揭示神经网络表征内在维度估计的理论与实践偏差
Rethinking Intrinsic Dimension Estimation in Neural Representations
- 发现主流估计算法无法捕捉真实内在维度
- 实证表明现有方法报告的维度值存在系统性偏误
- 为表征分析提供更可靠的维度评估新视角
神经网络表征分析已成为理解模型内部机制的重要研究方向。尽管已有多种方法用于探索表征特性，但基于内在维度（ID）的研究路径尤为突出。然而，该方法虽带来重要洞见并推动大量后续工作，其关键局限长期未被正视。本文从理论和实证两方面揭示：当前主流的内在维度估计算法实际上并未追踪到表征的真实内在维度。我们进一步分析文献中常见ID相关结果的潜在驱动因素，并在此基础上提出对神经表征内在维度估计的新理解。
原文摘要 · Abstract (English)
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.
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