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docs/techs/OMSCS/CS7641-Machine-Learning/Supervised_Learning/3.Neural_networks.md
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# Neural Networks | ||
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Cell body -> Nevron -> Axon -> Synapses. | ||
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Perceptron | ||
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![NN](../images/SL3_Neural_Networks.png) | ||
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## Artificial Neural Networks | ||
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![NN](../images/SL3_ANN.png) | ||
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![ANN](../images/SL 3 - Neural Networks Artificial Neural Networks.png) | ||
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We need to pay attention to | ||
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* Activation function | ||
* firing threshold | ||
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### How powerful is perceptron unit? | ||
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One activation function computes the half plane. | ||
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![perceptron](../images/SL3_perceptron_Unit.png) | ||
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What's the nice and short computing in the following? | ||
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### Boolean: AND | ||
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![perceptron_func](../images/SL3_perceptron_AND.png) | ||
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### Boolean: OR | ||
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![OR-Func](../images/SL3_perception_OR.png) | ||
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### Boolean: Not | ||
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![Unit-Not](../images/SL3_perception_NOT.png) | ||
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### XOR as Perceptron Network | ||
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![XOR](../images/SL3_perception_XOR.png) | ||
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## Perceptron Training | ||
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Given examples, find weights that map inputs to outputs. | ||
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* Perceptron rule (**threshold**) | ||
* Gradient descent / delta rule (**un-thresholded**) | ||
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### Perceptron rules | ||
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Single Unit | ||
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The halting problem for iterations. | ||
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![perceptron-training](../images/SL3_perceptron_training.png) | ||
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## Gradient Descent | ||
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Avoid Non-linear separability issues. | ||
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![Gradient-descent](../images/SL3_Gradient_descent.png) | ||
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### Comparison of Learning rules | ||
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#### Perceptron analysis | ||
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guarantee to finite convergence only if linear separability | ||
$$ | ||
\Delta W_i = \eta (y - y') x_i | ||
$$ | ||
Eta = learning-rate | ||
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y = target | ||
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y' = output | ||
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#### Gradient Descent analysis | ||
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Calculus, robust, converge to local optimum | ||
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$$ | ||
\Delta W_i = \eta (y - a) x_i | ||
$$ | ||
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#### Comparing learning rules | ||
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![comparison-learning-rules](../images/SL3_compariso_of_learning_rules.png) | ||
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## Sigmoid - differentiable threshold | ||
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![Sigmoid](../images/SL3_sigmoid.png) | ||
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## Neural Network Sketch |
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