Establishes non-identifiability results and query lower bounds showing transpose-free matvec access provides limited information for core linear algebra tasks.
Data complexity estimates for operator learning.arXiv preprint arXiv:2405.15992, 2024
4 Pith papers cite this work. Polarity classification is still indexing.
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Zero-shot super-resolution is information-theoretically impossible for some simple operators but possible under Hölder smoothness of outputs, accompanied by generalization bounds.
FNOs achieve polynomial sample complexity for learning time-T solution operators of dissipative evolution equations when those operators admit stable spectral discretizations, with rates depending on smoothness, dimension, and nonlinearity type.
Introduces variation spaces for nonlinear operators and derives dimension-independent approximation bounds of order N^{-1/2} plus encoding errors for encoder-decoder two-layer networks, yielding algebraic rates under polynomial encoding decay.
citing papers explorer
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Transpose-free linear algebra
Establishes non-identifiability results and query lower bounds showing transpose-free matvec access provides limited information for core linear algebra tasks.
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Is Zero-Shot Super-Resolution Possible in Operator Learning?
Zero-shot super-resolution is information-theoretically impossible for some simple operators but possible under Hölder smoothness of outputs, accompanied by generalization bounds.
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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators
FNOs achieve polynomial sample complexity for learning time-T solution operators of dissipative evolution equations when those operators admit stable spectral discretizations, with rates depending on smoothness, dimension, and nonlinearity type.
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Efficient Approximation for Encoder--Decoder Neural Operators via Variation Spaces
Introduces variation spaces for nonlinear operators and derives dimension-independent approximation bounds of order N^{-1/2} plus encoding errors for encoder-decoder two-layer networks, yielding algebraic rates under polynomial encoding decay.