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Lecture 7: Convolutional Neural Networks

Lecture 7: Convolutional Neural Networks Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 1 27 Jan 2016. 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 ( plots or figures)? Quantitatively, what kind of analysis will you use to evaluate and/or compare your results ( what performance metrics or statistical tests)?

Convolutional Neural Networks. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 2 27 Jan 2016 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

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Transcription of Lecture 7: Convolutional Neural Networks

1 Lecture 7: Convolutional Neural Networks Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 1 27 Jan 2016. 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 ( plots or figures)? Quantitatively, what kind of analysis will you use to evaluate and/or compare your results ( what performance metrics or statistical tests)?

2 Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 2 27 Jan 2016. 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 Lecture 7 - 3 27 Jan 2016. 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 Lecture 7 - 4 27 Jan 2016. Dropout Forces the network to have a redundant representation. has an ear X. has a tail is furry X cat score has claws mischievous X. look Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 5 27 Jan 2016. Convolutional Neural Networks [LeNet-5, LeCun 1980]. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 6 27 Jan 2016. A bit of history: Hubel & Wiesel, 1959.

3 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. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 7 27 Jan 2016. Hierarchical organization Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 8 27 Jan 2016. Convolutional Neural Networks (First without the brain stuff). Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 9 27 Jan 2016. Convolution Layer 32x32x3 image 32 height 32 width 3 depth Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 10 27 Jan 2016. Convolution Layer 32x32x3 image 5x5x3 filter 32. Convolve the filter with the image slide over the image spatially, computing dot products . 32. 3. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 11 27 Jan 2016. Convolution Layer Filters always extend the full depth of the input volume 32x32x3 image 5x5x3 filter 32.

4 Convolve the filter with the image slide over the image spatially, computing dot products . 32. 3. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 12 27 Jan 2016. 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 ( 5*5*3 = 75-dimensional dot product + bias). 3. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 13 27 Jan 2016. Convolution Layer activation map 32x32x3 image 5x5x3 filter 32. 28. convolve (slide) over all spatial locations 32 28. 3 1. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 14 27 Jan 2016. consider a second, green filter Convolution Layer 32x32x3 image activation maps 5x5x3 filter 32. 28. convolve (slide) over all spatial locations 32 28. 3 1. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 15 27 Jan 2016. For example, if we had 6 5x5 filters, we'll get 6 separate activation maps: activation maps 32.

5 28. Convolution Layer 32 28. 3 6. We stack these up to get a new image of size 28x28x6! Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 16 27 Jan 2016. Preview: ConvNet is a sequence of Convolution Layers, interspersed with activation functions 32 28. CONV, ReLU. 6. 5x5x3. 32 filters 28. 3 6. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 17 27 Jan 2016. Preview: ConvNet is a sequence of Convolutional Layers, interspersed with activation functions 32 28 24.. CONV, CONV, CONV, ReLU ReLU ReLU. 6 10. 5x5x3 5x5x6. 32 filters 28 filters 24. 3 6 10. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 18 27 Jan 2016. Preview [From recent Yann LeCun slides]. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 19 27 Jan 2016. Preview [From recent Yann LeCun slides]. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 20 27 Jan 2016. one filter =>. one activation map example 5x5 filters (32 total).

6 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 Lecture 7 - 21 27 Jan 2016. preview: Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 22 27 Jan 2016. A closer look at spatial dimensions: activation map 32x32x3 image 5x5x3 filter 32. 28. convolve (slide) over all spatial locations 32 28. 3 1. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 23 27 Jan 2016. A closer look at spatial dimensions: 7. 7x7 input (spatially). assume 3x3 filter 7. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 24 27 Jan 2016. A closer look at spatial dimensions: 7. 7x7 input (spatially). assume 3x3 filter 7. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 25 27 Jan 2016. A closer look at spatial dimensions: 7. 7x7 input (spatially). assume 3x3 filter 7.

7 Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 26 27 Jan 2016. A closer look at spatial dimensions: 7. 7x7 input (spatially). assume 3x3 filter 7. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 27 27 Jan 2016. A closer look at spatial dimensions: 7. 7x7 input (spatially). assume 3x3 filter => 5x5 output 7. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 28 27 Jan 2016. 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 Lecture 7 - 29 27 Jan 2016. 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 Lecture 7 - 30 27 Jan 2016. A closer look at spatial dimensions: 7. 7x7 input (spatially). assume 3x3 filter applied with stride 2. => 3x3 output! 7. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 31 27 Jan 2016.

8 A closer look at spatial dimensions: 7. 7x7 input (spatially). assume 3x3 filter applied with stride 3? 7. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 32 27 Jan 2016. A closer look at spatial dimensions: 7. 7x7 input (spatially). assume 3x3 filter applied with stride 3? 7 doesn't fit! cannot apply 3x3 filter on 7x7 input with stride 3. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 33 27 Jan 2016. N. Output size: (N - F) / stride + 1. F. N = 7, F = 3: F N. stride 1 => (7 - 3)/1 + 1 = 5. stride 2 => (7 - 3)/2 + 1 = 3. stride 3 => (7 - 3)/3 + 1 = :\. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 34 27 Jan 2016. In practice: Common to zero pad the border 0 0 0 0 0 0. input 7x7. 0 3x3 filter, applied with stride 1. 0 pad with 1 pixel border => what is the output? 0. 0. (recall:). (N - F) / stride + 1. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 35 27 Jan 2016.

9 In practice: Common to zero pad the border 0 0 0 0 0 0. input 7x7. 0 3x3 filter, applied with stride 1. 0 pad with 1 pixel border => what is the output? 0. 7x7 output! 0. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 36 27 Jan 2016. In practice: Common to zero pad the border 0 0 0 0 0 0. input 7x7. 0 3x3 filter, applied with stride 1. 0 pad with 1 pixel border => what is the output? 0. 7x7 output! 0. in general, common to see CONV layers with stride 1, filters of size FxF, and zero-padding with (F-1)/2. (will preserve size spatially). F = 3 => zero pad with 1. F = 5 => zero pad with 2. F = 7 => zero pad with 3. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 37 27 Jan 2016. Remember back to . 32x32 input convolved repeatedly with 5x5 filters shrinks volumes spatially! (32 -> 28 -> 24 ..). Shrinking too fast is not good, doesn't work well. 32 28 24.. CONV, CONV, CONV, ReLU ReLU ReLU.

10 6 10. 5x5x3 5x5x6. 32 filters 28 filters 24. 3 6 10. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 38 27 Jan 2016. Examples time: Input volume: 32x32x3. 10 5x5 filters with stride 1, pad 2. Output volume size: ? Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 39 27 Jan 2016. Examples time: Input volume: 32x32x3. 10 5x5 filters with stride 1, pad 2. Output volume size: (32+2*2-5)/1+1 = 32 spatially, so 32x32x10. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 40 27 Jan 2016. Examples time: Input volume: 32x32x3. 10 5x5 filters with stride 1, pad 2. Number of parameters in this layer? Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 41 27 Jan 2016. Examples time: Input volume: 32x32x3. 10 5x5 filters with stride 1, pad 2. Number of parameters in this layer? each filter has 5*5*3 + 1 = 76 params (+1 for bias). => 76*10 = 760. Fei-Fei Li & Andrej Karpathy & Justin Johnson Lecture 7 - 42 27 Jan 2016.

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