Relative Flatness and Generalization

Henning Petzka, Michael Kamp, Linara Adilova, Cristian Sminchisescu, Mario Boley: Relative Flatness and Generalization. In: Advances in Neural Information Processing Systems, Curran Associates, Inc., 2021.

Abstract

Flatness of the loss curve is conjectured to be connected to the generalization ability of machine learning models, in particular neural networks. While it has been empirically observed that flatness measures consistently correlate strongly with generalization, it is still an open theoretical problem why and under which circumstances flatness is connected to generalization, in particular in light of reparameterizations that change certain flatness measures but leave generalization unchanged. We investigate the connection between flatness and generalization by relating it to the interpolation from representative data, deriving notions of representativeness, and feature robustness. The notions allow us to rigorously connect flatness and generalization and to identify conditions under which the connection holds. Moreover, they give rise to a novel, but natural relative flatness measure that correlates strongly with generalization, simplifies to ridge regression for ordinary least squares, and solves the reparameterization issue.

    BibTeX (Download)

    @inproceedings{petzka2021relative,
    title = {Relative Flatness and Generalization},
    author = {Henning Petzka and Michael Kamp and Linara Adilova and Cristian Sminchisescu and Mario Boley},
    year  = {2021},
    date = {2021-12-07},
    urldate = {2021-12-07},
    booktitle = {Advances in Neural Information Processing Systems},
    publisher = {Curran Associates, Inc.},
    abstract = {Flatness of the loss curve is conjectured to be connected to the generalization ability of machine learning models, in particular neural networks. While it has been empirically observed that flatness measures consistently correlate strongly with generalization, it is still an open theoretical problem why and under which circumstances flatness is connected to generalization, in particular in light of reparameterizations that change certain flatness measures but leave generalization unchanged. We investigate the connection between flatness and generalization by relating it to the interpolation from representative data, deriving notions of representativeness, and feature robustness. The notions allow us to rigorously connect flatness and generalization and to identify conditions under which the connection holds. Moreover, they give rise to a novel, but natural relative flatness measure that correlates strongly with generalization, simplifies to ridge regression for ordinary least squares, and solves the reparameterization issue.},
    keywords = {deep learning, flatness, generalization, Hessian, learning theory, relative flatness, theory of deep learning},
    pubstate = {published},
    tppubtype = {inproceedings}
    }
    

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