Question

4. Back to diamonds. Consider the diamond generalization that has two input Xi and X2 and a single output Z. (This perceptron should have three layers and 6 edges, with 2 X inputs, 2 Y intermediates, and a single Z output.) Assume that all neurons are 'integrate and fire', and each can have a threshold of or 1. Assume that neurons have voltage 0, unless the weighted inputs exceed K, in which case they assume voltage 1. Weights on the edges can be positive or negative real numbers. (a) Design weights such that this circuit computes the XOR (exclusive-or) function, where Z-1 if either X,-1 or X-=l but Z-0 if both X,-1 and X2-1 . This function is denoted Z-X, XOR X2. (b) Design weights such that his circuit computes the equals' function, in which Z-1 only if Xi and X2 are the same (both 0 or both 1), and Z-0 otherwise (that is, Z Xi EQ X2).

Answer 1

4.

Solution:

Given data is,

Consider the diamond generalization that has two input X1 and X2 and a single output Z. This two-layer perceptron pattern has 6 edges. Assume that all neurons are ‘integrate and fire’, and each can have a threshold of K=1 or K=-1. Assume that neurons have voltage 0, unless the weighted inputs exceed K, in which case they assume voltage 1. Weights on the edges can be positive or negative real numbers.

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