Neural Network Toolbox User's Guide

Network Architecturesn{1} = net.IW{1,1}*p + net.b{1};Multiple Layers of NeuronsA network can have several layers. Each layer has a weight matrix W, a biasvector b, and an output vector a. To distinguish between the weight matrices,output vectors, etc., for each of these layers in our figures, we append thenumber of the layer as a superscript to the variable of interest. You can see theuse of this layer notation in the three-layer network shown below, and in theequations at the bottom of the figure.Input Layer 1 Layer 2 Layer 3p1p2p3p 1R f 1iw 1,1 1, 11iw 1,1 S, R1n 1 a 111b 11 n 1 a 1 2f 12b1n1S 1 lw 2,1 1,111n 2 a 21f 2 1b 21 n 2 a22f 2 2n2S 2 lw 3,2 1,111n 3 a 31f 3 1b 31 n 3 a32f 3 2b 32 n3S 3b 2221 11a 1 a 3S 1a f 2 S S1 f 2 2f 33lw 2,1 lw 3,2S 2 , S 1S 3 , Sb 21 b 3S 1 b 2 S 2 S 3 a1 = f1 (IW1,1p +b1) a2 = f2 (LW2,1a1 +b2) a3 =f3 (LW3,2 a2 + b3)a3 =f3 (LW3,2 f2 (LW2,1f1 (IW1,1p +b1)+ b2)+ b3)The network shown above has R 1 inputs, S 1 neurons in the first layer, S 2neurons in the second layer, etc. It is common for different layers to havedifferent numbers of neurons. A constant input 1 is fed to the biases for eachneuron.Note that the outputs of each intermediate layer are the inputs to the followinglayer. Thus layer 2 can be analyzed as a one-layer network with S 1 inputs, S 2neurons, and an S 2 xS 1 weight matrix W 2 . The input to layer 2 is a 1 ; the output2-11