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arxiv: 1612.05849 · v2 · pith:MUIOGPOR · submitted 2016-12-18 · cs.CC · math.MG

A Note on Pointwise Dimensions

Neil Lutz This is my paper

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classification cs.CC math.MG
keywords dimensionsnotepointwisealgorithmicclassicalconnectiondescribesindividual
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This short note describes a connection between algorithmic dimensions of individual points and classical pointwise dimensions of measures.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Pointwise Complexity for Gaussian Fields: Upper Envelopes, Algorithmic Lower Bounds, and Separation

    math.PR 2026-06 unverdicted novelty 7.0

    Proves pointwise majorizing-measure theorem for Gaussian processes, records Bayesian algorithmic lower bounds, and constructs a separation example among different complexity measures.

  2. Pointwise Complexity for Gaussian Fields: Upper Envelopes, Algorithmic Lower Bounds, and Separation

    math.PR 2026-06 unverdicted novelty 7.0

    Establishes a variance-aware pointwise majorizing-measure theorem for Gaussian fields, records Bayesian algorithmic lower bounds, and constructs a separation example among classical, algorithmic, and pointwise quantities.

  3. Pointwise Generalization in Deep Neural Networks

    cs.LG 2026-05 unverdicted novelty 7.0

    Proposes pointwise Riemannian Dimension from feature eigenvalues to derive tighter, representation-aware generalization bounds for deep networks in the nonlinear regime.