The total loss of H versus some F versus some tuple of measures µis computed as the expected value of ℓ(H, a,F (a)) when a is picked at random according to the product measure ofµ

It uses an arbitrary loss function ℓthat takes in a hypothesis H, a tuple a, a label y∈Λ, outputs a “penalty”ℓ(H,a,y )∈R≥0that H incurs at the point a when compared to the la

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Some model-theoretic consequences of high-arity uniform convergence, part I

math.LO · 2026-05-11 · unverdicted · novelty 7.0

Certain families of sets in R^n that are non-definable and have unbounded VC-dimension are uniformly approximately definable in the real field.

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Some model-theoretic consequences of high-arity uniform convergence, part I math.LO · 2026-05-11 · unverdicted · none · ref 4
Certain families of sets in R^n that are non-definable and have unbounded VC-dimension are uniformly approximately definable in the real field.

The total loss of H versus some F versus some tuple of measures µis computed as the expected value of ℓ(H, a,F (a)) when a is picked at random according to the product measure ofµ

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