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Is it possible to create an ANN, which takes some data in the output just increments some counter? For example, every pass would increase the number given by a binary representation using 4 output neurons. I remember reading that the output should be same given the same input. So is that possible?
I don’t think this is actually possible if one sticks to the original notion of a neural network, which is a composition of functions, each taking a weighted sum of the outputs of the previous layer as an input and producing a singe output value. The weights are usually trained to reproduce the known outputs on certain input values. The backpropagation algorithm I believe you are referring to updates the weights in a certain fashion, and the idea of making one of the weights work as a counter doesn’t really make any sense.