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• W3206818904 abstract "Finding a quantitative theory of neural network generalization has long beena central goal of deep learning research. We extend recent results todemonstrate that, by examining the eigensystem of a neural network's neuraltangent kernel, one can predict its generalization performance when learningarbitrary functions. Our theory accurately predicts not only testmean-squared-error but all first- and second-order statistics of the network'slearned function. Furthermore, using a measure quantifying the learnabilityof a given target function, we prove a new no-free-lunch theoremcharacterizing a fundamental tradeoff in the inductive bias of wide neuralnetworks: improving a network's generalization for a given target function mustworsen its generalization for orthogonal functions. We further demonstrate theutility of our theory by analytically predicting two surprising phenomena -worse-than-chance generalization on hard-to-learn functions and nonmonotonicerror curves in the small data regime - which we subsequently observe inexperiments. Though our theory is derived for infinite-width architectures, wefind it agrees with networks as narrow as width 20, suggesting it is predictiveof generalization in practical neural networks. Code replicating our results isavailable at https://github.com/james-simon/eigenlearning." @default.
• W3206818904 created "2021-10-25" @default.
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• W3206818904 date "2021-10-08" @default.
• W3206818904 modified "2023-09-27" @default.
• W3206818904 title "Neural Tangent Kernel Eigenvalues Accurately Predict Generalization" @default.
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• W3206818904 hasPublicationYear "2021" @default.
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