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This paper critiques the use of intrinsic dimension (ID) estimators for analyzing neural representations, demonstrating both theoretically and empirically that common estimators fail to accurately reflect the true underlying ID. They identify factors driving previously reported ID-related results, suggesting these may be driven by other properties of the representations. The authors propose a new perspective on ID estimation in neural representations, though the specifics of this new perspective are not detailed in the abstract.
Common methods for estimating the complexity of neural network representations are fundamentally flawed, potentially invalidating a large body of prior work.
The analysis of neural representation has become an integral part of research aiming to better understand the inner workings of neural networks. While there are many different approaches to investigate neural representations, an important line of research has focused on doing so through the lens of intrinsic dimensions (IDs). Although this perspective has provided valuable insights and stimulated substantial follow-up research, important limitations of this approach have remained largely unaddressed. In this paper, we highlight a crucial discrepancy between theory and practice of IDs in neural representations, theoretically and empirically showing that common ID estimators are, in fact, not tracking the true underlying ID of the representation. We contrast this negative result with an investigation of the underlying factors that may drive commonly reported ID-related results on neural representation in the literature. Building on these insights, we offer a new perspective on ID estimation in neural representations.
