Few-Shot Learning by Dimensionality Reduction in Gradient Space

Martin Gauch, Maximilian Beck, Thomas Adler, Dmytro Kotsur, Stefan Fiel, Hamid Eghbal-zadeh, Johannes Brandstetter, Johannes Kofler, Markus Holzleitner, Werner Zellinger, Daniel Klotz, Sepp Hochreiter, Sebastian Lehner
Proceedings of The 1st Conference on Lifelong Learning Agents, PMLR 199:1043-1064, 2022.

Abstract

We introduce SubGD, a novel few-shot learning method which is based on the recent finding that stochastic gradient descent updates tend to live in a low-dimensional parameter subspace. In experimental and theoretical analyses, we show that models confined to a suitable predefined subspace generalize well for few-shot learning. A suitable subspace fulfills three criteria across the given tasks: it (a) allows to reduce the training error by gradient flow, (b) leads to models that generalize well, and (c) can be identified by stochastic gradient descent. SubGD identifies these subspaces from an eigendecomposition of the auto-correlation matrix of update directions across different tasks. Demonstrably, we can identify low-dimensional suitable subspaces for few-shot learning of dynamical systems, which have varying properties described by one or few parameters of the analytical system description. Such systems are ubiquitous among real-world applications in science and engineering. We experimentally corroborate the advantages of SubGD on three distinct dynamical systems problem settings, significantly outperforming popular few-shot learning methods both in terms of sample efficiency and performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v199-gauch22a, title = {Few-Shot Learning by Dimensionality Reduction in Gradient Space}, author = {Gauch, Martin and Beck, Maximilian and Adler, Thomas and Kotsur, Dmytro and Fiel, Stefan and Eghbal-zadeh, Hamid and Brandstetter, Johannes and Kofler, Johannes and Holzleitner, Markus and Zellinger, Werner and Klotz, Daniel and Hochreiter, Sepp and Lehner, Sebastian}, booktitle = {Proceedings of The 1st Conference on Lifelong Learning Agents}, pages = {1043--1064}, year = {2022}, editor = {Chandar, Sarath and Pascanu, Razvan and Precup, Doina}, volume = {199}, series = {Proceedings of Machine Learning Research}, month = {22--24 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v199/gauch22a/gauch22a.pdf}, url = {https://proceedings.mlr.press/v199/gauch22a.html}, abstract = {We introduce SubGD, a novel few-shot learning method which is based on the recent finding that stochastic gradient descent updates tend to live in a low-dimensional parameter subspace. In experimental and theoretical analyses, we show that models confined to a suitable predefined subspace generalize well for few-shot learning. A suitable subspace fulfills three criteria across the given tasks: it (a) allows to reduce the training error by gradient flow, (b) leads to models that generalize well, and (c) can be identified by stochastic gradient descent. SubGD identifies these subspaces from an eigendecomposition of the auto-correlation matrix of update directions across different tasks. Demonstrably, we can identify low-dimensional suitable subspaces for few-shot learning of dynamical systems, which have varying properties described by one or few parameters of the analytical system description. Such systems are ubiquitous among real-world applications in science and engineering. We experimentally corroborate the advantages of SubGD on three distinct dynamical systems problem settings, significantly outperforming popular few-shot learning methods both in terms of sample efficiency and performance.} }
Endnote
%0 Conference Paper %T Few-Shot Learning by Dimensionality Reduction in Gradient Space %A Martin Gauch %A Maximilian Beck %A Thomas Adler %A Dmytro Kotsur %A Stefan Fiel %A Hamid Eghbal-zadeh %A Johannes Brandstetter %A Johannes Kofler %A Markus Holzleitner %A Werner Zellinger %A Daniel Klotz %A Sepp Hochreiter %A Sebastian Lehner %B Proceedings of The 1st Conference on Lifelong Learning Agents %C Proceedings of Machine Learning Research %D 2022 %E Sarath Chandar %E Razvan Pascanu %E Doina Precup %F pmlr-v199-gauch22a %I PMLR %P 1043--1064 %U https://proceedings.mlr.press/v199/gauch22a.html %V 199 %X We introduce SubGD, a novel few-shot learning method which is based on the recent finding that stochastic gradient descent updates tend to live in a low-dimensional parameter subspace. In experimental and theoretical analyses, we show that models confined to a suitable predefined subspace generalize well for few-shot learning. A suitable subspace fulfills three criteria across the given tasks: it (a) allows to reduce the training error by gradient flow, (b) leads to models that generalize well, and (c) can be identified by stochastic gradient descent. SubGD identifies these subspaces from an eigendecomposition of the auto-correlation matrix of update directions across different tasks. Demonstrably, we can identify low-dimensional suitable subspaces for few-shot learning of dynamical systems, which have varying properties described by one or few parameters of the analytical system description. Such systems are ubiquitous among real-world applications in science and engineering. We experimentally corroborate the advantages of SubGD on three distinct dynamical systems problem settings, significantly outperforming popular few-shot learning methods both in terms of sample efficiency and performance.
APA
Gauch, M., Beck, M., Adler, T., Kotsur, D., Fiel, S., Eghbal-zadeh, H., Brandstetter, J., Kofler, J., Holzleitner, M., Zellinger, W., Klotz, D., Hochreiter, S. & Lehner, S.. (2022). Few-Shot Learning by Dimensionality Reduction in Gradient Space. Proceedings of The 1st Conference on Lifelong Learning Agents, in Proceedings of Machine Learning Research 199:1043-1064 Available from https://proceedings.mlr.press/v199/gauch22a.html.

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