arXiv：cs.LG· Arjhun Swaminathan, Mete Akg\"un·· 5 小时前AI 评分32
图像分类器决策区域单连通的实证证据
Empirical Evidence for Simply Connected Decision Regions in Image Classifiers
AI 导读
研究者对预训练图像分类器展开实证研究，用自适应四边形网格在同标签边界闭环固定的条件下检验该闭环能否在决策区域内被曲面填充。在所有受试预训练分类器上，每个被测试的闭环都存在可接受的填充，结果与测试分辨率下决策区域单连通的经验证据一致。平均分数调整后的随机初始化分类器所需的构建代价比训练后的分类器高数个数量级，而带已知孔洞的解析对照在分辨率阈值及以上的孔洞半径处仍无法解决缠绕闭环。
正文
Abstract:The topology of a classifier's decision regions determines how inputs with the same predicted label can be connected and deformed without changing that prediction. Prior empirical work constructed paths between same-label images within a single region, but did not examine whether loops bound surfaces within that region. We investigate this question using adaptive quadrilateral meshes with targeted repair of off-label interior vertices, while holding the same-label boundary loop fixed. A finite-resolution acceptance criterion distinguishes completed constructions from those left unresolved at the refinement ceiling. Across the pretrained classifiers studied, every tested loop admits an accepted filling. Construction effort varies by orders of magnitude within classes and is greater for mean-score-adjusted randomly initialised classifiers than for trained classifiers. An analytic control with a known hole leaves winding loops unresolved at the tested hole radii at or above the resolution threshold. These results provide empirical evidence consistent with simply connected decision regions at the tested resolution.
| Subjects: | Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.06380 [cs.CV] |
| (or arXiv:2605.06380v2 [cs.CV] for this version) | |
| https://doi.org/10.48550/arXiv.2605.06380 arXiv-issued DOI via DataCite |
Submission history
From: Arjhun Swaminathan [view email]
[v1]
Thu, 7 May 2026 14:59:17 UTC (1,532 KB)
[v2]
Wed, 7 Oct 2026 14:53:05 UTC (4,681 KB)
来源：arXiv：cs.LG · arxiv.org