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Is it possible to run a neural network in the reverse order?

If we have a neural network, such as a multi-level perceptron backpropagation neural network that uses sigmoidal logistics activation functions, is it possible to supply network outputs and calculate a set of input data? Since we can cancel the activation function using the natural logarithm and inverse operations until we get the sum consisting of all the weights multiplied by their inputs, I would think that at least we could get a lot of possible inputs that the specified output will generate value.

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Since there is an infinite number of possibilities for distributing the result to the feeding neurons, this is possible only for each layer, where the number of receiving neurons is equal to the number of feeding neurons. There it is a simple linear equation, which reduces to the problem of matrix multiplication / inversion, which can be easily solved.

If the number of neurons, where the number of receiving neurons (n) is less than the number of feeding neurons (m), you have a manifold with m - n dimensions as the solution space.

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