# 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 $$z,w$$.

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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