Physical interpretation of the Manifold Hypothesishttps://mathoverflow.net/q/351368/56328?stw=2 …
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Perhaps there’s some minimum lower dimension for any data which preserves its most relevant characteristics. “Empirically, this is observed to be true for many kinds of data including text data and natural images.” Does there generally exist some latent structure or intrinsic...
... dynamics in some data which are important & the rest can be reduced away? Mean field modelling comes to mind — captures processes by coarse graining essential shape of data, w/o having all underlying parameters. I’m not confident this is the answer, but an interesting theory
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Do you mean an intrinsic dimension for particular data or all data? If the former then that's the basis of manifold learning, finding the intrinsic dimension of the data. If you mean an intrinsic dimension for all data I am not sure that would work.
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You could define an equivalence relation on all dynamical systems where you map a dynamical system to the dimension of its phase space. If you order these systems in terms of their dimension you will find that you don't have an upper-bound.
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