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Example: Finding Weights for AND Operation

  • There are two input weights W1 and W2 and a treshold W0. For each training pattern the perceptron needs to satisfay the following equation:
        out = g(W1*a1 + W2*a2 – W0) = sign(W1*a1 + W2*a2 – W0)
  • For a binary AND there are four training data items available that lead to four inequalities:
    • W1*0 + W2*0 – W0 < 0        ⇒ W0 > 0
    • W1*0 + W2*1 – W0 < 0        ⇒ W2 < W0
    • W1*1 + W2*0 – W0 < 0        ⇒ W1 < W0
    • W1*1 + W2*1 – W0 ≥ 0        ⇒ W1 + W2 ≥ W0
  • There is an obvious infinite number of solutions that realize a logical AND; e.g. W1 = 1, W2 = 1 and W0 = 1.5.

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