎𝟐
𝟐𝟏.𝟏𝟗
𝟑𝟑.𝟓𝟖
𝟗.𝟎𝟏
pool-2
ORIG, AVG-p
128
21.03
31.12
18.63
20.49
45.77
8.30
pool-2
ORIG, MAX-p
128
19.47
28.29
16.05
24.60
43.39
11.28
pool-2
next, 𝑝=1
128
20.98
30.93
18.59
19.89
45.62
8.01
pool-2
next, 𝑝=2
128
20.65
30.95
19.01
21.18
48.27
9.60
pool-2
last, 𝑝=1
128
25.84
33.24
20.25
37.29
53.72
18.52
pool-2
last, 𝑝=2
128
𝟐𝟔.𝟐𝟎
𝟑𝟑.𝟒𝟕
𝟐𝟎.𝟓𝟎
𝟑𝟖.𝟒𝟐
𝟓𝟒.𝟐𝟐
𝟏𝟗.𝟒𝟑
8/9/2019
Towards Deep Understanding on CNN

116. Results: Separate Layers (cont.)
Model
Dims
C-256
I-67
S-397
P-37
F-102
B-200
conv-3-3
ORIG, AVG-p
256
26.44
36.42
22.73
27.78
49.70
10.47
conv-3-3
ORIG, MAX-p
256
24.18
33.27
19.71
31.43
48.02
13.85
conv-3-3
next, 𝑝=1
256
27.29
36.97
22.84
28.89
50.62
10.93
conv-3-3
next, 𝑝=2
256
27.62
37.36
23.41
30.38
54.06
12.73
conv-3-3
last, 𝑝=1
256
34.50
39.40
25.84
49.41
60.53
24.21
conv-3-3
last, 𝑝=2
256
𝟑𝟓.𝟐𝟗
𝟑𝟗.𝟔𝟖
𝟐𝟔.𝟎𝟐
𝟓𝟎.𝟓𝟕
𝟔𝟏.𝟎𝟔
𝟐𝟓.𝟐𝟕
pool-3
ORIG, AVG-p
256
29.17
37.98
23.59
29.88
52.44
11.00
pool-3
ORIG, MAX-p
256
26.53
34.65
20.83
33.68
50.93
13.66
pool-3
next, 𝑝=1
256
29.09
38.12
24.05
30.08
52.26
10.89
pool-3
next, 𝑝=2
256
29.55
38.61
24.31
31.98
55.06
12.65
pool-3
last, 𝑝=1
256
36.96
41.02
26.73
50.91
62.41
24.58
pool-3
last, 𝑝=2
256
𝟑𝟕.𝟒𝟎
𝟒𝟏.𝟒𝟓
𝟐𝟕.𝟐𝟐
𝟓𝟏.𝟗𝟔
𝟔𝟑.𝟎𝟔
𝟐𝟓.𝟒𝟕
8/9/2019
Towards Deep Understanding on CNN

117. Results: Separate Layers (cont.)
Model
Dims
C-256
I-67
S-397
P-37
F-102
B-200
conv-4-3
ORIG, AVG-p
512
49.62
59.66
42.03
55.57
76.98
21.45
conv-4-3
ORIG, MAX-p
512
47.73
55.83
40.10
59.40
75.72
23.39
conv-4-3
next, 𝑝=1
512
51.83
60.37
43.59
59.29
78.54
25.01
conv-4-3
next, 𝑝=2
512
53.52
60.65
44.17
63.40
80.48
31.07
conv-4-3
last, 𝑝=1
512
61.62
62.45
45.43
75.29
85.91
52.26
conv-4-3
last, 𝑝=2
512
𝟔𝟏.𝟗𝟖
𝟔𝟐.𝟕𝟒
𝟒𝟓.𝟖𝟕
𝟕𝟕.𝟔𝟏
𝟖𝟔.𝟎𝟖
𝟓𝟒.𝟏𝟐
pool-4
ORIG, AVG-p
512
60.39
66.49
49.73
66.76
85.56
28.56
pool-4
ORIG, MAX-p
512
57.92
62.96
47.29
69.23
84.39
30.01
pool-4
next, 𝑝=1
512
60.59
66.48
49.55
66.28
85.68
28.40
pool-4
next, 𝑝=2
512
62.06
66.94
50.10
72.40
87.36
37.49
pool-4
last, 𝑝=1
512
68.20
67.20
51.04
81.04
91.22
57.41
pool-4
last, 𝑝=2
512
𝟔𝟖.𝟔𝟎
𝟔𝟕.𝟒𝟎
𝟓𝟏.𝟑𝟎
𝟖𝟐.𝟓𝟔
𝟗𝟐.𝟎𝟎
𝟓𝟗.𝟐𝟓
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Towards Deep Understanding on CNN

118. Results: Separate Layers (cont.)
Model
Dims
C-256
I-67
S-397
P-37
F-102
B-200
conv-5-3
ORIG, AVG-p
512
77.40
74.66
59.47
88.36
94.03
55.44
conv-5-3
ORIG, MAX-p
512
75.93
71.38
57.03
87.10
91.30
55.19
conv-5-3
next, 𝑝=1
512
80.31
𝟕𝟒.𝟖𝟎
59.63
90.29
94.84
67.64
conv-5-3
next, 𝑝=2
512
80.73
74.52
𝟓𝟗.𝟕𝟒
𝟗𝟏.𝟓𝟔
95.16
𝟕𝟑.𝟏𝟒
conv-5-3
last, 𝑝=1
512
80.77
73.68
59.10
90.73
95.40
69.32
conv-5-3
last, 𝑝=2
512
𝟖𝟎.𝟖𝟒
73.58
58.96
91.19
𝟗𝟓.𝟕𝟎
69.75
pool-5
ORIG, AVG-p
512
81.40
𝟕𝟒.𝟗𝟑
𝟓𝟓.𝟐𝟐
91.78
94.70
69.72
pool-5
ORIG, MAX-p
512
79.61
71.88
54.04
89.43
90.01
68.52
pool-5
next, 𝑝=1
512
81.50
72.70
53.83
92.01
95.41
71.96
pool-5
next, 𝑝=2
512
81.58
72.63
53.57
𝟗𝟐.𝟑𝟎
95.40
𝟕𝟑. 𝟐𝟏
pool-5
last, 𝑝=1
512
81.60
72.58
53.93
92.20
𝟗𝟓.𝟒𝟑
72.47
pool-5
last, 𝑝=2
512
𝟖𝟏.𝟔𝟖
72.68
53.79
92.18
95.41
72.51
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119. Towards Deep Understanding on CNN
Results: All Layers
Model
C-256
I-67
S-397
P-37
F-102
B-200
Murray et.al., CVPR’14 − − −
56.8
84.6
33.3
Kobayashi et.al., CVPR’15
58.3
64.8 − − −
30.0
Xie et.al., ICCV’15
60.25
64.93
50.12
63.49
86.45
50.81
Ravazian et.al., CVPR’14 −
69.0 − −
86.8
61.8
Qian et.al., CVPR’15 − − −
81.18
89.45
67.86
Xie et.al., ICMR’15 −
70.13
54.87
90.03
86.82
62.02
ORIG, AVG-pooling
84.02
78.02
62.30
93.02
95.70
73.35
ORIG, MAX-pooling
84.38
77.32
61.87
93.20
95.98
74.76
next, 𝑝=1
84.43
78.01
62.26
92.91
96.02
74.37
next, 𝑝=2
84.64
78.23
62.50
93.22
96.26
74.61
last, 𝑝=1
84.94
78.40
62.69
93.40
96.35
75.47
last, 𝑝=2
𝟖𝟓.𝟎𝟔
𝟕𝟖.𝟔𝟓
𝟔𝟐.𝟗𝟕
𝟗𝟑.𝟒𝟓
𝟗𝟔.𝟒𝟎
𝟕𝟓.𝟔𝟐
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Towards Deep Understanding on CNN

120. Towards Deep Understanding on CNN
ImageNet Experiments
Evaluated on the ImageNet (ILSVRC2012) dataset
Baseline: VGGNet (16-layer and 19-layer models)
For each testing image, we forward-propagate the input signal, then compute the InterActive features on the second-to-last (fc-7) layer, and finally use the InterActive feature to update the fc-8 layer and get the prediction results
8/9/2019
Towards Deep Understanding on CNN

121. Towards Deep Understanding on CNN
Results on ILSVRC2012
We test on the 16-layer and 19-layer VGGNets, as well as the combined model (averaging the neuron response on the output layer)
Model
top-1 error
top-5 error
VGGNet-16, original
24.2%
7.1%
VGGNet-16, InterActive
23.8%
6.9%
VGGNet-19, original
24.0%
7.0%
VGGNet-19, InterActive
23.5%
6.7%
VGGNet-combined, original
23.6%
6.7%
VGGNet-combined, InterActive
23.2%
6.5%
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Towards Deep Understanding on CNN

122. Towards Deep Understanding on CNN
Summary
Gradient carries rich information
The inter-layer gradient: the likelihood of convolution
The layer score: the prior given by probability
Back-propagation gives the chance to consider context
The receptive field of each neuron is enlarged
In the next configuration: same as the neurons in the next layer
In the last configuration: the entire image
Large benefit is obtained on low-level layers (features)
Result: a soft spatial weighting scheme
Working better than both sum-pooling and max-pooling
Generalized to a wide range of image classification tasks
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Towards Deep Understanding on CNN

123. Towards Deep Understanding on CNN
Outline
Introduction
Towards Deep Understanding on CNN
Neuron-level: the Max-Conv Operator
Mid-level: the GNPP Algorithm
Regularization: the DisturbLabel Algorithm
Feature Visualization: the InterActive Algorithm
Conclusions and Future Work
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Towards Deep Understanding on CNN

124. Towards Deep Understanding on CNN
Conclusions
Although CNN is a powerful machine learning tool, many aspects of its behavior still remain unclear
We are not treating each neural network as a black-box, but to explore the inner structure and working mechanism of the model
We are looking forward to finding some useful clues for the future research
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Towards Deep Understanding on CNN

125. Towards Deep Understanding on CNN
Future Directions
Explainability
Efficiency
Learning: supervised vs. unsupervised
Structure: fixed vs. variable
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Towards Deep Understanding on CNN

126. Towards Deep Understanding on CNN
Thanks!
Questions, please?
8/9/2019
Towards Deep Understanding on CNN