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Neural Networks Many slides attributable to: Prof. Mike Hughes - PowerPoint PPT Presentation

Oct 18, 2022 •222 likes •674 views

Tufts COMP 135: Introduction to Machine Learning https://www.cs.tufts.edu/comp/135/2019s/ Neural Networks Many slides attributable to: Prof. Mike Hughes Erik Sudderth (UCI), Emily Fox (UW), Finale Doshi-Velez (Harvard) James, Witten, Hastie,

  1. Tufts COMP 135: Introduction to Machine Learning https://www.cs.tufts.edu/comp/135/2019s/ Neural Networks Many slides attributable to: Prof. Mike Hughes Erik Sudderth (UCI), Emily Fox (UW), Finale Doshi-Velez (Harvard) James, Witten, Hastie, Tibshirani (ISL/ESL books) 2

  2. Objectives Today : Neural Networks day 10 • How to learn feature representations • Feed-forward neural nets • Single neuron = linear function + activation • Multi-layer perceptrons (MLPs) • Universal approximation • The Rise of Deep Learning: • Success stories on Images and Language Mike Hughes - Tufts COMP 135 - Fall 2020 3

  3. What will we learn? Evaluation Supervised Training Learning Data, Label Pairs Performance { x n , y n } N measure Task n =1 Unsupervised Learning data label x y Reinforcement Learning Prediction Mike Hughes - Tufts COMP 135 - Fall 2020 4

  4. Task: Binary Classification y is a binary variable Supervised (red or blue) Learning binary classification x 2 Unsupervised Learning Reinforcement Learning x 1 Mike Hughes - Tufts COMP 135 - Fall 2020 5

  5. Example: Hotdog or Not https://www.theverge.com/tldr/2017/5/14/15639784/hbo- silicon-valley-not-hotdog-app-download Mike Hughes - Tufts COMP 135 - Fall 2020 6

  6. Text Sentiment Classification Mike Hughes - Tufts COMP 135 - Fall 2020 7

  7. Image Classification Mike Hughes - Tufts COMP 135 - Fall 2020 8

  8. Feature Transform Pipeline Data, Label Pairs { x n , y n } N n =1 Feature, Label Pairs Performance Task { φ ( x n ) , y n } N measure n =1 label data φ ( x ) y x Mike Hughes - Tufts COMP 135 - Fall 2020 9

  9. Predicted Probas vs Binary Labels Mike Hughes - Tufts COMP 135 - Fall 2020 10

  10. Decision Boundary is Linear { x ∈ R 2 : σ ( w T ˜ x ) = 0 . 5 } ←→ { x ∈ R 2 : w T ˜ x = 0 } Mike Hughes - Tufts COMP 135 - Fall 2020 11

  11. Logistic Regr. Network Diagram 0 or 1 Credit: Emily Fox (UW) https://courses.cs.washington.edu/courses/cse41 6/18sp/slides/ Mike Hughes - Tufts COMP 135 - Fall 2020 12

  12. A “Neuron” or “Perceptron” Unit Non-linear Linear function activation with weights w function Credit: Emily Fox (UW) Mike Hughes - Tufts COMP 135 - Fall 2020 13

  13. “Inspired” by brain biology Slide Credit: Bhiksha Raj (CMU) Mike Hughes - Tufts COMP 135 - Fall 2020 14

  14. Challenge: Find w for these functions X_1 X_2 y X_1 X_2 y 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 Credit: Emily Fox (UW) Mike Hughes - Tufts COMP 135 - Fall 2020 15

  15. Challenge: Find w for these functions X_1 X_2 y X_1 X_2 y 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 Mike Hughes - Tufts COMP 135 - Fall 2020 Credit: Emily Fox (UW) 16

  16. What we can’t do with linear decision boundary classifiers X_1 X_2 y 0 0 0 0 1 1 1 0 1 1 1 0 Mike Hughes - Tufts COMP 135 - Fall 2020 17

  17. Idea: Compose Neurons together! φ ( x ) y x transform classify Mike Hughes - Tufts COMP 135 - Fall 2020 18

  18. Can you find w to solve XOR? AND/ ? ? OR ? ? ? ? ? ? ? ? ? Mike Hughes - Tufts COMP 135 - Fall 2020 19

  19. Can you find w to solve XOR? ? ? ? ? ? ? ? ? ? Mike Hughes - Tufts COMP 135 - Fall 2020 20

  20. Can you find w to solve XOR? Mike Hughes - Tufts COMP 135 - Fall 2020 21

  21. 1D Input + 3 hidden units Mike Hughes - Tufts COMP 135 - Fall 2020 22

  22. 1D Input + 3 hidden units Example functions (before final threshold) f ( x 1 ) f ( x 1 ) Intuition: Piece-wise step function Partitioning input space into regions Mike Hughes - Tufts COMP 135 - Fall 2020 23

  23. MLPs can approximate any functions with enough hidden units! Mike Hughes - Tufts COMP 135 - Fall 2020 24

  24. Neuron Design What’s wrong with hard step activation function? Non-linear Linear function activation with weights w function Credit: Emily Fox (UW) Mike Hughes - Tufts COMP 135 - Fall 2020 25

  25. Neuron Design What’s wrong with hard step activation function? Not smooth! Gradient is zero almost everywhere, so hard to train weights! Non-linear Linear function activation with weights w function Credit: Emily Fox (UW) Mike Hughes - Tufts COMP 135 - Fall 2020 26

  26. Which Activation Function? Non-linear Linear function activation with weights w function Credit: Emily Fox (UW) Mike Hughes - Tufts COMP 135 - Fall 2020 27

  27. Activation Functions Advice Credit: Emily Fox (UW) Mike Hughes - Tufts COMP 135 - Fall 2020 28

  28. Exciting Applications: Computer Vision Mike Hughes - Tufts COMP 135 - Fall 2020 29

  29. Object Recognition from Images Mike Hughes - Tufts COMP 135 - Fall 2020 30

  30. Deep Neural Networks for Object Recognition Scores for each possible object category Decision: “ leopard ” Mike Hughes - Tufts COMP 135 - Fall 2020 31

  31. Deep Neural Networks for Object Recognition Scores for each possible object category Decision: “ mushroom ” Mike Hughes - Tufts COMP 135 - Fall 2020 32

  32. Each Layer Extracts “Higher Level” Features Mike Hughes - Tufts COMP 135 - Fall 2020 33

  33. More layers = less error! ImageNet challenge 1000 categories, 1.2 million images in training set top 5 classification error (%) shallow 2010 2011 2012 2013 2014 2015 Credit: KDD Tutorial by Sun, Xiao, & Choi: http://dl4health.org/ Figure idea originally from He et. al., CVPR 2016 Mike Hughes - Tufts COMP 135 - Fall 2020 34

  34. 2012 ImageNet Challenge Winner Mike Hughes - Tufts COMP 135 - Fall 2020 35

  35. State of the art Results Mike Hughes - Tufts COMP 135 - Fall 2020 36

  36. Semantic Segmentation Mike Hughes - Tufts COMP 135 - Fall 2020 37

  37. Object Detection Mike Hughes - Tufts COMP 135 - Fall 2020 38

  38. Exciting Applications: Natural Language (Spoken and Written) Mike Hughes - Tufts COMP 135 - Fall 2020 39

  39. Reaching Human Performance in Speech-to-Text https://arxiv.org/pdf/1610.05256.pdf Mike Hughes - Tufts COMP 135 - Fall 2020 40

  40. Gains in Translation Quality https://ai.googleblog.com/2016/09/a-neural-network-for-machine.html Mike Hughes - Tufts COMP 135 - Fall 2020 41

  41. Any Disadvantages? Mike Hughes - Tufts COMP 135 - Fall 2020 42

  42. Deep Neural Networks can overfit! 1 layer Many layers Few units / layer Many units / layer Underfitting Overfitting Mike Hughes - Tufts COMP 135 - Fall 2020 43

  43. Ways to avoid overfitting • More training data! • L2 / L1 penalties on weights • More tricks (next week) …. • Early stopping • Dropout • Data augmentation Mike Hughes - Tufts COMP 135 - Fall 2020 44

  44. Objectives Today : Neural Networks Unit 1/2 • How to learn feature representations • Feed-forward neural nets • Single neuron = linear function + activation • Multi-layer perceptrons (MLPs) • Universal approximation • The Rise of Deep Learning: • Success stories on Images and Language Mike Hughes - Tufts COMP 135 - Fall 2020 45

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