Quantifying the Benefit of Using Differentiable Learning over Tangent Kernels

Eran Malach, Pritish Kamath, Emmanuel Abbe, Nathan Srebro
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:7379-7389, 2021.

Abstract

We study the relative power of learning with gradient descent on differentiable models, such as neural networks, versus using the corresponding tangent kernels. We show that under certain conditions, gradient descent achieves small error only if a related tangent kernel method achieves a non-trivial advantage over random guessing (a.k.a. weak learning), though this advantage might be very small even when gradient descent can achieve arbitrarily high accuracy. Complementing this, we show that without these conditions, gradient descent can in fact learn with small error even when no kernel method, in particular using the tangent kernel, can achieve a non-trivial advantage over random guessing.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-malach21a, title = {Quantifying the Benefit of Using Differentiable Learning over Tangent Kernels}, author = {Malach, Eran and Kamath, Pritish and Abbe, Emmanuel and Srebro, Nathan}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {7379--7389}, 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/malach21a/malach21a.pdf}, url = {https://proceedings.mlr.press/v139/malach21a.html}, abstract = {We study the relative power of learning with gradient descent on differentiable models, such as neural networks, versus using the corresponding tangent kernels. We show that under certain conditions, gradient descent achieves small error only if a related tangent kernel method achieves a non-trivial advantage over random guessing (a.k.a. weak learning), though this advantage might be very small even when gradient descent can achieve arbitrarily high accuracy. Complementing this, we show that without these conditions, gradient descent can in fact learn with small error even when no kernel method, in particular using the tangent kernel, can achieve a non-trivial advantage over random guessing.} }
Endnote
%0 Conference Paper %T Quantifying the Benefit of Using Differentiable Learning over Tangent Kernels %A Eran Malach %A Pritish Kamath %A Emmanuel Abbe %A Nathan Srebro %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-malach21a %I PMLR %P 7379--7389 %U https://proceedings.mlr.press/v139/malach21a.html %V 139 %X We study the relative power of learning with gradient descent on differentiable models, such as neural networks, versus using the corresponding tangent kernels. We show that under certain conditions, gradient descent achieves small error only if a related tangent kernel method achieves a non-trivial advantage over random guessing (a.k.a. weak learning), though this advantage might be very small even when gradient descent can achieve arbitrarily high accuracy. Complementing this, we show that without these conditions, gradient descent can in fact learn with small error even when no kernel method, in particular using the tangent kernel, can achieve a non-trivial advantage over random guessing.
APA
Malach, E., Kamath, P., Abbe, E. & Srebro, N.. (2021). Quantifying the Benefit of Using Differentiable Learning over Tangent Kernels. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:7379-7389 Available from https://proceedings.mlr.press/v139/malach21a.html.

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