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I've programmed a non-directional neural network. So kind of like the brain, all neurons are updated at the same time, and there are no explicit layers.

Now I'm wondering, how does pain work? How can I structure a neural network so that a "pain" signal will make it want to do anything to get rid of said pain?

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Artificial neural networks do not recognize such a thing as "pain", but may actually be trained in order to avoid certain states. You have to train the network to perform certain actions when it receives this particular signal for pain. When the model becomes more refined(performing experiments on your model again and again), this signal starts looking like a real pain signal, but it's nothing more than a specific training of the network.

The artificial neural network has a realistic mechanism to perform various tasks. This particular training is known as neural network training. 

The whole working mechanism of neural network reacting to pain is given in the following link:https://www.pnas.org/content/116/5/1782

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