[mafribe]

This is wrong!

The term hyperplane already assumes that the hypothesis space that your learning algorithm searches has some kind of dimension and is some variant of an Euclidean / vector space (and its generalisations). This is not the case for many forms of ML, for example grammar induction (where the hypothesis space is Chomsky-style grammars) or inductive logic programming (hypothesis space are Prolog (or similar) programs), or, more generally, program synthesis (where programs form the hypothesis space).

[adamnemecek]

It can also just be some sort of partitioning. I would be really surprised if there was no partitioning of some space.

[mafribe]

Note that "some sort of partitioning" isn't a hyperplane. A partition is a set-theoretic concept. A hyperplane is (a generalisation of) a geometric concept, so has much more structure.

[adamnemecek]

Alright how about coalgebra.