On the Spectral Bias of Neural Networks

Nasim Rahaman, Aristide Baratin, Devansh Arpit, Felix Draxler, Min Lin, Fred Hamprecht, Yoshua Bengio, Aaron Courville
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:5301-5310, 2019.

Abstract

Neural networks are known to be a class of highly expressive functions able to fit even random input-output mappings with 100% accuracy. In this work we present properties of neural networks that complement this aspect of expressivity. By using tools from Fourier analysis, we highlight a learning bias of deep networks towards low frequency functions – i.e. functions that vary globally without local fluctuations – which manifests itself as a frequency-dependent learning speed. Intuitively, this property is in line with the observation that over-parameterized networks prioritize learning simple patterns that generalize across data samples. We also investigate the role of the shape of the data manifold by presenting empirical and theoretical evidence that, somewhat counter-intuitively, learning higher frequencies gets easier with increasing manifold complexity.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-rahaman19a, title = {On the Spectral Bias of Neural Networks}, author = {Rahaman, Nasim and Baratin, Aristide and Arpit, Devansh and Draxler, Felix and Lin, Min and Hamprecht, Fred and Bengio, Yoshua and Courville, Aaron}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {5301--5310}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/rahaman19a/rahaman19a.pdf}, url = {https://proceedings.mlr.press/v97/rahaman19a.html}, abstract = {Neural networks are known to be a class of highly expressive functions able to fit even random input-output mappings with 100% accuracy. In this work we present properties of neural networks that complement this aspect of expressivity. By using tools from Fourier analysis, we highlight a learning bias of deep networks towards low frequency functions – i.e. functions that vary globally without local fluctuations – which manifests itself as a frequency-dependent learning speed. Intuitively, this property is in line with the observation that over-parameterized networks prioritize learning simple patterns that generalize across data samples. We also investigate the role of the shape of the data manifold by presenting empirical and theoretical evidence that, somewhat counter-intuitively, learning higher frequencies gets easier with increasing manifold complexity.} }
Endnote
%0 Conference Paper %T On the Spectral Bias of Neural Networks %A Nasim Rahaman %A Aristide Baratin %A Devansh Arpit %A Felix Draxler %A Min Lin %A Fred Hamprecht %A Yoshua Bengio %A Aaron Courville %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-rahaman19a %I PMLR %P 5301--5310 %U https://proceedings.mlr.press/v97/rahaman19a.html %V 97 %X Neural networks are known to be a class of highly expressive functions able to fit even random input-output mappings with 100% accuracy. In this work we present properties of neural networks that complement this aspect of expressivity. By using tools from Fourier analysis, we highlight a learning bias of deep networks towards low frequency functions – i.e. functions that vary globally without local fluctuations – which manifests itself as a frequency-dependent learning speed. Intuitively, this property is in line with the observation that over-parameterized networks prioritize learning simple patterns that generalize across data samples. We also investigate the role of the shape of the data manifold by presenting empirical and theoretical evidence that, somewhat counter-intuitively, learning higher frequencies gets easier with increasing manifold complexity.
APA
Rahaman, N., Baratin, A., Arpit, D., Draxler, F., Lin, M., Hamprecht, F., Bengio, Y. & Courville, A.. (2019). On the Spectral Bias of Neural Networks. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:5301-5310 Available from https://proceedings.mlr.press/v97/rahaman19a.html.

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