The completeness axiom renders the explanation of a post-hoc XAI method only locally faithful to the model, i.e. for a single decision. For the trustworthy application of XAI, in particular for high-stake decisions, a more global model understanding is required. Recently, concept-based methods have been proposed, which are however not guaranteed to be bound to the actual model reasoning. To circumvent this problem, we propose Multi-dimensional Concept Discovery (MCD) as an extension of previous approaches that fulfills a completeness relation on the level of concepts. Our method starts from general linear subspaces as concepts and does neither require reinforcing concept interpretability nor re-training of model parts. We propose sparse subspace clustering to discover improved concepts and fully leverage the potential of multi-dimensional subspaces. MCD offers two complementary analysis tools for concepts in input space: (1) concept activation maps, that show where a concept is expressed within a sample, allowing for concept characterization through prototypical samples, and (2) concept relevance heatmaps, that decompose the model decision into concept contributions. Both tools together enable a detailed understanding of the model reasoning, which is guaranteed to relate to the model via a completeness relation. This paves the way towards more trustworthy concept-based XAI. We empirically demonstrate the superiority of MCD against more constrained concept definitions.

翻译：完备性公理使得事后可解释人工智能（XAI）方法对模型的解释仅在局部层面（即针对单一决策）具有保真性。为实现XAI的可信应用，特别是在高风险决策场景中，需要更全局的模型理解。近期提出的基于概念的方法虽被广泛应用，但无法保证其与模型实际推理过程的绑定关系。为解决该问题，我们提出多维度概念发现（MCD）作为现有方法的扩展，其在概念层面满足完备性关系。该方法以一般线性子空间作为概念起点，既无需强化概念可解释性，也无需重新训练模型组件。我们采用稀疏子空间聚类发现优化后的概念，并充分利用多维度子空间的潜力。MCD为输入空间中的概念提供两种互补分析工具：（1）概念激活图，用于展示概念在样本中的表达位置，支持通过原型样本进行概念表征；（2）概念相关性热力图，将模型决策分解为各概念的贡献。两种工具结合可实现对模型推理过程的精细理解，并通过完备性关系保证该理解与模型的实际关联。这为构建更可信的概念型XAI铺平了道路。实验表明，MCD相比于更具约束性的概念定义方法具有显著优越性。