arXiv：cs.AI· Ekkehard Schnoor, Jawher Said, Malik Tiomoko, Wojciech Samek, Alexander Jung·· 19 小时前
α-TCAV：用概念激活向量做测试的统一框架
$\alpha$-TCAV: A Unified Framework for Testing with Concept Activation Vectors
AI 导读
针对标准 TCAV 因使用不连续指示函数导致评分不稳定的缺陷，研究者提出 α-TCAV，用平滑函数替换不连续指示函数，并将 TCAV 作为其极限情形纳入统一参数化框架。该框架给出两种有原则的参数选择：一种在仅用单个 CAV 时即可匹配 Multi-TCAV 的均值且方差不大，另一种给出概念正向影响模型输出的校准概率。
正文
Abstract:Concept Activation Vectors (CAV) and the Testing with CAVs (TCAV) method are fundamental tools for concept-based explainability in deep learning, yet their practical utility is limited by the variability across different samples of concept and non-concept examples. We analyze this stochastic nature of CAVs, and identify a fundamental flaw in the standard TCAV score, its instability by using a discontinuous indicator function. To address this, we introduce $\alpha$-TCAV, a parameterized unified framework that replaces the discontinuous indicator with a smooth function, which recovers TCAV as a limiting case. Under realistic assumptions, we characterize the score distributions and derive principled parameter choices: one matches the mean of its averaged counterpart, Multi-TCAV, with no larger variance using a single CAV; the other provides a calibrated probability that the concept positively influences the model output. Our analysis and experiments provide practical guidance and challenge the established practice of splitting the sampling budget across multiple CAVs.
| Comments: | 26 pages, 12 figures |
| Subjects: | Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Probability (math.PR) |
| Cite as: | arXiv:2605.15688 [stat.ML] |
| (or arXiv:2605.15688v2 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2605.15688 arXiv-issued DOI via DataCite |
Submission history
From: Ekkehard Schnoor [view email]
[v1]
Fri, 15 May 2026 07:22:59 UTC (968 KB)
[v2]
Mon, 12 Oct 2026 14:01:28 UTC (1,610 KB)
来源：arXiv：cs.AI · arxiv.org