Continuity constraints between observed and latent space

by Tik0   Last Updated September 22, 2018 00:19 AM

Given a generative model as shown below, I am interested in the analysis of the to observable variables $x,y$ given the latent space $z,w$.

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Do you know if there exists a general continuity constraint for the manifolds so that I can say something like $\Delta x \Leftrightarrow \Delta z \Leftrightarrow \Delta y$ (where $\Delta$ denotes a change or small pertubation)? Further, is there something like a discontinuity constraint like: If $\Delta x\not{\propto} \Delta y$, then there exist some latent $w$ which is not shared by the observations.

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