Sep 20 In-Class Exercise .
Hey Everyone,
Post your solutions to the Sep 20 In-Class Exercise to this thread.
Best, Chris
Below is a link to an abstract showing how to do it:
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[[http://ieeexplore.ieee.org/abstract/document/1223966/|Solving parity-N problems with feedforward neural networks]]
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You can click the "Download PDF" and see equations 3, 4, and 5 with Fig. 1(b).
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For boolean formulas, you can build always build a two layer perceptron with n+1 neurons where n is the number of satisfying assignments for the formula.
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'''Input Perceptrons:'''
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For each satisfying assignment x', you set \theta and the summation appropriately that ''only that single satisfying assignment'' makes the neuron's output 1 and all other inputs make it zero.
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Example: \vec{x} =<0,1,1> is satisfying the perceptron for this assignment is:
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g_i = { (1 if -x_1 + x_2 + x_3 \geq 2), (0 mbox( otherwise.)) :}
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'''Output Perceptron: ''' This is essentially an "OR" gate.
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y(\vec{g}) = { (1 if \sum_{i=1}^n g_i >0), (0 mbox( otherwise.)) :}
There are four points that we need: 001 010 100 111
For 111, P1 will have weights [1/3,1/3,1/3]
For 001, 010, we can have P2 as [-1, 1, 0]
For 100, we can have P3 as [1, -1, -1]
Now, a P4 with output from these three as inputs, with weights [1,1,1]
Set theta as 1
(Edited: 2017-09-20)
Par_3(x_1, x_2, x_3)
Image of planes:
The dotted planes represent perceptrons needed.
(Edited: 2017-09-20)
