What Makes a Latent Space Shared? Direct and Recoverable Compatibility in Motion VAEs

arXiv:2610.17376v1 Announce Type: new Abstract: A shared latent space is often assumed to make representations from different schemas directly interchangeable, yet sharing parameters, dimensionality, or a prior does not determine how corresponding instances are expressed in latent coordinates. We show that this assumption conflates recoverable correspondence, direct compatibility, and decoder reuse. In a controlled multi-schema motion VAE on HumanML3D, even identical inputs yield only $5.9$--$17.7\%$ raw Recall@1 and $0.221$--$0.484$ paired-token cosine, despite correspondence being almost per

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