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AdaDim: Dimensionality Adaptation for SSL Representational Dynamics

A key factor in effective Self-Supervised learning (SSL) is preventing dimensional collapse, which is where higher-dimensional representation spaces span a lower-dimensional subspace. Therefore, SSL optimization strategies involve guiding a model to produce representations ($R$) with a higher dimensionality. Dimensionality is either optimized through a dimension-contrastive approach that encourages feature decorrelation or through a sample-contrastive method that promotes a uniform spread of sample representations. Both families of SSL algorithms also utilize a projection head that maps $R$ into a lower-dimensional embedding space $Z$. Recent work has characterized the projection head as a filter of irrelevant features from the SSL objective by reducing 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 the problem is lacking in terms of an understanding of the underlying training dynamics that influences both terms, as well as how the values of $H(R)$ and $I(R;Z)$ arrived at the end of training reflect the downstream performance of an SSL model. We address both gaps in the literature by demonstrating that increases in $H(R)$ due to feature decorrelation at the start of training lead to a 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 arrive at an optimal intermediate point for both. We develop a method called AdaDim to exploit these observed training dynamics by adaptively weighting between losses based on feature decorrelation and uniform sample spread.

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