LDReg: Local Dimensionality Regularized Self-Supervised Learning
This addresses a specific bottleneck in self-supervised learning for improving representation quality, though it is incremental as it builds on prior work on dimensional collapse.
The paper tackles the problem of local dimensional collapse in self-supervised learning, where representations can be high-dimensional globally but collapse locally, degrading downstream task performance. The proposed LDReg method improves representation quality by increasing local intrinsic dimensionality, as demonstrated through experiments.
Representations learned via self-supervised learning (SSL) can be susceptible to dimensional collapse, where the learned representation subspace is of extremely low dimensionality and thus fails to represent the full data distribution and modalities. Dimensional collapse also known as the "underfilling" phenomenon is one of the major causes of degraded performance on downstream tasks. Previous work has investigated the dimensional collapse problem of SSL at a global level. In this paper, we demonstrate that representations can span over high dimensional space globally, but collapse locally. To address this, we propose a method called $\textit{local dimensionality regularization (LDReg)}$. Our formulation is based on the derivation of the Fisher-Rao metric to compare and optimize local distance distributions at an asymptotically small radius for each data point. By increasing the local intrinsic dimensionality, we demonstrate through a range of experiments that LDReg improves the representation quality of SSL. The results also show that LDReg can regularize dimensionality at both local and global levels.