The XOR problem in artificial NN is a known problem which is said to have slowed down the development of neural networks for 12 years. You can read about this in the article https://medium.com/@jayeshbahire/the-xor-problem-in-neural-networks-50006411840b So here is one of possible solutions to this problem. I use three neurons, which are trained to perform logical operations NOT, OR and AND and then their composition by OR-neuron so that they perform XOR as its mainterm form.
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Tiny neural network made of three neurons that implements logical operation XOR
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