新研究利用 Fisher 宽度和基准测试探索数据流形几何

报道来源 [5]

1. arXiv cs.LG TIER_1 English(EN) · Vu Khac Ky · 2026-06-18 04:00

   Fisher 宽度：统计流形上的复杂性几何度量

   arXiv:2606.18306v1 Announce Type: new Abstract: Gaussian width is a central geometric complexity measure in high-dimensional probability, compressed sensing, convex optimization, and learning theory. It quantifies the average extent of a set along random directions, thereby captu…

2. arXiv cs.LG TIER_1 English(EN) · Marios Koulakis, Constantin Seibold · 2026-06-16 04:00

   数据流形在显微镜下

   arXiv:2606.15760v1 Announce Type: new Abstract: A significant gap exists between theory and practice in deep learning. Generalization and approximation error bounds are often derived for simplified models or are too loose to be informative. Many rely on the manifold hypothesis an…

3. Hugging Face Daily Papers TIER_1 English(EN) · 2026-06-14 00:00

   数据流形在显微镜下

   A benchmarking framework is introduced to study data-manifold geometry by extending dSprites and COIL-20 datasets with additional transformation dimensions and dense sampling, enabling accurate estimation of curvature, reach, and volume for theoretical analysis and validation.

4. arXiv stat.ML TIER_1 English(EN) · Vu Khac Ky · 2026-06-16 07:04

   Fisher 宽度：统计流形上的复杂性几何度量

   Gaussian width is a central geometric complexity measure in high-dimensional probability, compressed sensing, convex optimization, and learning theory. It quantifies the average extent of a set along random directions, thereby capturing the effective dimension of constraint sets,…

5. arXiv stat.ML TIER_1 English(EN) · Constantin Seibold · 2026-06-14 11:45

   数据流形在显微镜下

   A significant gap exists between theory and practice in deep learning. Generalization and approximation error bounds are often derived for simplified models or are too loose to be informative. Many rely on the manifold hypothesis and on geometric regularity such as intrinsic dime…