Tube-volume bounds for smooth Pfaffian hypersurfaces yield condition-number tails for Pfaffian neural classifiers, with polynomial-in-width control for single-layer rational-weight sigmoids.
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Hub-and-spoke systems from symbolic dynamics can have completely positive mean dimension without uniformly positive mean dimension or entropy, with proofs linking entropy and mean dimension properties at the level of fixed covers.
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Tubular Neighbourhoods of Pfaffian Sets and Applications to Neural Networks
Tube-volume bounds for smooth Pfaffian hypersurfaces yield condition-number tails for Pfaffian neural classifiers, with polynomial-in-width control for single-layer rational-weight sigmoids.
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Uniformly Positive Mean Dimension
Hub-and-spoke systems from symbolic dynamics can have completely positive mean dimension without uniformly positive mean dimension or entropy, with proofs linking entropy and mean dimension properties at the level of fixed covers.