Zero-shot super-resolution is information-theoretically impossible for some simple operators but possible under Hölder smoothness of outputs, accompanied by generalization bounds.
arXiv preprint arXiv:2211.08875 , year=
4 Pith papers cite this work. Polarity classification is still indexing.
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Proves sharp operator-norm concentration and expectation bounds for sample cross-covariances of sub-Gaussian and Gaussian vectors, governed by effective ranks of the marginal covariances.
Safety certification of dynamical systems is reformulated as direct classification via kernel embeddings on trajectories, bypassing recursive DP to avoid error compounding and support non-Markovian dynamics.
A linear estimator for the Schrödinger evolution operator is introduced that enforces weak unitarity, supplies uniform prediction error bounds and time-extrapolation bounds, and reports up to 100x lower relative error than FNO and DeepONet on hydrogen, ion-trap, and optical-lattice Hamiltonians.
citing papers explorer
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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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Concentration Inequalities for Sample Cross-Covariances
Proves sharp operator-norm concentration and expectation bounds for sample cross-covariances of sub-Gaussian and Gaussian vectors, governed by effective ranks of the marginal covariances.
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Safety Certification is Classification
Safety certification of dynamical systems is reformulated as direct classification via kernel embeddings on trajectories, bypassing recursive DP to avoid error compounding and support non-Markovian dynamics.
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Operator Learning for Schr\"{o}dinger Equation: Unitarity, Error Bounds, and Time Generalization
A linear estimator for the Schrödinger evolution operator is introduced that enforces weak unitarity, supplies uniform prediction error bounds and time-extrapolation bounds, and reports up to 100x lower relative error than FNO and DeepONet on hydrogen, ion-trap, and optical-lattice Hamiltonians.