reviews: 
Comments: This paper introduces an axiomatic framework for generating concept-based explanations for a given model. This approach generalizes existing methods, such as TCAV and the completeness score, under specific conditions.
Strengths: Interpretable and explainable machine learning holds substantial societal implications, warranting its significance as a crucial area of research.

Concept explanation emerges as a compelling avenue within the realm of interpretable machine learning.

The axiomatic approach to concept explanation is interesting and makes sense to me.
Weaknesses: Some assertions within the paper are inaccurate. Specifically, the authors incorrectly categorize SHAP and LIME as model-specific techniques that necessitate white-box access to the model. Contrary to these claims, SHAP and LIME are model-agnostic and can operate on black-box models. They generate explanations by probing the model with varying input combinations to obtain SHAP and LIME scores.

Furthermore, the terminology used in the problem formulation section lacks precision. The term "measure" is ambiguously defined— it is unclear whether it refers to a "score" or "measurement," or to a "measure" in the context of measure theory. A more mathematically rigorous exposition of the problem setting would be beneficial.

While the abstract and the introduction draw a grand picture of a unified approach that encompasses different existing methods, but ultimately only discussed TCAV and completeness-aware explanations in the paper. The proposed measure is also somewhat similar to how [1] parameterizes a self-explaining neural network (e.g., the product of h(x) and c(x)). 

Additional points of concern include: (1) the assertion that the proposed approach subsumes TCAV is not entirely accurate. According to Theorem 4.2, it approximates TCAV in an asymptotic sense rather than subsuming it exactly. (2) The claim that the approach unifies TCAV and completeness-aware explanations is also not entirely precise. Specifically, the class-conditioned variant of the proposed method is linearly correlated with a subset of the completeness score, while its concept-conditioned variant approximates the continuous case of TCAV.

From Section 3, it seems the proposed approach is limited to binary classification. This is a limitation. Would it be generalizable to other cases, e.g., multi-class classification? 

Another significant issue that I have is the absence of comparative results with baseline methods. Unless I overlooked it, the paper does not present any performance metrics juxtaposed with at least TCAV and completeness-aware explanations. Such comparative analysis is essential for rigorously assessing the technical and empirical merits of the proposed approach. Without it, evaluating the method's substantive contribution becomes challenging.

[1] Towards Robust Interpretability with Self-Explaining Neural Networks. NeurIPS 2018.
Recommendation: 3: reject, not good enough
Reviewer confidence: 5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.
Soundness/correctness: 3 good
Clarity: 3 good