Convolutional Neural Networks (CNN)
- 1. Convolutional Neural Networks Gaurav Mittal 2012CSB1013 IIT Ropar [email protected] 1 Lenet-5 (Lecun-98), Convolutional Neural Network for digits recognition
- 3. What are CNNs? Essentially neural networks that use convolution in place of general matrix multiplication in at least one of their layers. 3http://goodfeli.github.io/dlbook/contents/convnets.html
- 4. Motivation 4
- 5. Detection or Classification Tasks 5Andrew Ng: Deep Learning, Self-Taught Learning and Unsupervised Feature Learning
- 6. What to do with this data? 6Andrew Ng: Deep Learning, Self-Taught Learning and Unsupervised Feature Learning
- 7. Feature Representations 7Andrew Ng: Deep Learning, Self-Taught Learning and Unsupervised Feature Learning
- 8. Feature Representations 8Andrew Ng: Deep Learning, Self-Taught Learning and Unsupervised Feature Learning
- 9. How is computer perception done? 9Andrew Ng: Deep Learning, Self-Taught Learning and Unsupervised Feature Learning
- 11. Computer Vision Features 11Andrew Ng: Deep Learning, Self-Taught Learning and Unsupervised Feature Learning
- 12. Audio Features 12Andrew Ng: Deep Learning, Self-Taught Learning and Unsupervised Feature Learning
- 13. NLP Features 13Andrew Ng: Deep Learning, Self-Taught Learning and Unsupervised Feature Learning
- 14. 14 Certainly, coming up with features is difficult, time-consuming and requires expert knowledge. A lot of time is spend tuning the features which are often hand-crafted! Andrew Ng: Deep Learning, Self-Taught Learning and Unsupervised Feature Learning
- 17. Learning non-linear functions 17www.cse.ust.hk/~leichen/courses/FYTG.../FYTGS5101-Guoyangxie.pdf
- 19. Biologically Inspired! 19Andrew Ng: Deep Learning, Self-Taught Learning and Unsupervised Feature Learning
- 20. Features Learned by Deep Training 20
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- 24. Distinguished Features 24 Locally Receptive Fields Shared Weights Spatial or Temporal Sub-sampling http://neuralnetworksanddeeplearning.com/chap6.html
- 25. Typical CNN Layer 25 Input Convolutional Stage: Affine Transform Detector Stage: Nonlinearity Pooling Stage Normalization Stage (Optional) Output: Feature Map
- 26. Typical CNN Layer 26 Input Convolutional Stage: Affine Transform Detector Stage: Nonlinearity Pooling Stage Normalization Stage (Optional) Output: Feature Map
- 27. Convolution The convolution of f and g, written as f∗g, is defined as the integral of the product of the two functions after one is reversed and shifted: Convolution is commutative. Can be viewed as a weighted average operation at every moment (for this w need to be a valid probability density function) Discrete Convolution (one-axis): 27https://www.wikipedia.org/
- 28. Cross-Correlation • For continuous functions f and g, the cross-correlation is defined as: where f* denotes the complex conjugate of f and τ is the lag • Again, cross-correlation is commutative • For discrete functions, it is defined as: 28https://www.wikipedia.org/
- 29. Convolution and Cross-Correlation in Images For a 2-D image H and a 2-D kernel F, 29
- 30. How do they differ? 30 Convolution is equivalent to flipping the filter in both dimensions (bottom to top, right to left) and applying cross- correlation For symmetric kernels, both result in the same output. Many machine learning libraries implement cross-correlation but call it convolution!
- 31. 2-D Convolution (without kernel flipping) 31 Example of 'valid' 2-D convolution (without kernel flipping) where a 3x4 matrix convolved with a 2x2 kernel to output a 2x3 matrix http://goodfeli.github.io/dlbook/contents/convnets.html
- 32. 2-D Convolution in Action! 32http://i.stack.imgur.com/I7DBr.gif
- 33. Variants 33 • Add zero-padding to the image enough for every pixel to be visited k times in each direction, with output size: (m + k - 1) x (m + k - 1)Full • With no zero-padding, kernel is restricted to traverse only within the image, with output size: (m - k + 1) x (m - k + 1)Valid • Add zero-padding to the image to have the output of the same size as the image, i.e., m x mSame Stride s • Down-sampling the output of convolution by sampling only every s pixels in each direction. • For instance, the output of 'valid' convolution with stride s results in an output of size m − k + s s x m − k + s s http://goodfeli.github.io/dlbook/contents/convnets.html
- 36. Local Receptive Field/Sparse Connectivity Convolution exploits the property of spatial local- correlations in the image by enforcing local connectivity pattern between neurons of adjacent layers Drastic reduce in the number of free parameters compared to fully connected network reducing overfitting and more importantly, computational complexity of the network. 36
- 37. Indirect Global Connectivity 37 • Receptive fields of units in deeper layers larger than shallow layers • Though direct connections are very sparse, deeper layers indirectly connected to most of the input image • Effect increases with strided convolution or pooling
- 38. Example 38 Input neurons representing a 28x28 image (such as from MNIST dataset) http://neuralnetworksanddeeplearning.com/chap6.html
- 39. Example 39 Every hidden layer neuron has a local receptive field of region 5x5 pixels http://neuralnetworksanddeeplearning.com/chap6.html
- 40. Example 40 And so on, the first hidden layer is built! (28 - 5 + 1) = 24 x 24 neurons in the hidden layer on 'valid' convolution Size of the hidden layer can be changed using another variant of convolution http://neuralnetworksanddeeplearning.com/chap6.html
- 41. Shared Weights and Bias • All neuron in the hidden layer share the same parameterization (weight vector and bias) forming a 'Feature Map‘ • (Shared Weights, Bias) →Kernel/Filter • Now, the gradient of a shared weight is sum of the gradients of the parameters being shared. 41
- 42. Shared Weights and Bias • Translation Equivariance o Allows features to be detected regardless of their position in the visual field. (Feature is a kind of input pattern that will cause a neuron to activate, for eg. an edge) o All neurons in the first hidden layer detect exactly the same feature, just at different locations. o CNNs are well adapted to translation invariance of images: move a picture of a cat, and it's still an image of a cat! • Further reduces the number of free parameters, achieving better generalization and computational performance. 42
- 43. Typical CNN Layer 43 Input Convolutional Stage: Affine Transform Detector Stage: Nonlinearity Pooling Stage Normalization Stage (Optional) Output: Feature Map
- 44. Non-Linear Activation Function • Sigmoid: • Tanh: • Rectified Linear Unit (ReLU): Most popular activation function for DNN as of 2015, avoids saturation issues, makes learning faster 44 Sigmoid Tanh ReLU
- 45. Feature Map - Obtained by convolution of the image with a linear filter, adding a bias term and applying a non-linear function Require a number of such feature maps at each layer to capture sufficient features in the image Let 𝑘 𝑡𝑡 feature map at a given layer be 𝑥 𝑘 , whose filters are determined by 𝑊𝑘 and bias 𝑏 𝑘, then 𝑥 𝑘 with sigmoid, 𝜎 function for non-linearity and filter of size m x m is obtained as: 𝑥 𝑘 𝑖𝑖 = 𝜎 𝑊 𝑘 ∗ 𝑎 ij + 𝑏 𝑘 = 𝜎 � � 𝑤 𝑎𝑎 𝑦 𝑘−1 𝑖+𝑎 𝑗+𝑏 𝑚−1 𝑏=0 𝑚−1 𝑎=0 𝑖𝑖 + 𝑏 𝑘 45
- 46. • Each hidden layer is compose of multiple feature maps, 𝑥 𝑘 , 𝑘 = 0. . 𝐾 • Weights, W of a hidden layer can be represented in a 4D tensor containing elements for every combination of destination feature map, source feature map, source vertical position, and source horizontal position. • Biases, b can be represented as a vector containing one element for every destination feature map. 46
- 47. Typical CNN Layer 47 Input Convolutional Stage: Affine Transform Detector Stage: Nonlinearity Pooling Stage Normalization Stage (Optional) Output: Feature Map
- 48. Pooling Non-linear down-sampling to simplify the information in output from convolutional layer. Variants: Max pooling (popular) Weighted average based on distance L2 norm of neighborhood Reduces computation for upper layers by reporting summary statistics (only with stride > 1) Provides translation invariance (Infinitely strong prior that learning must be invariant to small translations) Useful property, if we care more about whether some feature is present than exactly where it is, thus adds robustness to position 48 Bottom view has been shifted by 1 pixel w.r.t. Top view. Every value in the bottom row has changed, but only half the values in the top row has changed!
- 49. Typical CNN Layer 49 Input Convolutional Stage: Affine Transform Detector Stage: Nonlinearity Pooling Stage Normalization Stage (Optional) Output: Feature Map
- 50. Normalization (Optional) Locally the response is normalized using some distance based weighted average function 50
- 51. Putting It All Together! 51 Lenet-5 (Lecun-98), Convolutional Neural Network for digits recognition Lecun 1998
- 52. Backpropagation • Loss function o For Classification • Softmax Function with negative log likelihood o For Regression • Mean squared error • Weight Update where 𝜂 - learning rate, 𝛼 - momentum, 𝜆 - weight decay 52
- 53. Backpropagation • Convolutional Layer o With error function, E, and filter output 𝒙𝒍 , Thus, the error is propagated to the previous layer. • Pooling Layer o Do not actually learn themselves, just reduce the size of the problem by introducing sparseness. o Reduces region of k x k size to a single value during forward propagation. o Error propagated back to the place where it came from, thus errors are rather sparse. 53 http://andrew.gibiansky.com/blog/machine-learning/convolutional-neural-networks/
- 54. Theano 54
- 55. What is Theano? • Theano is a Python-based Math Expression Compiler whose syntax is quite similar to NumPy. • Open-source project developed and maintained by ML group at Université de Montréal. • User composes mathematical expressions in a high-level description mimicking NumPy's syntax and semantics which allows Theano to provide symbolic differentiation. 55http://deeplearning.net/
- 56. Key Features • Single implementation compatible with both CPU and GPU. • Theano on its own optimizes using CUDA C++ for GPU. • Easy to implement back-propagation in CNN, as it automatically computes all the mappings involved. • Creates a graph with the various inputs involved, differentiating using chain rule. 56 Fitting a multi-layer perceptron to simulated data with SGD having 784 inputs, 500 hidden units, a 10-way classification and training 60 examples at a time http://deeplearning.net/
- 57. Sneak Peek into Theano... 57http://deeplearning.net/
- 58. Theano-based implementations for Deep Learning Caffe Torch Keras Other Frameworks: cuDNN DIGITS 58
- 59. Caffe 59
- 60. Key Features • Deep learning framework (essentially for training CNNs) developed by Berkeley Vision and Learning Center (BVLC) • Speed: Able to process over 60M images per day with a single Nvidia K40 GPU, thus considered to be the fastest convnet implementation available. • Expressive Architecture: Allows models and optimization to be defined as configuration files rather than hard-coding, with ability to switch between CPU and GPU by a single flag. 60www.caffe.berkeleyvision.org
- 61. Sneak Peek into Caffe 61 Convolutional Layer Max Pooling Layer Solver
- 62. Age and Gender Classification using Convolutional Neural Networks Gil Levi and Tal Hassner The Open University of Israel IEEE Workshop on Analysis and Modeling of Faces and Gestures (AMFG), at the IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), Boston, June 2015 62
- 63. Overview Uses deep-convolutional neural networks (CNN) for the task of automatic age and gender classification. Despite the very challenging nature of the images in the Adience dataset and the simplicity of the network design used, the method significantly outperforms existing state of the art by substantial margins. 63
- 64. Dataset - The Adience Benchmark • Consists of images automatically uploaded to Flickr from smartphones. • Viewing conditions of these images are highly unconstrained, thus capturing extreme variations in head pose, lightning conditions, blur, occlusion, expressions and more. • Includes roughly 26K images of 2,284 subjects. • For the tests, in-plane aligned version of the faces is used. 64 Faces from Adience benchmark (above) and breakdown into different classes (below)
- 65. Network Architecture 65 All 3 RGB channels First, resized to 256 x 256, then cropped to 227 x 227 96 filters size 3x7x7 384 filters size 256x3x3 Both fully connected layers contain 512 neurons followed by ReLU and dropout layer Output to class labels (age / gender) 256 filters size 96x5x5 Each convolutional layer is followed by rectified linear operator (ReLU), max pooling layer of 3x3 regions with 2-pixel strides and a local normalization layer
- 66. Measures to reduce overfitting • Lean network architecture using just 3 convolutional layers and 2 fully connected layers considering the size of the dataset and labels involved (8 age classes and 2 gender classes) • Dropout learning: Randomly set the output value of network neurons to 0 with a dropout ratio of 0.5 (50% chance) • Weight decay: Used to keep the magnitude of weights close to zero • Data Augmentation: Took random crop of 227x227 from image of 256x256 and randomly mirrored it in each forward-backward training pass All these measures help in keeping the number of free parameters in the network low reducing complexity and thus over-fitting 66
- 67. Experiments 5-fold cross validation based on pre- specified subject exclusive folds distribution What they used • Trained on Amazon GPU machine with 1,536 CUDA cores and 4 GB GDDR5 RAM What I used • Trained on Nvidia Quadro K2200 with 640 CUDA cores and 4 GB GDDR5 RAM 67 Solver
- 68. Results Method Accuracy Paper Reimplementation Single-Crop 85.9 ±1.4 86.7 ± 1.5 Over-Sample 86.8 ± 1.4 87.4 ± 0.9 68 Gender Classification Age Estimation Method Accuracy Paper Reimplementation Exact One-off Exact One-off Single-Crop 49.5 ± 4.4 84.6 ± 1.7 49.5 ± 3.6 85.4 ± 1.8 Over-Sample 50.7 ± 5.1 84.7 ± 2.2 50.6 ± 5.0 85.8 ± 1.5
- 69. Results - Age Estimation Confusion Matrix 69 Predicted Labels ActualLabels 0-2 4-6 8-13 15-20 25-32 38-43 48-53 60- 0-2 0.741 0.139 0 0.028 0 0 0 0.093 4-6 0.057 0.654 0.135 0.135 0 0 0 0.019 8-13 0 0.114 0 0.828 0.057 0 0 0 15-20 0.018 0.119 0.065 0.653 0.106 0.015 0.010 0.010 25-32 0.009 0.094 0.009 0.471 0.292 0.037 0.037 0.047 38-43 0.02 0 0 0.22 0.56 0.14 0.06 0 48-53 0 0.1 0.033 0.067 0.133 0.267 0.4 0 60- 0.238 0.012 0 0.008 0 0 0 0.740 Predicted Labels ActualLabels 0-2 4-6 8-13 15-20 25-32 38-43 48-53 60- 0-2 0.699 0.147 0.028 0.006 0.005 0.008 0.007 0.009 4-6 0.256 0.573 0.166 0.023 0.010 0.011 0.010 0.005 8-13 0.027 0.223 0.552 0.150 0.091 0.068 0.055 0.061 15-20 0.003 0.019 0.081 0.239 0.106 0.055 0.049 0.028 25-32 0.006 0.029 0.138 0.510 0.613 0.461 0.260 0.108 38-43 0.004 0.007 0.023 0.058 0.149 0.293 0.339 0.268 48-53 0.002 0.001 0.004 0.007 0.017 0.055 0.146 0.165 60- 0.001 0.001 0.008 0.007 0.009 0.050 0.134 0.357 Paper Reimplementation
- 70. References • http://deeplearning.net/tutorial/ • http://goodfeli.github.io/dlbook/contents/convnets.html • http://neuralnetworksanddeeplearning.com/chap6.html • http://deeplearning.net/software/theano/tutorial/ • http://andrew.gibiansky.com/blog/machine-learning/convolutional-neural-networks/ • Andrew Ng: Deep Learning, Self-Taught Learning and Unsupervised Feature Learning • www.caffe.berkeleyvision.org • http://www.openu.ac.il/home/hassner/Adience/index.html • https://www.wikipedia.org/ • www.cse.ust.hk/~leichen/courses/FYTG.../FYTGS5101-Guoyangxie.pdf • LeCun, Yann, et al. "Gradient-based learning applied to document recognition."Proceedings of the IEEE 86.11 (1998): 2278-2324. • Bergstra, James, et al. "Theano: a CPU and GPU math expression compiler."Proceedings of the Python for scientific computing conference (SciPy). Vol. 4. 2010. • Gil Levi and Tal Hassner, Age and Gender Classification using Convolutional Neural Networks, IEEE Workshop on Analysis and Modeling of Faces and Gestures (AMFG), at the IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), Boston, June 2015 70