Concept Gradient: Concept-based Interpretation Without Linear Assumption.

Bai, Andrew; Yeh, Chih-Kuan; Ravikumar, Pradeep; Lin, Y. C.; Hsieh, Cho-Jui.

Concept-based interpretations of black-box models are often more intuitive for humans to understand. The most widely adopted approach for concept-based interpretation is Concept Activation Vector (CAV). CAV relies on learning a linear relation between some latent representation of a given model and concepts. The linear separability is usually implicitly assumed but does not hold true in general. In this work, we started from the original intent of concept-based interpretation and proposed Concept Gradient (CG), extending concept-based interpretation beyond linear concept functions. We showed that for a general (potentially non-linear) concept, we can mathematically evaluate how a small change of concept affecting the model’s prediction, which leads to an extension of gradient-based interpretation to the concept space. We demonstrated empirically that CG outperforms CAV in both toy examples and real world datasets.

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