Building a neural network
Building a neural network
The syntax for building a neural network is similar to building a neuron. Rather than pontificating about how this is done, we give two examples. You may have to spend a little time digesting what is going on, but afterwards, you should be able to build your own custom neural network.
Single hidden layer
Single hidden layer
biases1={.3,-.4};weights1={{.7},{-.2}};biases2={.4};weights2={{.9,.7}};activation=Ramp;layer1=LinearLayer[2,"Biases"biases1,"Weights"weights1];layer2=LinearLayer[1,"Biases"biases2,"Weights"weights2];network1=NetChain[{layer1,activation,layer2,activation},"Input"1];Plot[{network1[x]},{x,-10,10},PlotRange{-3,3},PlotStyleThickness[0.01]]
Two hidden layers
Two hidden layers
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biases1={.3,-.4};weights1={{.7},{-.2}};biases2={1.4,-.7};weights2={{.9,-.9},{1.2,.5}};biases3={.1};weights3={{.9,-.8}};activation=Ramp;layer1=LinearLayer[2,"Biases"biases1,"Weights"weights1];layer2=LinearLayer[2,"Biases"biases2,"Weights"weights2];layer3=LinearLayer[1,"Biases"biases3,"Weights"weights3];network2=NetChain[{layer1,activation,layer2,activation,layer3,activation},"Input"1];Plot[{network2[x]},{x,-15,15},PlotRange{-4,4},PlotStyleThickness[0.015]]
Mystery function
Mystery function
Find a neural network whose output function has the following graph:
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g[x_]:=Ramp[x-1]+Ramp[-x-1]+2;Plot[{g[x]},{x,-10,10},PlotRange{-5,5},PlotStyle{Thickness[0.015]}]
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HINT:TheanswerisaneuralnetworkwithonehiddenlayerandRampactivationfunctions.Yourjobistofindtheappropriateweights.Youcanthinkdeeplyaboutwhattheseoughttobe,orexperimentabit.Usethefollowingcodetostart:
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biases1={.3,-.4};weights1={{.7},{-.2}};biases2={.4};weights2={{.9,.7}};activation=Ramp;layer1=LinearLayer[2,"Biases"biases1,"Weights"weights1];layer2=LinearLayer[1,"Biases"biases2,"Weights"weights2];network=NetChain[{layer1,activation,layer2,activation},"Input"1];Plot[{g[x],network[x]},{x,-10,10},PlotRange{-5,5},PlotLegends{"g(x)","neural network"},PlotStyle{Thickness[0.015],Thickness[0.006]}]
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