Mul7layer Perceptrons


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1 Lecture Slides for INTRODUCTION TO Machine Learning 2nd Edi7on CHAPTER 11: Mul7layer Perceptrons ETHEM ALPAYDIN The MIT Press, 2010 Edited and expanded for CS 4641 by Chris Simpkins h1p://
2 Overview Neural networks, brains, and computers Perceptrons Training Classification and regression Linear separability Multilayer perceptrons Universal approximation Backpropagation 2
3 Neural Networks Networks of processing units (neurons) with connec7ons (synapses) between them Large number of neurons: Large connec7vity: 10 5 Parallel processing Distributed computa7on/memory Robust to noise, failures 3
4 Understanding the Brain Levels of analysis (Marr, 1982) 1. ComputaOonal theory 2. RepresentaOon and algorithm 3. Hardware implementaoon Reverse engineering: From hardware to theory Parallel processing: SIMD vs MIMD Neural net: SIMD with modifiable local memory Learning: Update by training/experience 4
5 Perceptron (RosenblaS, 1962) 5
6 What a Perceptron Does Regression: y=wx+w 0 Classifica7on: y=1(wx+w 0 >0) y y s y w 0 x 0 =+1 w x x w 0 w x w 0 Linear fit Linear discrimination 6
7 Regression: K Outputs ClassificaOon: 7
8 Training Online (instances seen one by one) vs batch (whole sample) learning: No need to store the whole sample Problem may change in Ome Wear and degradaoon in system components Stochas7c gradient descent: Update ayer a single pazern Generic update rule (LMS rule): 8
9 Training a Perceptron: Regression Regression (Linear output): to Machine Learning The MIT Press (V1.1) 9
10 ClassificaOon Single sigmoid output K>2 so4max outputs Same as for linear discriminants from chapter 10 except we update after each instance 10
11 Learning Boolean AND 11
12 XOR No w 0, w 1, w 2 sa7sfy: (Minsky and Papert, 1969) to Machine Learning The MIT Press (V1.1) 12
13 MulOlayer Perceptrons (Rumelhart et al., 1986) 13
14 MLP as Universal Approximator x 1 XOR x 2 = (x 1 AND ~x Lecture Notes 2 ) OR (~x for E Alpaydın 1 AND x 2004 Introduction 2 ) 14
15 BackpropagaOon 15
16 Regression Backward Forward x 16
17 Regression with MulOple Outputs y i v ih w hj z h x j 17
18 18
19 19
20 w h x+w 0 z h v h z h 20
21 Two Class DiscriminaOon One sigmoid output y t for P(C 1 x t ) and P(C 2 x t ) 1 y t 21
22 K>2 Classes 22
23 MulOple Hidden Layers MLP with one hidden layer is a universal approximator (Hornik et al., 1989), but using mul7ple layers may lead to simpler networks 23
24 Improving Convergence Momentum Adap7ve learning rate 24
25 Overfibng/Overtraining Number of weights: H (d+1)+(h+1)k 25
26 Conclusion Perceptrons handle linearly separable problems Multilayer perceptrons handle any problem Logistic discrimination functions enable gradient descent based packpropagation Solves the structural credit assignment problem Susceptible to local optima Susceptible to overfitting 26
27 27
28 Structured MLP (Le Cun et al, 1989) 28
29 Weight Sharing 29
30 Hints (Abu Mostafa, 1995) Invariance to translaoon, rotaoon, size Virtual examples Augmented error: E =E+λ h E h If x and x are the same : E h =[g(x θ) g(x θ)] 2 ApproximaOon hint: 30
31 Tuning the Network Size DestrucOve Weight decay: ConstrucOve Growing networks (Ash, 1989) (Fahlman and Lebiere, 1989) 31
32 Bayesian Learning Consider weights w i as random vars, prior p(w i ) Weight decay, ridge regression, regularizaoon cost=data misfit + λ complexity More about Bayesian methods in chapter 14 32
33 Dimensionality ReducOon 33
34 34
35 Learning Time Applica7ons: Sequence recognioon: Speech recognioon Sequence reproducoon: Time series predicoon Sequence associaoon Network architectures Time delay networks (Waibel et al., 1989) Recurrent networks (Rumelhart et al., 1986) 35
36 Time Delay Neural Networks 36
37 Recurrent Networks 37
38 Unfolding in Time 38
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