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Limitations of Simple Perceptrons

  • XOR:
    • 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
  • The 2nd and 3rd inequalities are not compatible with inequality 4, and there is no solution to the XOR problem.
  • XOR requires two separation hyperplanes!
  • There is thus a need for more complex networks that combine simple perceptrons to address more sophisticated classification tasks.

Speaker notes:

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