Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness

DOI10.1016/j.neunet.2020.06.024zbMath1475.68315arXiv1905.11427OpenAlexW3039204554WikidataQ97517817 ScholiaQ97517817MaRDI QIDQ2057701

Pengzhan Jin, Lu Lu, George Em. Karniadakis, Yi-Fa Tang

Publication date: 7 December 2021

Published in: Neural Networks (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.11427

zbMATH Keywords

neural networksdata distributiongeneralization errorlearnabilitycover complexityneural network smoothness

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07)

Related Items (6)

Approximation capabilities of measure-preserving neural networks ⋮ Reliable extrapolation of deep neural operators informed by physics or sparse observations ⋮ Quantification on the generalization performance of deep neural network with Tychonoff separation axioms ⋮ Physics-Informed Neural Networks with Hard Constraints for Inverse Design ⋮ Mosaic flows: a transferable deep learning framework for solving PDEs on unseen domains ⋮ Deep learning architectures for nonlinear operator functions and nonlinear inverse problems

Uses Software

• ImageNet
• Adam
• COIL-100
• COIL-20
• AlexNet

Cites Work

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• Balls in \(\mathbb{R}^k\) do not cut all subsets of \(k+2\) points
• Multilayer feedforward networks are universal approximators
• Large-Scale Machine Learning with Stochastic Gradient Descent
• Robust Large Margin Deep Neural Networks
• 10.1162/153244303321897690
• On the information bottleneck theory of deep learning
• Approximation by superpositions of a sigmoidal function
• The elements of statistical learning. Data mining, inference, and prediction

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