# MLP with backpropagation learning of AND function from pylab import *

# training vectors (Boolean AND function and constant input) X=array([[0,0,1,1],[0,1,0,1],[1,1,1,1]]) Y=array([0,0,0,1])

# model specifications Ni=3; Nh=3; No=1;

#parameter and array initialization Ntrials=2000 h=zeros(Nh); y=zeros(No) wh=randn(Nh,Ni); wo=randn(No,Nh) dwh=zeros(wh.shape); dwo=zeros(wo.shape) dh=zeros(Nh); do=zeros(No) error=zeros(Ntrials)

for trial in range(Ntrials): #pick example pattern randomly pat=randint(4); x=X[:,pat] #calculate hidden states of sigmoid nodes for ih in range(Nh): #for each hidden node sumInput=0 for ii in range(Ni): #loop over input features sumInput=sumInput+wh[ih,ii]*x[ii] h[ih]=1/(1+exp(-sumInput)) #calclate output (prediction) with sigm=oid nodes for io in range(No): #for each output node sumInput=0; for ih in range(Nh): #loop over inputs from hidden sumInput=sumInput+wo[io,ih]*h[ih]; y[io]=1/(1+exp(-sumInput)) # delta term for each layer (objective function error) for io in range(No): #for each output node do[io]=y[io]*(1-y[io])*(Y[pat]-y[io]) sumInput=0 for ih in range(Nh): #for each hidden node sumInput=0; #backpropgation starts for io in range(No): sumInput=sumInput+wo[io,ih]*do[io] dh[ih]=h[ih]*(1-h[ih])*sumInput #update weights with momentum for io in range(No): for ih in range(Nh): dwo[io,ih]=0.9*dwo[io,ih]+h[ih]*do[io]; wo[io,ih]=wo[io,ih]+0.1*dwo[io,ih]; for ih in range(Nh): for ii in range(Ni): dwh[ih,ii]=0.9*dwh[ih,ii]+x[ii]*dh[ih]; wh[ih,ii]=wh[ih,ii]+0.1*dwh[ih,ii]; # test all pattern for pat in range(4): x=X[:,pat] #calculate prediction for ih in range(Nh): #for each hidden node sumInput=0 for ii in range(Ni): #loop over input features sumInput=sumInput+wh[ih,ii]*x[ii] h[ih]=1/(1+exp(-sumInput)) for io in range(No): #for each output node sumInput=0; for ih in range(Nh): #loop over inputs from hidden sumInput=sumInput+wo[io,ih]*h[ih]; y[io]=1/(1+exp(-sumInput)) #y[io]=round(y[io]) error[trial]=error[trial]+abs(y-Y[pat]); plot(error); show()

1. 150 marks, 40 marks for Grads] Implement a multi-layer perceptron (MLP) by modifying the MLP progranm from the class to solve the XOR problem and train it to translate the digital letters given in file pattern1 into the corresponding ASCII representation. Plot a training curve and interpret your result:s