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Learning a Group Element from Its Action: Galois Correspondences, Optimal ERM, and an Abel-Ruffini Threshold for the Natarajan Dimension
We study learning an unknown element $g$ of a group acting with finite orbits on a countable set, from examples $(x,gx)$. After a sample on $A$, the consistent hypotheses are the restrictions of a coset of the pointwise stabilizer of $A$, and the sample forces exactly the labels of points this stabi
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