Catastrophic Fisher Explosion: Early Phase Fisher Matrix Impacts Generalization

Stanislaw Jastrzebski, Devansh Arpit, Oliver Astrand, Giancarlo B Kerg, Huan Wang, Caiming Xiong, Richard Socher, Kyunghyun Cho, Krzysztof J Geras
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:4772-4784, 2021.

Abstract

The early phase of training a deep neural network has a dramatic effect on the local curvature of the loss function. For instance, using a small learning rate does not guarantee stable optimization because the optimization trajectory has a tendency to steer towards regions of the loss surface with increasing local curvature. We ask whether this tendency is connected to the widely observed phenomenon that the choice of the learning rate strongly influences generalization. We first show that stochastic gradient descent (SGD) implicitly penalizes the trace of the Fisher Information Matrix (FIM), a measure of the local curvature, from the start of training. We argue it is an implicit regularizer in SGD by showing that explicitly penalizing the trace of the FIM can significantly improve generalization. We highlight that poor final generalization coincides with the trace of the FIM attaining a large value early in training, to which we refer as catastrophic Fisher explosion. Finally, to gain insight into the regularization effect of penalizing the trace of the FIM, we show that it limits memorization by reducing the learning speed of examples with noisy labels more than that of the examples with clean labels.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-jastrzebski21a, title = {Catastrophic Fisher Explosion: Early Phase Fisher Matrix Impacts Generalization}, author = {Jastrzebski, Stanislaw and Arpit, Devansh and Astrand, Oliver and Kerg, Giancarlo B and Wang, Huan and Xiong, Caiming and Socher, Richard and Cho, Kyunghyun and Geras, Krzysztof J}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {4772--4784}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/jastrzebski21a/jastrzebski21a.pdf}, url = {https://proceedings.mlr.press/v139/jastrzebski21a.html}, abstract = {The early phase of training a deep neural network has a dramatic effect on the local curvature of the loss function. For instance, using a small learning rate does not guarantee stable optimization because the optimization trajectory has a tendency to steer towards regions of the loss surface with increasing local curvature. We ask whether this tendency is connected to the widely observed phenomenon that the choice of the learning rate strongly influences generalization. We first show that stochastic gradient descent (SGD) implicitly penalizes the trace of the Fisher Information Matrix (FIM), a measure of the local curvature, from the start of training. We argue it is an implicit regularizer in SGD by showing that explicitly penalizing the trace of the FIM can significantly improve generalization. We highlight that poor final generalization coincides with the trace of the FIM attaining a large value early in training, to which we refer as catastrophic Fisher explosion. Finally, to gain insight into the regularization effect of penalizing the trace of the FIM, we show that it limits memorization by reducing the learning speed of examples with noisy labels more than that of the examples with clean labels.} }
Endnote
%0 Conference Paper %T Catastrophic Fisher Explosion: Early Phase Fisher Matrix Impacts Generalization %A Stanislaw Jastrzebski %A Devansh Arpit %A Oliver Astrand %A Giancarlo B Kerg %A Huan Wang %A Caiming Xiong %A Richard Socher %A Kyunghyun Cho %A Krzysztof J Geras %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-jastrzebski21a %I PMLR %P 4772--4784 %U https://proceedings.mlr.press/v139/jastrzebski21a.html %V 139 %X The early phase of training a deep neural network has a dramatic effect on the local curvature of the loss function. For instance, using a small learning rate does not guarantee stable optimization because the optimization trajectory has a tendency to steer towards regions of the loss surface with increasing local curvature. We ask whether this tendency is connected to the widely observed phenomenon that the choice of the learning rate strongly influences generalization. We first show that stochastic gradient descent (SGD) implicitly penalizes the trace of the Fisher Information Matrix (FIM), a measure of the local curvature, from the start of training. We argue it is an implicit regularizer in SGD by showing that explicitly penalizing the trace of the FIM can significantly improve generalization. We highlight that poor final generalization coincides with the trace of the FIM attaining a large value early in training, to which we refer as catastrophic Fisher explosion. Finally, to gain insight into the regularization effect of penalizing the trace of the FIM, we show that it limits memorization by reducing the learning speed of examples with noisy labels more than that of the examples with clean labels.
APA
Jastrzebski, S., Arpit, D., Astrand, O., Kerg, G.B., Wang, H., Xiong, C., Socher, R., Cho, K. & Geras, K.J.. (2021). Catastrophic Fisher Explosion: Early Phase Fisher Matrix Impacts Generalization. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:4772-4784 Available from https://proceedings.mlr.press/v139/jastrzebski21a.html.

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