• There has been a belief that a linear transform is insufficient to transform one embedding space into another when the semantics are similar, but recent research has shown that this may not be the case.
  • Models tend to learn similar representations of the same thing, making mapping between them straightforward.
  • Research in machine learning could benefit from a more empirical approach, observing and demonstrating findings like the invariant nature of embeddings to rotations and scaling.
  • The invariant nature of operations in vector space opens up the possibility of performing computations on data without knowing its specific content, potentially enabling homomorphic computation.

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