Title: AdaDim: Dimensionality Adaptation for SSL Representational Dynamics
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: Self Supervised Learning, Representation Learning, Information Theory, Learning Dynamics

Abstract: A key factor in effective Self-Supervised learning (SSL) is preventing dimensional collapse, where higher-dimensional representation spaces ($R$) span a lower-dimensional subspace. Therefore, SSL optimization strategies involve guiding a model to produce $R$ with a higher dimensionality ($H(R)$) through objectives that encourage decorrelation of features or sample uniformity in $R$. A higher $H(R)$ indicates that $R$ has greater feature diversity which is useful for generalization to downstream tasks. Alongside dimensionality optimization, SSL algorithms also utilize a projection head that maps $R$ into an embedding space $Z$. Recent work has characterized the projection head as a filter of noisy or irrelevant features from the SSL objective by reducing the mutual information $I(R;Z)$.  Therefore, the current literature's view is that a good SSL representation space should have a high $H(R)$ and a low $I(R;Z)$. However, this view of SSL is lacking in terms of an understanding of the underlying training dynamics that influences the relationship between both terms. For this reason, we directly oppose the current literature's view of SSL representation spaces and instead assert that the best performing $R$ is one arrives at an ideal balance between both $H(R)$ and $I(R;Z)$. Our findings reveal that increases in $H(R)$ due to feature decorrelation at the start of training lead to correspondingly higher $I(R;Z)$, while increases in $H(R)$ due to samples distributing uniformly in a high-dimensional space at the end of training cause $I(R;Z)$ to plateau or decrease. Furthermore, our analysis shows that the best performing SSL models do not have the highest $H(R)$ nor the lowest $I(R;Z)$, but effectively arrive at a balance between both. To take advantage of this analysis, we introduce AdaDim, a training strategy that leverages SSL training dynamics by adaptively balancing between increasing $H(R)$ through feature decorrelation and sample uniformity as well as gradual regularization of $I(R;Z)$ as training progresses. We show performance improvements of up to 3% over common SSL baselines despite our method not utilizing expensive techniques such as queues, clustering, predictor networks, or student-teacher architectures.

TL;DR: This paper identifies and exploits the SSL relationship between dimensionality of the representation space and mutual information between the encoder and projector.