This isn't a problem with machine learning, but rather with low bias approximators. They fit the data well and can interpolate but have no mathematical reason to extrapolate. A lot of work, including in deep learning, deals with yielding better extrapolation by introducing bias.
A system is a machine that can be described by a single global transition function (if the function changes you have a different system). Building a system amounts to traversing the implementation space of transition functions. There is no magic boundary between biology and comp
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Actually a system is an arbitrary concurrent, interactive union of what you describe, including nondeterminism. You're going to search in that space?
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To the degree to which a system exists, it must be implemented. Understood like this, a system can be described by its source code, i.e. as a computable function. (Nondeterminism is not a challenge to this.)
End of conversation
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