Neural flow operators with composition and separation structures are proven to universally approximate any operator in finite and infinite dimensions, recovering ResNet-type and plain architectures via time discretizations.
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Wahkon unifies Kolmogorov superposition with RKHS regularization to produce a deep network whose penalized estimator is exactly the MAP under a hierarchical GP prior and achieves minimax-optimal rates.
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Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approcimations
Neural flow operators with composition and separation structures are proven to universally approximate any operator in finite and infinite dimensions, recovering ResNet-type and plain architectures via time discretizations.
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Wahkon: A Statistically Principled Deep RKHS Superposition Network
Wahkon unifies Kolmogorov superposition with RKHS regularization to produce a deep network whose penalized estimator is exactly the MAP under a hierarchical GP prior and achieves minimax-optimal rates.