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And why would you restrict yourself to the original encoding space and to the Euclidean distance? These are completely arbitrary choices (and completely biased). There's an infinity of possibly encodings of the data you could have chosen, and an infinity of distance functions.https://twitter.com/k_saifullaah/status/1409972975835566081 …
Perhaps a different culture would always present data on a sphere and would use geodesic distance as the default. I don't know! There should no reason whatsoever to expect an arbitrary encoding and an arbitrary distance to result in an interpolative problem space.
The correct encoding and distance to use is of course the ones that are natural to the data -- that is to say, the latent manifold of the data. Which *is* an interpolative space for many problems (hence why deep learning models are able to generalize).
Saying "I expect the problem to be linearly interpolative in the original encoding space" is equivalent to saying "linear regression with *no* feature engineering is enough to solve any prediction problem." Which we have known to be nonsensical since long before computers existed
We have started looking at other geometries. Hyperbolic neural networks has been developing as an area over the last few years!
Even divergence functions
And an infinity of latent manifolds
anyone out there have recommendations of good geometries and distance functions for encoding directed acyclic graphs?
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