Neural Network Assignment
Due December 10th
The first two questions are required. Question three is 10% extra credit.
1. You are given a simple Perceptron with 3 inputs, A, B, and C that uses a step
function with threshold of 0.5 (on the step boundary the output of the step
function is not defined). Find weights between 0 and 1 such that the output is:
a. (A and B) or C
b. A and (B or C)
2. You are given the following Perceptron to train on the xor function. Fill out the
table provided in order to determine what the new weights will be after two
training iterations. Use the weight modification rules provided in class for a
sigmoidal excitation function, with the following change. For the hidden and
output neurons, there is a bias that is applied to the sigmoid functions. This can be
interpreted as implied neuron that always fires and whose weight is set equal to
that bias. This allows one to learn biases for the neurons as well as learning the
weights. Use ร = 0.5.
wbias,h1 wa,h1 wb,h1 wbias,h2 wa,h2 wb,h2 wbias,o wh1,o wh2,o
Initial weights 0.68 0.38 0.83 0.5 0.71 0.43 0.30 0.19 0.19
Timestep Case erro errh1 errh2 ?w
bias,h1 ?w
a,h1 ?w
b,h1 ?w
bias,h2 ?w
a,h2 ?w
b,h2 ?w
bias,o ?wh1,o ?w
h2,o
1 a=0,b=0 -0.0279 -0.00312 0 0 0 0
a=0,b=1
a=1,b=0
a=1,b=1
wbias,h1 wa,h1 wb,h1 wbias,h2 wa,h2 wb,h2 wbias,o wh1,o wh2,o
New weights 0.37989
2 a=0,b=0
a=0,b=1
a=1,b=0
a=1,b=1
a
b
h1
h2
o
