A Note on Pointwise Dimensions
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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
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Pointwise Complexity for Gaussian Fields: Upper Envelopes, Algorithmic Lower Bounds, and Separation
Proves pointwise majorizing-measure theorem for Gaussian processes, records Bayesian algorithmic lower bounds, and constructs a separation example among different complexity measures.
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Pointwise Complexity for Gaussian Fields: Upper Envelopes, Algorithmic Lower Bounds, and Separation
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.
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Pointwise Generalization in Deep Neural Networks
Proposes pointwise Riemannian Dimension from feature eigenvalues to derive tighter, representation-aware generalization bounds for deep networks in the nonlinear regime.
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