I found several papers about how to build a perceptron able to solve the XOR problem. The papers describe a solution where the heaviside step function is replaced by a non-monotonic activation function. Here are the papers:

I also found this related post on Stackoverflow.

Can we really solve the XOR problem with a simple perceptron?

The use of a non-monotonic activation function is not really common, so I don't really know. Papers about this idea are scarce. Generally, the main solution is to build a multilayer perceptron.


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