Learning with Hyperspherical Uniformity

Weiyang Liu, Rongmei Lin, Zhen Liu, Li Xiong, Bernhard Schölkopf, Adrian Weller
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1180-1188, 2021.

Abstract

Due to the over-parameterization nature, neural networks are a powerful tool for nonlinear function approximation. In order to achieve good generalization on unseen data, a suitable inductive bias is of great importance for neural networks. One of the most straightforward ways is to regularize the neural network with some additional objectives. L2 regularization serves as a standard regularization for neural networks. Despite its popularity, it essentially regularizes one dimension of the individual neuron, which is not strong enough to control the capacity of highly over-parameterized neural networks. Motivated by this, hyperspherical uniformity is proposed as a novel family of relational regularizations that impact the interaction among neurons. We consider several geometrically distinct ways to achieve hyperspherical uniformity. The effectiveness of hyperspherical uniformity is justified by theoretical insights and empirical evaluations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-liu21d, title = { Learning with Hyperspherical Uniformity }, author = {Liu, Weiyang and Lin, Rongmei and Liu, Zhen and Xiong, Li and Sch{\"o}lkopf, Bernhard and Weller, Adrian}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {1180--1188}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/liu21d/liu21d.pdf}, url = {https://proceedings.mlr.press/v130/liu21d.html}, abstract = { Due to the over-parameterization nature, neural networks are a powerful tool for nonlinear function approximation. In order to achieve good generalization on unseen data, a suitable inductive bias is of great importance for neural networks. One of the most straightforward ways is to regularize the neural network with some additional objectives. L2 regularization serves as a standard regularization for neural networks. Despite its popularity, it essentially regularizes one dimension of the individual neuron, which is not strong enough to control the capacity of highly over-parameterized neural networks. Motivated by this, hyperspherical uniformity is proposed as a novel family of relational regularizations that impact the interaction among neurons. We consider several geometrically distinct ways to achieve hyperspherical uniformity. The effectiveness of hyperspherical uniformity is justified by theoretical insights and empirical evaluations. } }
Endnote
%0 Conference Paper %T Learning with Hyperspherical Uniformity %A Weiyang Liu %A Rongmei Lin %A Zhen Liu %A Li Xiong %A Bernhard Schölkopf %A Adrian Weller %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-liu21d %I PMLR %P 1180--1188 %U https://proceedings.mlr.press/v130/liu21d.html %V 130 %X Due to the over-parameterization nature, neural networks are a powerful tool for nonlinear function approximation. In order to achieve good generalization on unseen data, a suitable inductive bias is of great importance for neural networks. One of the most straightforward ways is to regularize the neural network with some additional objectives. L2 regularization serves as a standard regularization for neural networks. Despite its popularity, it essentially regularizes one dimension of the individual neuron, which is not strong enough to control the capacity of highly over-parameterized neural networks. Motivated by this, hyperspherical uniformity is proposed as a novel family of relational regularizations that impact the interaction among neurons. We consider several geometrically distinct ways to achieve hyperspherical uniformity. The effectiveness of hyperspherical uniformity is justified by theoretical insights and empirical evaluations.
APA
Liu, W., Lin, R., Liu, Z., Xiong, L., Schölkopf, B. & Weller, A.. (2021). Learning with Hyperspherical Uniformity . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1180-1188 Available from https://proceedings.mlr.press/v130/liu21d.html.

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