arXiv：cs.LG· Aritra Das, Joseph T. Iosue, Victor V. Albert·· 4 小时前AI 评分30
HomID：在带各向异性嵌入的均匀流形上基准测试内在维度估计器
HomID : Benchmarking Intrinsic Dimension Estimators on Homogenous Manifolds with Anisotropic Embeddings
AI 导读
研究者提出 HomID，一组带各向异性嵌入的均匀空间，用于基准测试内在维度（ID）估计器。在相同资源分配下，原本在标准基准上表现良好的方法在 HomID 上系统性退化；对各向异性失真后的标准基准也出现性能下降。研究进一步证明，受控的各向异性失真会使这些方法所依赖的分布发生系统性偏移，为两种特定 ID 估计器的估计误差提供了具体机制。
正文
Abstract:The manifold hypothesis suggests that data lies on manifolds with smaller intrinsic dimension (ID) than their ambient dimension. However there is no empirical agreement on the estimates for ID from different estimators for realistic datasets. Thus it is important to test ID estimators (IDEs) with targeted stressors. In this work, we consider the role of anisotropy. To this end, we propose HomID, a collection of homogeneous spaces with anisotropic embedding, for benchmarking ID estimators. We observe that methods that perform well on standard benchmarks systematically degrade on HomID under identical resource allocation. We further observe that anisotropic distortion of such benchmarks also results in performance degradation. Finally, we demonstrate that controlled anisotropic distortions induce systematic shifts in the distributions on which these methods rely, providing a concrete mechanism for the resulting estimation errors in two particular IDEs.
| Comments: | 17 figures, 37 pages |
| Subjects: | Machine Learning (cs.LG); Disordered Systems and Neural Networks (cond-mat.dis-nn); Metric Geometry (math.MG); Data Analysis, Statistics and Probability (physics.data-an); Quantum Physics (quant-ph) |
| Cite as: | arXiv:2510.01335 [cs.LG] |
| (or arXiv:2510.01335v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2510.01335 arXiv-issued DOI via DataCite |
Submission history
From: Aritra Das [view email]
[v1]
Wed, 1 Oct 2025 18:03:02 UTC (2,859 KB)
[v2]
Wed, 7 Oct 2026 00:49:48 UTC (3,431 KB)
来源：arXiv：cs.LG · arxiv.org