Exploring the Gap between Collapsed & Whitened Features in Self-Supervised Learning
Abstract
Avoiding feature collapse, when a Neural Network (NN) encoder maps all inputs to a constant vector, is a shared implicit desideratum of various methodological advances in self-supervised learning (SSL). To that end, whitened features have been proposed as an explicit objective to ensure uncollapsed features \cite{zbontar2021barlow,ermolov2021whitening,hua2021feature,bardes2022vicreg}. We identify power law behaviour in eigenvalue decay, parameterised by exponent $\beta{\geq}0$, as a spectrum that bridges between the collapsed & whitened feature extremes. We provide theoretical & empirical evidence highlighting the factors in SSL, like projection layers & regularisation strength, that influence eigenvalue decay rate, & demonstrate that the degree of feature whitening affects generalisation, particularly in label scarce regimes. We use our insights to motivate a novel method, PMP (PostMan-Pat), which efficiently post-processes a pretrained encoder to enforce eigenvalue decay rate with power law exponent $\beta$, & find that PostMan-Pat delivers improved label efficiency and transferability across a range of SSL methods and encoder architectures.
BibTeX
@InProceedings{pmlr-v162-he22c,
title = {Exploring the Gap between Collapsed & Whitened Features in Self-Supervised Learning},
author = {He, Bobby and Ozay, Mete},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {8613--8634},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/he22c/he22c.pdf},
url = {https://proceedings.mlr.press/v162/he22c.html},
abstract = {Avoiding feature collapse, when a Neural Network (NN) encoder maps all inputs to a constant vector, is a shared implicit desideratum of various methodological advances in self-supervised learning (SSL). To that end, whitened features have been proposed as an explicit objective to ensure uncollapsed features \cite{zbontar2021barlow,ermolov2021whitening,hua2021feature,bardes2022vicreg}. We identify power law behaviour in eigenvalue decay, parameterised by exponent $\beta{\geq}0$, as a spectrum that bridges between the collapsed & whitened feature extremes. We provide theoretical & empirical evidence highlighting the factors in SSL, like projection layers & regularisation strength, that influence eigenvalue decay rate, & demonstrate that the degree of feature whitening affects generalisation, particularly in label scarce regimes. We use our insights to motivate a novel method, PMP (PostMan-Pat), which efficiently post-processes a pretrained encoder to enforce eigenvalue decay rate with power law exponent $\beta$, & find that PostMan-Pat delivers improved label efficiency and transferability across a range of SSL methods and encoder architectures.}
}