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This article says that all any multilayer perceptron with a linear on-off functions for all the neurons can be reduced to a two-layered perceptron.

Now, consider a two input/one output perceptron. The theory says that it impossible to model XOR function with this kind of perceptron, because it can represent only linearly separable function and XOR is not linearly separable.

In this article (at the bottom of the page) the author shows a 3-layer on-off perceptron which does represent XOR.
According to the wikipedia article, this perceptron can reduced to a two-layer perceptron and according to the another part of theory, it cannot model XOR.

Can anyone spread some light on this? Thanks.

(I'm not sure this the right place to ask this question. The AI site in Area 51 was closed.)

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The neural net in the second article doesn't use linear activation functions. It uses thresholded on-off functions (e.g. f(x) = 1 if x > threshold, else 0), hence can model XOR. (A linear activation function would just be f(x) = x).

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