# Advanced Section #1: Linear Algebra and Hypothesis Testing ...

Lecture 9: Convolutional Neural Networks 2 CS109B Data Science 2 Pavlos Protopapas and Mark Glickman 1 Outline 1. Review from last lecture 2. BackProp of MaxPooling layer 3. A bit of history 4. Layers Receptive Field 5. Saliency maps 6. Transfer Learning 7. CNN for text analysis (example) CS109B, PROTOPAPAS, GLICKMAN 2 Outline 1. Review from last lecture 2. BackProp of MaxPooling layer 3. A bit of history 4. Layers Receptive Field 5. Saliency maps 6. Transfer Learning 7. CNN for text analysis (example)

CS109B, PROTOPAPAS, GLICKMAN 3 From last lecture + ReLU + ReLU CS109B, PROTOPAPAS, GLICKMAN 4 Examples I have a convolutional layer with 16 3x3 filters that takes an RGB image as input. What else can we define about this layer?

Activation function Stride Padding type How many parameters does the layer have? 16 x 3 x 3 x 3 + 16 = 448 Number of Size of Number of filters Filters channels of prev layer Biases (one per filter) CS109B, PROTOPAPAS, GLICKMAN 5 Examples Let C be a CNN with the following disposition:

Input: 32x32x3 images Conv1: 8 3x3 filters, stride 1, padding=same Conv2: 16 5x5 filters, stride 2, padding=same Flatten layer Dense1: 512 nodes Dense2: 4 nodes How many parameters does this network have? (8 x 3 x 3 x 3 + 8) + (16 x 5 x 5 x 8 + 16) + (16 x 16 x 16 x 512 + 512) + (512 x 4 + Conv2 4) Conv1 Dense1 Dense2 CS109B, PROTOPAPAS, GLICKMAN 6 What do CNN layers learn? Each CNN layer learns filters of increasing complexity. The first layers learn basic feature detection filters: edges, corners, etc. The middle layers learn filters that detect parts of objects. For faces, they might learn to respond to eyes, noses, etc. The last layers have higher representations: they

learn to recognize full objects, in different shapes and positions. CS109B, PROTOPAPAS, GLICKMAN 7 CS109B, PROTOPAPAS, GLICKMAN 8 3D visualization of networks in action http://scs.ryerson.ca/~aharley/vis/conv/ https://www.youtube.com/watch?v=3JQ3hYko51Y CS109B, PROTOPAPAS, GLICKMAN 9 Outline 1. Review from last lecture 2. BackProp of MaxPooling layer 3. A bit of history 4. Layers Receptive Field 5. Saliency maps 6. Transfer Learning 7. CNN for text analysis (example)

CS109B, PROTOPAPAS, GLICKMAN 10 Backward propagation of Maximum Pooling Layer Forward mode, 3x3 stride 1 2 4 8 3 6 9 3 4 2 5 5

4 6 3 1 2 3 1 3 4 2 7 4 5 7

CS109B, PROTOPAPAS, GLICKMAN 11 Backward propagation of Maximum Pooling Layer Forward mode, 3x3 stride 1 2 4 8 3 6 9 3 4 2 5 5

4 6 3 1 2 3 1 3 4 2 7 4 5 7

9 CS109B, PROTOPAPAS, GLICKMAN 12 Backward propagation of Maximum Pooling Layer Forward mode, 3x3 stride 1 2 4 8 3 6 9 3 4 2 5

5 4 6 3 1 2 3 1 3 4 2 7 4 5

7 9 8 CS109B, PROTOPAPAS, GLICKMAN 13 Backward propagation of Maximum Pooling Layer Forward mode, 3x3 stride 1 2 4 8 3 6 9 3 4

2 5 5 4 6 3 1 2 3 1 3 4 2 7

4 5 7 9 8 CS109B, PROTOPAPAS, GLICKMAN 8 14 Backward propagation of Maximum Pooling Layer Forward mode, 3x3 stride 1 2 4 8 3 6

9 3 4 2 5 9 8 8 5 4 6 3 1 9

6 6 2 3 1 3 4 7 7 7 2 7 4 5

7 CS109B, PROTOPAPAS, GLICKMAN 15 Backward propagation of Maximum Pooling Layer Backward mode. Large fonts represents the values of the derivatives of the current layer (max-pool) and small font the corresponding value of the previous layer. 2 4 8 3 6 9 3 4 2

5 19 38 18 5 4 6 3 1 19 46 26 2 3

1 3 4 67 27 17 2 7 4 5 7 CS109B, PROTOPAPAS, GLICKMAN 16 Backward propagation of Maximum Pooling Layer

Backward mode. Large fonts represents the values of the derivatives of the current layer (max-pool) and small font the corresponding value of the previous layer. 2 4 8 3 6 9 3 4 2 5 19 38

18 5 4 6 3 1 19 46 26 2 3 1 3 4

67 27 17 2 7 4 5 7 CS109B, PROTOPAPAS, GLICKMAN 17 Backward propagation of Maximum Pooling Layer Backward mode. Large fonts represents the values of the derivatives of the current layer (max-pool) and small font the corresponding value of the previous layer. 2 4

8 3 6 9 3 4 2 5 19 38 18 5 4 6

3 1 19 46 26 2 3 1 3 4 67 27 17 2

7 4 5 7 CS109B, PROTOPAPAS, GLICKMAN 18 Backward propagation of Maximum Pooling Layer Backward mode. Large fonts represents the values of the derivatives of the current layer (max-pool) and small font the corresponding value of the previous layer. +1 2 4 8 3

6 9 3 4 2 5 19 38 18 5 4 6 3 1

19 46 26 2 3 1 3 4 67 27 17 2 7 4

5 7 CS109B, PROTOPAPAS, GLICKMAN 19 Backward propagation of Maximum Pooling Layer Backward mode. Large fonts represents the values of the derivatives of the current layer (max-pool) and small font the corresponding value of the previous layer. +1 2 4 8 3 6 9 3

4 2 5 19 38 18 5 4 6 3 1 19 46 26

2 3 1 3 4 67 27 17 2 7 4 5 7 CS109B, PROTOPAPAS, GLICKMAN

20 Backward propagation of Maximum Pooling Layer Backward mode. Large fonts represents the values of the derivatives of the current layer (max-pool) and small font the corresponding value of the previous layer. +1 2 4 9 +3 8 3 6 3 4

2 5 19 38 18 5 4 6 3 1 19 46 26 2

3 1 3 4 67 27 17 2 7 4 5 7 CS109B, PROTOPAPAS, GLICKMAN 21

Backward propagation of Maximum Pooling Layer Backward mode. Large fonts represents the values of the derivatives of the current layer (max-pool) and small font the corresponding value of the previous layer. +1 2 4 9 +3 8 3 6 3 4 2 5

19 38 18 5 4 6 3 1 19 46 26 2 3 1

3 4 67 27 17 2 7 4 5 7 CS109B, PROTOPAPAS, GLICKMAN 22 Backward propagation of Maximum Pooling Layer Backward mode. Large fonts represents the values of the derivatives of the current layer (max-pool) and small font the

corresponding value of the previous layer. +1 2 4 9 +3 8 3 6 3 4 2 5 19

38 18 5 4 6 3 1 19 46 26 2 3 1 3

4 67 27 17 2 7 4 5 7 CS109B, PROTOPAPAS, GLICKMAN 23 Backward propagation of Maximum Pooling Layer Backward mode. Large fonts represents the values of the derivatives of the current layer (max-pool) and small font the corresponding value of the previous layer. +1

2 4 9 +4 8 3 6 3 4 2 5 19 38 18

5 4 6 3 1 19 46 26 2 3 1 3 4 67

27 17 2 7 4 5 7 CS109B, PROTOPAPAS, GLICKMAN 24 Outline 1. Review from last lecture 2. BackProp of MaxPooling layer 3. A bit of history 4. Layers Receptive Field 5. Saliency maps 6. Transfer Learning 7. CNN for text analysis (example)

CS109B, PROTOPAPAS, GLICKMAN 25 Initial ideas The first piece of research proposing something similar to a Convolutional Neural Network was authored by Kunihiko Fukushima in 1980, and was called the NeoCognitron1. Inspired by discoveries on visual cortex of mammals. Fukushima applied the NeoCognitron to hand-written character recognition. End of the 80s: several papers advanced the field Backpropagation published in French by Yann LeCun in 1985 (independently discovered by other researchers as well) TDNN by Waiber et al., 1989 - Convolutional-like network trained with backprop. Backpropagation applied to handwritten zip code recognition by LeCun et al., 1989

K. Fukushima. Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position. Biological Cybernetics, 36(4): 93-202, 1980. 1 CS109B, PROTOPAPAS, GLICKMAN 26 LeNet 1 November 1998: LeCun publishes one of his most recognized papers describing a modern CNN architecture for document recognition, called LeNet1. Not his first iteration, this was in fact LeNet-5, but this paper is the commonly cited publication when talking about LeNet. LeCun, Yann, et al. "Gradient-based learning applied to document recognition." Proceedings of the IEEE 86.11 (1998): 2278-2324. CS109B, PROTOPAPAS, GLICKMAN 27 AlexNet

Developed by Alex Krizhevsky, Ilya Sutskever and Geoffrey Hinton at Utoronto in 2012. More than 25000 citations. Destroyed the competition in the 2012 ImageNet Large Scale Visual Recognition Challenge. Showed benefits of CNNs and kickstarted AI revolution. top-5 error of 15.3%, more than 10.8 percentage points lower than runner-up. AlexNet Main contributions: Trained on ImageNet with data augmentation Increased depth of model, GPU training (five to six days) Smart optimizer and Dropout layers ReLU activation! CS109B, PROTOPAPAS, GLICKMAN 28

ZFNet Introduced by Matthew Zeiler and Rob Fergus from NYU, won ILSVRC 2013 with 11.2% error rate. Decreased sizes of filters. Trained for 12 days. Paper presented a visualization technique named Deconvolutional Network, which helps to examine different feature activations and their relation to the input space. CS109B, PROTOPAPAS, GLICKMAN 29 VGG Introduced by Simonyan and Zisserman (Oxford) in 2014 Simplicity and depth as main points. Used 3x3 filters exclusively and 2x2 MaxPool layers with stride 2.

Showed that two 3x3 filters have an effective receptive field of 5x5. As spatial size decreases, depth increases. Trained for two to three weeks. Still used as of today. CS109B, PROTOPAPAS, GLICKMAN 30 GoogLeNet (Inception-v1) Introduced by Szegedy et al. (Google), 2014. Winners of ILSVRC 2014. Introduces inception module: parallel conv. layers with different filter sizes. Motivation: we dont know which filter size is best let the network decide. Key idea for future archs. No fully connected layer at the end. AvgPool instead. 12x fewer params than AlexNet. 1x1 convs to Reduce number of parameters Proto Inception module

Inception module CS109B, PROTOPAPAS, GLICKMAN 31 ResNet Presented by He et al. (Microsoft), 2015. Won ILSVRC 2015 in multiple categories. Main idea: Residual block. Allows for extremely deep networks. Authors believe that it is easier to optimize the residual mapping than the original one. Furthermore, residual block can decide to shut itself down if needed. Residual Block CS109B, PROTOPAPAS, GLICKMAN 32 ResNet

Presented by He et al. (Microsoft), 2015. Won ILSVRC 2015 in multiple categories. Main idea: Residual block. Allows for extremely deep networks. Authors believe that it is easier to optimize the residual mapping than the original one. Furthermore, residual block can decide to shut itself down if needed. Residual Block CS109B, PROTOPAPAS, GLICKMAN 33 DenseNet Proposed by Huang et al., 2016. Radical extension of ResNet idea. Each block uses every previous feature map as input. Idea: n computation of redundant features. All the previous information is available at each point. Counter-intuitively, it reduces the

number of parameters needed. CS109B, PROTOPAPAS, GLICKMAN 34 DenseNet Proposed by Huang et al., 2016. Radical extension of ResNet idea. Each block uses every previous feature map as input. Idea: n computation of redundant features. All the previous information is available at each point. Counter-intuitively, it reduces the number of parameters needed. CS109B, PROTOPAPAS, GLICKMAN 35

MobileNet Published by Howard et al., 2017. Extremely efficient network with decent accuracy. Main concept: depthwise-separable convolutions. Convolve each feature maps with a kernel, then use a 1x1 convolution to aggregate the result. This approximates vanilla convolutions without having to convolve large kernels through channels. CS109B, PROTOPAPAS, GLICKMAN 36 More on the greatest latest at a-sec later today CS109B, PROTOPAPAS, GLICKMAN 37

Outline 1. Review from last lecture 2. BackProp of MaxPooling layer 3. A bit of history 4. Layers Receptive Field 5. Saliency maps 6. Transfer Learning 7. CNN for text analysis (example) CS109B, PROTOPAPAS, GLICKMAN 38 Layers Receptive Field The receptive field is defined as the region in the input space that a particular CNNs feature is looking at (i.e. be affected by). Apply a convolution C with kernel size k = 3x3, padding size p = 1x1, stride s = 2x2 on an input map 5x5, we will get an output feature map 3x3 (green map). CS109B, PROTOPAPAS, GLICKMAN 39 Layers Receptive Field Applying the same convolution on top of the 3x3 feature map, we will get a 2x2 feature map (orange map)

CS109B, PROTOPAPAS, GLICKMAN 40 Dilated CNNs Lets look at the receptive field again in 1D, no padding, stride 1 and kernel 3x1 CS109B, PROTOPAPAS, GLICKMAN 41 Dilated CNNs (cont) Lets look at the receptive field again in 1D, no padding, stride 1 and kernel 3x1 CS109B, PROTOPAPAS, GLICKMAN 42 Dilated CNNs (cont) Lets look at the receptive field again in 1D, no padding, stride 1 and kernel 3x1 CS109B, PROTOPAPAS, GLICKMAN 43

Dilated CNNs (cont) Lets look at the receptive field again in 1D, no padding, stride 1 and kernel 3x1 CS109B, PROTOPAPAS, GLICKMAN 44 Dilated CNNs (cont) Lets look at the receptive field again in 1D, no padding, stride 1 and kernel 3x1. Skip some of the connections CS109B, PROTOPAPAS, GLICKMAN 45 Outline 1. Review from last lecture 2. BackProp of MaxPooling layer 3. A bit of history 4. Layers Receptive Field 5. Saliency maps 6. Transfer Learning 7. CNN for text analysis (example) CS109B, PROTOPAPAS, GLICKMAN

46 Saliency maps CS109B, PROTOPAPAS, GLICKMAN 47 Saliency maps (cont) If you are given an image of a dog and asked to classify it. Most probably you will answer immediately Dog! But your Deep Learning Network might not be as smart as you. It might classify it as a cat, a lion or Pavlos! What are the reasons for that? bias in training data no regularization or your network has seen too many celebrities CS109B, PROTOPAPAS, GLICKMAN 48 Saliency maps (cont) We want to understand what made my network give a certain class as output? Saliency Maps, they are a way to measure the spatial support of a particular class in a given image. Find me pixels responsible for the class C having

score S(C) when the image I is passed through my network. CS109B, PROTOPAPAS, GLICKMAN 49 Saliency maps (cont) We want to understand what made my network give a certain class as output? Saliency Maps, they are a way to measure the spatial support of a particular class in a given image. Find me pixels responsible for the class C having score S(C) when the image I is passed through my network. CS109B, PROTOPAPAS, GLICKMAN 50 Salience maps (cont) Question: How do we do that? We differentiate! For any function f(x, y, z), we can find the impact of variables x, y, z on fat any specific point (x0, y0, z0) by finding its partial derivative w.r.t these variables at that point. Similarly, to find the responsible pixels, we take the score function S,

for class C and take the partial derivatives w.r.t every pixel. CS109B, PROTOPAPAS, GLICKMAN 51 Salience maps (cont) Question: Easy Peasy? Sort of! Auto-grad can do this! 1. Forwar pass of the image through the network 2. Calculate the scores for every class 3. Enforce derivative of score S at last layer for all classes except class C to be 0. For C, set it to 1 4. Backpropagate this derivative till the start 5. Render them and you have your Saliency Map! Note: On step #2. Instead of doing softmax, we turn it to binary classification and use the probabilities. CS109B, PROTOPAPAS, GLICKMAN 52 Salience maps (cont) CS109B, PROTOPAPAS, GLICKMAN 53 Salience maps (cont)

Question: What do we do with color images? Take the saliency map for each channel and either take the max or average or use all 3 channels. [1]: Deep Inside Convolutional Networks: Visualising Image Classification Models and Salienc y Maps CS109B, PROTOPAPAS, GLICKMAN [2]: Attention-based Extraction of Structured Information from Street View Imagery 54 Outline 1. Review from last lecture 2. BackProp of MaxPooling layer 3. A bit of history 4. Layers Receptive Field 5. Saliency maps 6. Transfer Learning 7. CNN for text analysis (example) CS109B, PROTOPAPAS, GLICKMAN 55 Transfer Learning How do you make an image classifier that can be trained in a few hours (minutes) on a CPU?

Use pre-trained models, i.e., models with known weights. Main Idea: earlier layers of a network learn low level features, which can be adapted to new domains by changing weights at later and fully-connected layers. Example: use Imagenet trained with any sophisticated huge network. Then retrain it on a few thousand hotdog images and you get... CS109B, PROTOPAPAS, GLICKMAN 56 Hotdog or NotHotDog: https://youtu.be/ACmydtFDTGs (offensive language and tropes alert) CS109B, PROTOPAPAS, GLICKMAN 57 Transfer Learning (cont) 1. Get existing network weights 2. Un-freeze the head fully connected layers and train on your new images 3. Un-freeze the latest convolutional layers and train at a very low learning rate starting with the weights from the previously trained weights. This will change the latest layer convolutional weights without triggering large gradient updates which would have occurred had

we not done 2. See https://medium.com/@timanglade/how-hbos-silicon-valley-built-not-hotdog-with-mobiletensorflow-keras-react-native-ef03260747f3 CS109B, PROTOPAPAS, GLICKMAN and 58 CS109B, PROTOPAPAS, GLICKMAN 59 Outline 1. Review from last lecture 2. BackProp of MaxPooling layer 3. A bit of history 4. Layers Receptive Field 5. Saliency maps 6. Transfer Learning 7. CNN for text analysis (example) CS109B, PROTOPAPAS, GLICKMAN 60 Convolutional Neural Networks for Text Classification When applied to text instead of images, we have an 1 dimensional array representing the text.

Here the architecture of the ConvNets is changed to 1D convolutional-and-pooling operations. One of the most typically tasks in NLP where ConvNet are used is sentence classification, that is, classifying a sentence into a set of pre-determined categories by considering n-grams, i.e. its words or sequence of words, or also characters or sequence of characters. LETS SEE THIS THROUGH AN EXAMPLE CS109B, PROTOPAPAS, GLICKMAN 61 Beyond MobileNetV2 (https://arxiv.org/abs/1801.04381) Inception-Resnet, v1 and v2 ( https://arxiv.org/abs/1602.07261) Wide-Resnet (https://arxiv.org/abs/1605.07146) Xception (https://arxiv.org/abs/1610.02357) ResNeXt (https://arxiv.org/pdf/1611.05431) ShuffleNet, v1 and v2 ( https://arxiv.org/abs/1707.01083) Squeeze and Excitation Nets ( https://arxiv.org/abs/1709.01507 ) CS109B, PROTOPAPAS, GLICKMAN 62

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