FAM: Relative Flatness Aware Minimization

Linara Adilova, Amr Abourayya, Jianning Li, Amin Dada, Henning Petzka, Jan Egger, Jens Kleesiek, Michael Kamp
Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML), PMLR 221:37-49, 2023.

Abstract

Flatness of the loss curve around a model at hand has been shown to empirically correlate with its generalization ability. Optimizing for flatness has been proposed as early as 1994 by Hochreiter and Schmidthuber, and was followed by more recent successful sharpness-aware optimization techniques. Their widespread adoption in practice, though, is dubious because of the lack of theoretically grounded connection between flatness and generalization, in particular in light of the reparameterization curse—certain reparameterizations of a neural network change most flatness measures but do not change generalization. Recent theoretical work suggests that a particular relative flatness measure can be connected to generalization and solves the reparameterization curse. In this paper, we derive a regularizer based on this relative flatness that is easy to compute, fast, efficient, and works with arbitrary loss functions. It requires computing the Hessian only of a single layer of the network, which makes it applicable to large neural networks, and with it avoids an expensive mapping of the loss surface in the vicinity of the model. In an extensive empirical evaluation we show that this relative flatness aware minimization (FAM) improves generalization in a multitude of applications and models, both in finetuning and standard training. We make the code available at github.

Cite this Paper

BibTeX
@InProceedings{pmlr-v221-adilova23a, title = {FAM: Relative Flatness Aware Minimization}, author = {Adilova, Linara and Abourayya, Amr and Li, Jianning and Dada, Amin and Petzka, Henning and Egger, Jan and Kleesiek, Jens and Kamp, Michael}, booktitle = {Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML)}, pages = {37--49}, year = {2023}, editor = {Doster, Timothy and Emerson, Tegan and Kvinge, Henry and Miolane, Nina and Papillon, Mathilde and Rieck, Bastian and Sanborn, Sophia}, volume = {221}, series = {Proceedings of Machine Learning Research}, month = {28 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v221/adilova23a/adilova23a.pdf}, url = {https://proceedings.mlr.press/v221/adilova23a.html}, abstract = {Flatness of the loss curve around a model at hand has been shown to empirically correlate with its generalization ability. Optimizing for flatness has been proposed as early as 1994 by Hochreiter and Schmidthuber, and was followed by more recent successful sharpness-aware optimization techniques. Their widespread adoption in practice, though, is dubious because of the lack of theoretically grounded connection between flatness and generalization, in particular in light of the reparameterization curse—certain reparameterizations of a neural network change most flatness measures but do not change generalization. Recent theoretical work suggests that a particular relative flatness measure can be connected to generalization and solves the reparameterization curse. In this paper, we derive a regularizer based on this relative flatness that is easy to compute, fast, efficient, and works with arbitrary loss functions. It requires computing the Hessian only of a single layer of the network, which makes it applicable to large neural networks, and with it avoids an expensive mapping of the loss surface in the vicinity of the model. In an extensive empirical evaluation we show that this relative flatness aware minimization (FAM) improves generalization in a multitude of applications and models, both in finetuning and standard training. We make the code available at github.} }
Endnote
%0 Conference Paper %T FAM: Relative Flatness Aware Minimization %A Linara Adilova %A Amr Abourayya %A Jianning Li %A Amin Dada %A Henning Petzka %A Jan Egger %A Jens Kleesiek %A Michael Kamp %B Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML) %C Proceedings of Machine Learning Research %D 2023 %E Timothy Doster %E Tegan Emerson %E Henry Kvinge %E Nina Miolane %E Mathilde Papillon %E Bastian Rieck %E Sophia Sanborn %F pmlr-v221-adilova23a %I PMLR %P 37--49 %U https://proceedings.mlr.press/v221/adilova23a.html %V 221 %X Flatness of the loss curve around a model at hand has been shown to empirically correlate with its generalization ability. Optimizing for flatness has been proposed as early as 1994 by Hochreiter and Schmidthuber, and was followed by more recent successful sharpness-aware optimization techniques. Their widespread adoption in practice, though, is dubious because of the lack of theoretically grounded connection between flatness and generalization, in particular in light of the reparameterization curse—certain reparameterizations of a neural network change most flatness measures but do not change generalization. Recent theoretical work suggests that a particular relative flatness measure can be connected to generalization and solves the reparameterization curse. In this paper, we derive a regularizer based on this relative flatness that is easy to compute, fast, efficient, and works with arbitrary loss functions. It requires computing the Hessian only of a single layer of the network, which makes it applicable to large neural networks, and with it avoids an expensive mapping of the loss surface in the vicinity of the model. In an extensive empirical evaluation we show that this relative flatness aware minimization (FAM) improves generalization in a multitude of applications and models, both in finetuning and standard training. We make the code available at github.
APA
Adilova, L., Abourayya, A., Li, J., Dada, A., Petzka, H., Egger, J., Kleesiek, J. & Kamp, M.. (2023). FAM: Relative Flatness Aware Minimization. Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML), in Proceedings of Machine Learning Research 221:37-49 Available from https://proceedings.mlr.press/v221/adilova23a.html.

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