Cool paper! Am I understanding correctly that this focuses on single atomic representations? I.e. in practice, where you usually use atomic representations for each atom on the system, the degeneracies are not as problematic?
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Exact. Basically, that's what saves the day, and the reason why we could get this far without realizing the problem. However we suspect that this might show up as we push for greater accuracy. This is *very* similar to the problem of using only distances to describe a structure.
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Great paper! Can you share the data for the CH4 manifolds in Fig. 3? I'd love to reproduce the failures for our FCHL-type representations as well as the Behler ACSFs.
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Just mailed them. We checked already with ACFs and DeepMD. Unless you're using extra information besides distances and angles, they'll be degenerate.
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This is likely to affect your favorite representation, too. SOAP, symmetry functions, smooth DeepMD, FCHL, MBTR, ...
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