### Backpropagation can't do parity generalisation

Chris Thornton

It is accepted that the early connectionist learning methods such as the perceptron algorithm cannot solve parity learning problems. But since the early 1980s, there have been many demonstrations purporting to show that the backpropagation method *can* do so. However these demonstrations are misleading. Backpropagation in fact reliably *fails* to solve parity problems when they are posed as genuine, supervised learning problems, i.e., as problems involving generalisation. Thus backpropagation is subject to some of the same limitations as the perceptron method.

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