In the field of Natural Language Processing the term "heterogeneous vector spaces" is often used when describing two different embedding spaces that are created from different types of data, usually having different dimensions. Google defines heterogeneous as "Math. incommensurable through being of different kinds, degrees, or dimensions", but I'm still not sure that heterogeneous is the term that can be applied from a mathematical point of view. Are there any formal definitions for heterogeneity between vector spaces?
2026-03-26 17:18:18.1774545498
Can two vector spaces be defined as heterogeneous?
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There is no recognized or commonly accepted mathematical meaning for "heterogeneous vector spaces".
That means any field (for example, natural language processing) in which that name well describes a useful construction is free to adopt it. Until it is well established it should be defined in each paper that needs it.