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Lecture 7: Convolutional Neural Networks Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 1 Administrative A2 is due Feb 5 (next

  1. Lecture 7: Convolutional Neural Networks Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 1

  2. Administrative A2 is due Feb 5 (next Friday) Project proposal due Jan 30 (Saturday) - ungraded, one paragraph - feel free to give 2 options, we can try help you narrow it - What is the problem that you will be investigating? Why is it interesting? - What data will you use? If you are collecting new datasets, how do you plan to collect them? - What method or algorithm are you proposing? If there are existing implementations, will you use them and how? How do you plan to improve or modify such implementations? - What reading will you examine to provide context and background? - How will you evaluate your results? Qualitatively, what kind of results do you expect (e.g. plots or figures)? Quantitatively, what kind of analysis will you use to evaluate and/or compare your results (e.g. what performance metrics or statistical tests)? Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 2

  3. Mini-batch SGD Loop: 1. Sample a batch of data 2. Forward prop it through the graph, get loss 3. Backprop to calculate the gradients 4. Update the parameters using the gradient Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 3

  4. Parameter We covered: sgd, updates momentum, nag, adagrad, rmsprop, adam (not in this vis), we did not cover adadelta Image credits: Alec Radford Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 4

  5. Dropout Forces the network to have a redundant representation. has an ear X has a tail X cat is furry score has claws X mischievous look Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 5

  6. Convolutional Neural Networks [LeNet-5, LeCun 1980] Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 6

  7. A bit of history: Hubel & Wiesel , 1959 RECEPTIVE FIELDS OF SINGLE NEURONES IN THE CAT'S STRIATE CORTEX 1962 RECEPTIVE FIELDS, BINOCULAR INTERACTION AND FUNCTIONAL ARCHITECTURE IN THE CAT'S VISUAL CORTEX 1968... Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 7

  8. Hierarchical organization Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 8

  9. Convolutional Neural Networks (First without the brain stuff) Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 9

  10. Convolution Layer 32x32x3 image height 32 width 32 depth 3 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 10

  11. Convolution Layer 32x32x3 image 5x5x3 filter 32 Convolve the filter with the image i.e. “slide over the image spatially, computing dot products” 32 3 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 11

  12. Convolution Layer Filters always extend the full depth of the input volume 32x32x3 image 5x5x3 filter 32 Convolve the filter with the image i.e. “slide over the image spatially, computing dot products” 32 3 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 12

  13. Convolution Layer 32x32x3 image 5x5x3 filter 32 1 number: the result of taking a dot product between the filter and a small 5x5x3 chunk of the image 32 (i.e. 5*5*3 = 75-dimensional dot product + bias) 3 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 13

  14. Convolution Layer activation map 32x32x3 image 5x5x3 filter 32 28 convolve (slide) over all spatial locations 28 32 3 1 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 14

  15. consider a second, green filter Convolution Layer activation maps 32x32x3 image 5x5x3 filter 32 28 convolve (slide) over all spatial locations 28 32 3 1 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 15

  16. For example, if we had 6 5x5 filters, we’ll get 6 separate activation maps: activation maps 32 28 Convolution Layer 28 32 3 6 We stack these up to get a “new image” of size 28x28x6! Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 16

  17. Preview: ConvNet is a sequence of Convolution Layers, interspersed with activation functions 32 28 CONV, ReLU e.g. 6 5x5x3 32 28 filters 3 6 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 17

  18. Preview: ConvNet is a sequence of Convolutional Layers, interspersed with activation functions 32 28 24 …. CONV, CONV, CONV, ReLU ReLU ReLU e.g. 6 e.g. 10 5x5x3 5x5x 6 32 28 24 filters filters 3 6 10 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 18

  19. Preview [From recent Yann LeCun slides] Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 19

  20. Preview [From recent Yann LeCun slides] Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 20

  21. one filter => example 5x5 filters one activation map (32 total) We call the layer convolutional because it is related to convolution of two signals: elementwise multiplication and sum of a filter and the signal (image) Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 21

  22. preview: Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 22

  23. A closer look at spatial dimensions: activation map 32x32x3 image 5x5x3 filter 32 28 convolve (slide) over all spatial locations 28 32 3 1 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 23

  24. A closer look at spatial dimensions: 7 7x7 input (spatially) assume 3x3 filter 7 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 24

  25. A closer look at spatial dimensions: 7 7x7 input (spatially) assume 3x3 filter 7 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 25

  26. A closer look at spatial dimensions: 7 7x7 input (spatially) assume 3x3 filter 7 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 26

  27. A closer look at spatial dimensions: 7 7x7 input (spatially) assume 3x3 filter 7 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 27

  28. A closer look at spatial dimensions: 7 7x7 input (spatially) assume 3x3 filter => 5x5 output 7 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 28

  29. A closer look at spatial dimensions: 7 7x7 input (spatially) assume 3x3 filter applied with stride 2 7 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 29

  30. A closer look at spatial dimensions: 7 7x7 input (spatially) assume 3x3 filter applied with stride 2 7 Fei-Fei Li & Andrej Karpathy & Justin Johnson Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - Lecture 7 - 27 Jan 2016 27 Jan 2016 30

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