An abstract framework for neural flows with composition and separation structures is proven to universally approximate any operator, recovering ResNet and plain architectures via discretization.
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3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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cs.LG 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
Derives explicit approximation and generalization rates for multi-input neural operators in Sobolev spaces that quantify each input's contribution to the error.
Smoothly activated DNNs (feedforward and residual) achieve non-asymptotic uniform convergence rates that mitigate the curse of dimensionality by adaptively using hierarchical composition structure of the target function.
citing papers explorer
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Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations
An abstract framework for neural flows with composition and separation structures is proven to universally approximate any operator, recovering ResNet and plain architectures via discretization.
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Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces
Derives explicit approximation and generalization rates for multi-input neural operators in Sobolev spaces that quantify each input's contribution to the error.
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Mitigating the Curse of Dimensionality in Uniform Convergence of Deep Neural Networks via Smooth Activations
Smoothly activated DNNs (feedforward and residual) achieve non-asymptotic uniform convergence rates that mitigate the curse of dimensionality by adaptively using hierarchical composition structure of the target function.