ROB 537: Learning-Based Control

Transcription

1 ROB 537: Learning-Based Control Week 6, Lecture 1 Deep Learning (based on lectures by Fuxin Li, CS 519: Deep Learning) Announcements: HW 3 Due TODAY Midterm Exam on 11/6 Reading: Survey paper on Deep Learning (Schmidhuber 2015) Learning: Mapping Inputs to Outputs In weeks 1-3 we talked about neural networks Message was: Neural networks use data to learn a mapping from inputs to outputs with a few caveats 1

2 Recall: Dog vs Cat Recall: Dog vs Cat Dog vs Cat: Cat 2

3 Recall: Recall: Dog vs Cat or??? Dog vs Cat: Cat Movement vs stayonary Dog maybe Indoor vs outdoor Dog Red vs not red animal Dog 3

4 Let s revisit what happens in such a mapping images/video Input: X ML Output: Y Label: Motorcycle Suggest tags Image search audio ML Speech recogniyon Music classificayon Speaker idenyficayon text ML Web search AnY- spam Machine translayon We want to map this picture to a label ML motorcycle 4

5 Why is this hard? You see this: But the camera sees this: Raw Representation pixel 1 Learning algorithm Input pixel 2 Raw image Motorbikes Non - Motorbikes pixel 2 pixel

6 Raw Representation pixel 1 Learning algorithm Input pixel 2 Raw image Motorbikes Non - Motorbikes pixel 2 pixel 1 What we Want handlebars Input wheel Feature representayon Eg, Does it have Handlebars? Wheels? Learning algorithm Raw image Motorbikes Non - Motorbikes Features pixel 2 Wheels pixel 1 Handlebars 6

7 Representation Wheels and handlebars represent key aspects of a motorcycle Looking for those allows an algorithm to recognize a motorbike What we did is feature engineering IdenYfy key features using domain knowledge Extract key features from image Map key features to labels Feature Engineering vs Feature Learning Feature engineering requires Domain knowledge Specific to data sets Labor intensive How about Feature learning? Edges, corners Circles Shapes? Deep Learning 7

8 Deep Learning: Let s learn the representation! pixels edges shapes object parts object models corners nose, eye Joe happy Deep Learning Neural Network architecture with many layers wait a minute is this new? Different than just neural networks? Yes and No 8

9 History of Neural Networks CyberneYcs ConnecYonism Deep Learning Three Waves of Neural Networks CyberneYcs 1950s and 60s Perceptron (Rosenblaf, 1957) Adaline, Madaline (Woodrow and Hoff 1959) ConnecYonism 1980s and early 90s BackpropagaYon (Rumelhart, Hinton, Williams 1986, Werbos 1981) Universal approximayon theorems (Cybenko 1989, Hornik et a 1991) Deep Learning 2005 onward (mostly 2010s) 9

10 Three Waves of Neural Networks CyberneYcs 1950s and 60s 1970s : Disillusionment 1 - XOR (Minski, Papert 1969) ConnecYonism 1980s and early 90s ~ : Disillusionment 2 - (Support Vector Machine ) Deep Learning 2005 onward (mostly 2010s) First Two Waves Focused on One hidden layer NNs Two hidden layer NNs 10

11 Third Wave: Deep Learning Neural Networks pixels edges shapes object parts object models Third Wave: Deep Learning Neural Networks 11

12 Why Didn t Deep NN Idea Catch on Before? BackpropagaYon doesn t like too many layers Gradient either goes to zero or blows up Training requires a lot of labeled training data How do you get millions of labeled images? The learning Yme does not scale well NNs may overfit, especially with many hidden layers Not enough compuyng power Why Didn t Deep NN Idea Catch on Before? 12

13 Back to Deep Learning What s going on in these layers? pixels edges shapes object parts object models What s going on between Layers? You re applying a Filter 13

14 Some Basic Concepts Subgradient RecYfier Linear Units (ReLU) Pooling Stride Padding Subgradient What if a funcyon is nondifferenyable? For a convex funcyon f(x): Non- differenyable f (x) f (x 0 ) c (x x 0 ) c is subgradient at x 0 Subgradient: approximate derivayve 14

15 Rectifier Linear Units AcYvaYon funcyon: RecYfier Linear Units (ReLU) f (x) = max(x, 0) Subgradient:! # f '(x) = " # $ 1 if x > 0 0 otherwise Pooling Pooling is downsampling You can average, take the max etc Example: 2x2 maxpooling : Why? Because exact locayon of object (or edge or face) doesn t mafer 15

16 Stride How much does the filter move at each step Stride 1: 7x7 to 5x5 Stride 2: 7x7 to 3x3 Padding NoYce as we applied filters, our dimension decreased What happens when you apply many layers? Padding keeps dimensionality of previous layer 5x5 and apply 3x3 filter: Padding Filter 16

17 Convolutional Neural Networks Exploit structure in image Neighboring pixels carry local correlayon Shapes carry long- range correlayon The Convolution Operator Sobel filter ConvoluYon * ConvoluYon 17

18 2D Convolution with Padding and Stride D Convolution with Padding and Stride = ( 1) 1=2 18

19 2D Convolution with Padding and Stride = ( 2) ( 1)+1 1= 1 2D Convolution with Padding and Stride =

20 2D Convolution with Padding and Stride = D Convolution with Padding and Stride =

21 2D Convolution with Padding and Stride = D Convolution with Padding and Stride =

22 2D Convolution with Padding and Stride = What s the shape of weights and input 3x3x3 +ReLU ConvoluYon Say, 64 filters 3x3x64 ConvoluYon 22

23 What s the shape of weights and input eg 64 filters level filters level 2 Input 224 x 224 x 3 3x3x3x64 Weights +ReLU Output1: 224 x 224 x 64 ConvoluYon 3x3x64x128 Output1: 224 x 224 x 128 Dramatic reduction on the number of parameters A fully- connected NN on 10- class, 256 x 256 image with 500 hidden units Num of params = * 3 * * 10 = 983 Million 1- hidden layer convoluyonal network on 256 x 256 image with 11x11 and 500 hidden units? Num of params = 11 * 11 * 3 * * 10 = 155, hidden layers convoluyonal network on 256 x 256 image with 11x11 3x3 sized filters and 500 hidden units in each layer? Num of params = 150, * 3 * 500 * * 10 = 24 Million 23

24 Recall: Deep Learning Neural Network Flow Convolution + Rectifier Linear Unit We need nonlinearity Make the gradient sparser and simpler to compute 24

25 Convolution + ReLU + Pooling Pooling allows invariance of features Pooling makes higher layers filters cover a larger region of the input State of the Art in Deep Learning 25

26 Computer Vision Image Classification Imagenet Over 1 million images, 1000 classes, different sizes, avg 482x415, color 1642% Deep CNN dropout in % 22 layer CNN (GoogLeNet) in % (Microsot Research Asia) super- human performance in 2015 Sources: Krizhevsky et al ImageNet ClassificaYon with Deep ConvoluYonal Neural Networks, Lee et al Deeply supervised nets 2014, Szegedy et al, Going Deeper with convoluyons, ILSVRC2014, Sanchez & Perronnin CVPR 2011, hfp://wwwclarifaicom/ Benenson, hfp://rodrigobgithubio/are_we_there_yet/build/classificayon_datasets_resultshtml Impact on speech recognition 26

27 Unsupervised Deep Learning CNN is most successful with a lot of training examples What can we do if we do not have any training example? Or have very few of them? Dimensionality Reduction: Principle Component Analysis Project data onto a new subspace Bases are orthogonal OpYmal under some assumpyons (Gaussian) AssumpYons almost never true in real data 27

28 Neural Network as PCA: Autoencoder Standard Neural network: But output is the input Goal: Minimize reconstrucyon error Input vector code Input vector Deep Autoencoder Input vector Many decoding layers Many Encoding Layers Input vector 28

29 Deep Learning in Neural Networks Engineering applicayons: Computer vision Speech recogniyon Natural Language Understanding RoboYcs 57 Back to Deep Learning Neural Network architecture with many layers wait a minute is this new? Different than just neural networks? Yes and No 29

30 Why Didn t Deep NN Idea Catch on Before? Not clear what deep fully connected networks learn BackpropagaYon doesn t like too many layers Gradient either goes to zero or blows up Training requires a lot of labeled training data Million+ labeled images (Amazon Mechanical Turk) The learning Yme does not scale well NNs tend to overfit, especially with many hidden layers Not enough compuyng power So What s New? ConvoluYon neural networks New acyvayon funcyons and subgradients ReLU Everything is on the internet A lot of labeled data Million+ labeled images (Amazon Mechanical Turk) More efficient learning algorithms: stochasyc gradient descent Pooling (dimensionality control) Much befer compuyng power GPUs 30

31 What s Next? Deep Learning: Methods and ApplicaYons, L Deng and D Yu, FoundaYons and Trends in Signal Processing, Vol 7, Nos 3 4, , 2013 (also, hfp://enwikipediaorg/wiki/hype_cycle ) What s Next? Deep Learning: Methods and ApplicaYons, L Deng and D Yu, FoundaYons and Trends in Signal Processing, Vol 7, Nos 3 4, ,