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As a proof of concept, we focus on kernel machines and on two simple realizations of data structure introduced in recent physics literature k-dimensional simplexes with prescribed geometric relations and spherical manifolds (equivalent to margin classification). Entropy, contrary to what happens for unstructured data, is nonmonotonic in the sample size, in contrast with the rigorous bounds. Moreover, data structure induces a transition beyond the storage capacity, which we advocate as a proxy of the nonmonotonicity, and ultimately a cu
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