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.
Deep network approximation characterized by number of neurons
3 Pith papers cite this work. Polarity classification is still indexing.
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A nonasymptotic generalization error upper bound for path-regularized multilayer neural networks with Lipschitz losses that exhibits double descent and is near-minimax optimal for ReLU regression.
Derives approximation rates and excess risk bounds for Frobenius norm-constrained DNNs learning sparse compositional functions on DAGs, applicable to multi-index models and binary trees while avoiding the curse of dimensionality.
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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Path Regularization: A Near-Complete and Optimal Nonasymptotic Generalization Theory for Multilayer Neural Networks and Double Descent Phenomenon
A nonasymptotic generalization error upper bound for path-regularized multilayer neural networks with Lipschitz losses that exhibits double descent and is near-minimax optimal for ReLU regression.
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Learning Sparse Compositional Functions with Norm-Constrained Neural Networks
Derives approximation rates and excess risk bounds for Frobenius norm-constrained DNNs learning sparse compositional functions on DAGs, applicable to multi-index models and binary trees while avoiding the curse of dimensionality.