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Learning Functions and Neural Networks II 24-787 Lecture 9 Luoting Fu Spring 2012

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Previous lecture 2 Applications Physiological basis Demos Perceptron Y = u(W 0 X 0 + W 1 X 1 + W b ) Y X0X0 X1X1 Δ W i = η (Y 0 -Y) X i x fHfH

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In this lecture Multilayer perceptron (MLP) – Representation – Feed forward – Back-propagation Break Case studies Milestones & forefront 3 2

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Perceptron 4 A 400-26 perceptron © Springer

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5 XOR Exclusive OR

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Root cause Consider a 2-1 perceptron, 6

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A single perceptron is limited to learning linearly separable cases. 7 Minsky M. L. and Papert S. A. 1969. Perceptrons. Cambridge, MA: MIT Press.

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9 Cybenko., G. (1989) "Approximations by superpositions of sigmoidal functions", Mathematics of Control, Signals, and Systems, 2 (4), 303-314 An MLP can learn any continuous function. A single perceptron is limited to learning linearly separable cases (linear function).

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How’s that relevant? Function approximation Intelligence 10 Waveform Words Recognition The road ahead Speed Bearing Wheel turn Pedal depression Regression

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17 ∞

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Matrix representation 19

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20 Knowledge learned by an MLP is encoded in its layers of weights.

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What does it learn? Decision boundary perspective 21

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What does it learn? Highly non-linear decision boundaries 22

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What does it learn? Real world decision boundaries 23

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24 Cybenko., G. (1989) "Approximations by superpositions of sigmoidal functions", Mathematics of Control, Signals, and Systems, 2 (4), 303-314 An MLP can learn any continuous function. Think Fourier.

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What does it learn? Weight perspective 25 An 64-M-3 MLP

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How does it learn? From examples By back propagation 26 0 1 2 3 4 5 6 7 8 9 Polar bear Not a polar bear

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Back propagation 27

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Gradient descent 28 “epoch”

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Back propagation 30

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Back propagation Steps 31 Think about this: What happens when you train a 10-layer MLP?

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Overfitting and cross-validation 32 Learning curve error

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Break 33

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Design considerations Learning task X - input Y - output D M K #layers Training epochs Training data – # – Source 34

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Case study 1: digit recognition 35 28 An 768-1000-10 MLP

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Case study 1: digit recognition 36

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Milestones: a race to 100% accuracy on MNIST 37

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Milestones: a race to 100% accuracy on MNIST 38 CLASSIFIER ERROR RATE (%) Reported by Perceptron12.0LeCun et al. 1998 2-layer NN, 1000 hidden units4.5LeCun et al. 1998 5-layer Convolutional net0.95LeCun et al. 1998 5-layer Convolutional net0.4Simard et al. 2003 6-layer NN 784-2500-2000-1500- 1000-500-10 (on GPU) 0.35Ciresan et al. 2010 See full list at http://yann.lecun.com/exdb/mnist/

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Milestones: a race to 100% accuracy on MNIST 39

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Milestones: a race to 100% accuracy on MNIST 40

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Case study 2: sketch recognition 41

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Case study 2: sketch recognition Convolutional neural network 42 Convolution Sub-sampling Product Matrices Element of a vector Or Scope Transf. Fun. Gain Sum Sine wave … (LeCun, 1998)

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Case study 2: sketch recognition 43

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Case study 2: sketch recognition 44

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Case study 3: autonomous driving 45 Pomerleau, 1995

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Case study 4: sketch beautification 46 Orbay and Kara, 2011

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Case study 4: sketch beautification 47

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Case study 4: sketch beautification 48

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Research forefront Deep belief network – Critique, or classify – Create, synthesize 49 Demo at: http://www.cs.toronto.edu/~hinton/adi/index.htm

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In summary 1.Powerful machinery 2.Feed-forward 3.Back propagation 4.Design considerations 50

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