Does anyone know if there is a theorem or counterexample establishing whether or not for any given binary classification task in some finite (possibly large) dimensional vector space of attributes, that there exists a polynomial classifier that can form a hyperplane sorting all the positive from negatively labelled data points? To clarify, I know that if a dataset is linearly separable, then we can find such a linear classifier. But my question is more general and asks if without knowing beforehand whether a dataset is separable at all, can we know ahead of time if there exists a polynomial classifier for any n-dimensional vector space of data points?

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