NN - neurons with "interval rules"

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Suppose you have a bunch of sequences corresponding to a bunch of numbers.

inputs = [[1, 1, 1, 1, 1, 0, 1, 1, 0],
[1, 1, 1, 1, 1, 0, 1, 1, 0],
[1, 1, 1, 1, 1, 0, 1, 1, 0],
[1, 1, 1, 1, 1, 0, 1, 1, 0],
...
[1, 1, 1, 1, 1, 0, 1, 1, 0]]

outputs = [-0.11, 0.72, -0.83, 1.13, ..., 0.45]

I am using a single neuron, nothing special, to train it on the data above, but there is a problem. A newly introduced sequence: S = [1, 1, 1, 1, 1, 0, 0, 0, 0], can only exists within a given interval, 0.0 < S < 0.1, and my neuron that i trained on the data above does of course not know this. Without this "rule" in mind the trained neuron thinks that sequence: S = 0.35. I need to somehow let it know that sequence: S, can only take on values within a given interval, question is; how? If at all possible... Any ideas on possible solutions?