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MULTI-LAYER PERCEPTRON Ranga Rodrigo February 8, 2014 1 INTRODUCTION • Perceptron can only be a linear classifier. • We can have a network of neurons (perceptron-like structures) with an input layer, one or more hidden layers, and an output layer. • Each layer consists of many neurons and the output of a layer is fed as inputs to all neurons of the next layer. 2 N1xN2 weights Layer 1 Layer 2 Layer k Layer L (output layer) 3 DESCRIPTION OF THE MLP • In each layer, there are Nk elements (neurons), k = 1, ...,L, denoted as Nki , N ik , i 1, , N k • Each neuron may be a sigmoidal neuron. • There are N0 inputs, to which signals x1(t), ..., xN0(t), are applied, notated in the form of a vector x [ x1 (t ),, x N0 (t )]T , t 1,2, • The output signal of i-th neuron in k-th layer is (k ) y denoted as i (t ) i 1, N k , k 1, , L . 4 DESCRIPTION OF PARAMETERS Input vector for kth layer Input for kth layer from the output of (k-1) layer (except for k=1, i = 0) weights of neuron 5 i-TH NEURON IN k-TH LAYER 6 FORWARD PASS Output signals of Lth layer Output desired signals 7 BACKPROPAGATION Weights update 8