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
3 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.
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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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.