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Axon: output

- 1. YONG Sopheaktra M1 Yoshikawa-Ma Laboratory 2015/07/26 Feedforward neural networks 1 (multilayer perceptrons)
- 2. Kyoto University • Artificial Neural Network • Perceptron Algorithm • Multi-layer perceptron (MLP) • Overfitting & Regularization Content 2
- 3. Kyoto University • An Artificial Neural Network (ANN) is a system that is based on biological neural network (brain). ▫ The brain has approximately 100 billion neurons, which communicate through electro-chemical signals ▫ Each neuron receives thousands of connections (signals) ▫ If the resulting sum of signals surpasses certain threshold, the response is sent • The ANN attempts to recreate the computational mirror of the biological neural network … Artificial Neural Network 3
- 4. Kyoto University 4
- 5. Kyoto University What is Perceptron? 5 • A perceptron models a neuron • It receives n inputs (feature vector) • It sum those inputs , calculated, then output • Used for linear or binary classification
- 6. Kyoto University 6 Perceptron • The perceptron consists of weights, the summation processor, and an activation function • A perceptron takes a weighted sum of inputs and outputs:
- 7. Kyoto University Weight & Bias 7 • Bias can also be treated as another input ▫ The bias allow to shift the line • The weights determine the slope
- 8. Kyoto University Transfer or Activation Functions 8 • The transfer function translate the input signals to output signals • It uses a threshold to produce an output • Some examples are ▫ Unit Step (threshold) ▫ Sigmoid (logistic regression) ▫ Piecewise linear ▫ Gaussian
- 9. Kyoto University 9 Unit Step (Threshold) • The output is set depending on whether the total input is greater or less than some threshold value.
- 10. Kyoto University 10 Piecewise Linear • The output is proportional to the total weighted output.
- 11. Kyoto University 11 Sigmoid function • It is used when the output is expected to be a positive number ▫ It generates outputs between 0 and 1
- 12. Kyoto University 12 Gaussian • Gaussian functions are bell-shaped curves that are continuous • It is used in radial basis function ANN (RBF kernel – Chapter 14) ▫ Output is real value
- 13. Kyoto University 13 The learning rate • To update the weights and bias to get smaller error • Help us control how much we change the weight and bias
- 14. Kyoto University 14 How the algorithm work? • Initialize the weights (zero or small random value) • Pick a learning rate (0 – 1) • For each training set • Compute the activation output ▫ Adjusting Error = differences between predicted and actual Update bias and weight • Repeating till the error is very small or zero • If the it is linear separable, we will found solution
- 15. Kyoto University 15 https://github.com/nsadawi/perceptronPerceptron.zip/Perceptron.java
- 16. Kyoto University 16 What if the data is non-linearly separable? • Because SLP is a linear classifier and if the data are not linearly separable, the learning process will never find the solution • For example: XOR problem
- 17. Kyoto University 17 Perceptron.zip/Perc.java
- 18. Kyoto University 18 XOR Classification (Xor_classification.zip)
- 19. Kyoto University 19 • A series of logistic regression models stacked on top of each other, with the final layer being either another logistic regression or a linear regression model, depending on whether we are solving a classification or regression problem. Multi-layer perceptron (MLP)
- 20. Kyoto University 20
- 21. Kyoto University 21 A closer look
- 22. Kyoto University 22
- 23. Kyoto University 23 • Use output error, to adjust the weights of inputs at the output layer • Calculate the error at the previous layer and use it to adjust the weights • Repeat this process of back-propagating errors through any number of layers • You may find mathematical equation of how to minimize cost function of neural network at 16.5.4 The backpropagation algorithm The Back Propagation Algorithm
- 24. Kyoto University 24 Convolutional neural networks http://yann.lecun.com/exdb/lenet/index.html • Designed to recognize visual patterns directly from pixel images with minimal preprocessing. • The purpose of multiple hidden units are used to learn non-linear combination of the original inputs (feature extraction) ▫ Individual Informative ▫ Each pixel in an image is not very informative ▫ But the combination will tell
- 25. Kyoto University 25
- 26. Kyoto University 26 Multiple-Classifier
- 27. Kyoto University 27 Machine-learning-ex3.zip
- 28. Kyoto University 28 Overfitting Problem
- 29. Kyoto University 29 Cross validation error
- 30. Kyoto University 30 • Simplifier the parameters/features ▫ Remove some unnecessary features • Regularization ▫ Adjusting the weight How to address it?
- 31. Kyoto University 31 • The MLP can overfit, esp. if the number of nodes is large • A simple way to prevent is early stopping ▫ Stopping the training procedure when the error on the validation set first start to increase • Techniques are ▫ Consistent Gaussian prior ▫ Weight pruning: smaller the parameters value ▫ Soft weight sharing: group of parameters value have similar value ▫ Semi-supervised embedding: used with deep learning NN ▫ Bayesian Inference Determine number of hidden units – faster than cross-validation Regularization
- 32. Kyoto University 32 Thanks You
- 33. Kyoto University • https://www.coursera.org/learn/machine-learning • https://www.youtube.com/playlist?list=PLea0WJq13cnCS4LLMeUuZmTx qsqlhwUoe • http://yann.lecun.com/exdb/lenet/index.html Reference 33

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