 Diagram of a Neuron  The Simple Perceptron  Multilayer Neural Network  What is Hidden Layer?  Why do we Need a Hidden Layer?  How do Multilayer Neural Networks Learn?

Neuron w1w1 w2w2 wnwn Y x1x1 x2x2 x3x3 Input signals WeightOutput Signals

w1 w2 Σ Th Threshold Linear Combiner Hard Limiter Y-output x1 x2  Step & sign activation function called hard limit functions.  Single neuron with adjustable synaptic weight and a hard limiter.

 A multilayer Perceptron is a feedforward network with one or more hidden layers  The network consists of:  an input layer of source neurons,  at least one middle or hidden layer of computation neurons  An output layer of computation neurons  The input signals are propagated in a forward direction on a layer-by-layer basis

 A hidden layer hides its desired output  Neurons in the hidden layer cannot be observed through the input/output behavior of the network.  There is no obvious way to know what the desired output of the hidden layer should be.

 The input layer accepts input signals from the outside world and redistributes these signals to all neurons in the hidden layer.  Neuron in the hidden layer detect the features; the weights of the neurons represent the features hidden in the input patterns.  The output layer accepts output signal from the hidden layer and establishes the output pattern of the entire network.

 Most popular method of learning is back-propagation.  Learning in a multi-layer network proceeds the same way as for a Perceptron  A training set of input patterns is presented to the network  The network computes the output pattern.  If there is an error, the weight are adjusted to reduce this error.  In multilayer network, there are many weights, each of which contributes to more than one output.

 A back-propagation network is a multilayer network that has three or four layers.  The layers are fully connected, i.e, every neuron in each layer is connected to every other neuron in the adjacent forward layer  A neuron determines its output in a manner similar to Rosenblatt’s Perceptron.

The net weighted input value is passed through the activation function. Unlike a Perceptron, neuron in the back propagation network use a sigmoid activation function:

 In three layer network, i,j and k refer to neurons in the input, hidden and output layers.  Input signal x 1, x 2, …….. x n are propagated through the network from left to right  Error signals e 1, e 2, e n from right to left.  The symbol W ij denotes the weight for the connection between neuron i in the input layer and neuron j in the hidden layer  The symbol W jk denotes the weight for the connection between neuron j in the hidden layer and neuron k in the output layer

 The error signal at the output of neuron k at iteration p is defined by,  The updated weight at the output layer is defined by,

 The error gradient is determined as the derivative of the activation function multiplied by the error at the neuron output,  Where y k (p) is the output of neuron k at iteration p and x k (p) is the net weighted input to neuron k,

 The weight correction for the hidden layer,

 Initialization : Set all the weights and threshold levels of the network to random numbers uniformly distributed inside a small range (Haykin 1994): (-2.4/F i, +2.4/F i ), Where F i is the total number of inputs of neuron i in the network.  Activation:  Calculate the actual outputs of the neurons in the hidden layer  Calculate the actual outputs of the neurons in the output layer  Weight Training: Update the weights in the back-propagation network propagating backward the errors associated with output neurons.  Iteration: Increase iteration p by one, go back to step 2 and repeat the process until the selected error criterion is satisfied.

(A) Calculate the actual outputs of the neurons in the hidden layer (B) Calculate the actual outputs of the neurons in the output layer

(A) Calculate the error gradient for the neurons in the output layer.

(B) Calculate the error gradient for the neurons in the hidden layer.

 [Negnevitsky, 2001] M. Negnevitsky “ Artificial Intelligence: A guide to Intelligent Systems”, Pearson Education Limited, England,  [Russel, 2003] S. Russell and P. Norvig Artificial Intelligence: A Modern Approach Prentice Hall, 2003, Second Edition  [Patterson, 1990] D. W. Patterson, “Introduction to Artificial Intelligence and Expert Systems”, Prentice-Hall Inc., Englewood Cliffs, N.J, USA,  [Minsky, 1974] M. Minsky “A Framework for Representing Knowledge”, MIT-AI Laboratory Memo 306, 1974.