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This paper establishes a collection of covering number bounds for linear function classes under various norm constraints on the inputs and matrices and explicitly incorporates rank constraints on the underlying matrix classes, allowing us to characterize how low-rank structures affect the metric entropy.
This work derives an explicit upper bound on the distribution approximation error in terms of the score approximation error, the diffusion noise schedule, and the terminal prior mismatch and provides a simple and explicit guarantee linking neural network approximation of score functions to approximation of the probabil...
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