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And is there an attack strategy that you can use to approximate the architecture of a machine learning system with the knowledge of class labels and some data points?

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This is known as a "model extraction attack", and there's a line of research in the computer security literature on this problem. For instance, you might look at the seminal paper by Papernot et al on the subject. A little time on Google Scholar should rapidly turn up dozens of papers on the subject.

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