Physical interpretation of the Manifold Hypothesishttps://mathoverflow.net/q/351368/56328?stw=2 …
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I don't understand the question yet. But one straightforward thought on neural manifold: Bottleneck-then-expansion strongly favors low-D representations in high-D space (though not guaranteed because of possible temporal multiplexing).
Here's the problem in two parts: In order to do ML we need to collect a lot of data from a data-generating process so this process must be stable. Empirically we observe that the intrinsic dimension d of the data is generally much smaller than the ambient dimension D. 1/2
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Might there be a reason why stable physical processes would tend to have low-dimensional phase spaces? 2/2
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Is there a part of my question which is unclear? Or is there is a false axiom embedded in my question? I actually wonder why I haven't seen any papers on the Manifold Hypothesis which directly attempt to address this question.
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