The problem with XOR is that you need a line with dimension N, where N is the number of distinct inputs to the XOR, to separate true from false in the truth spa

The problem with XOR is that you need a line with dimension N, where N is the number of distinct inputs to the XOR, to separate true from false in the truth space. What I demonstrated was up to 6 dimensional XOR functions being learned in Hopfield networks using Hebbian learning with an additional learning term. I ran a "wave of learning" over the network modifying that terms. In a sense it is a layer free network because no explicit later exists but in another sense the modulation provided a transient layers since the learning term caused different parts of the network to learn at different times out of sync with one another.