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XAI方法的解释仅对模型局部保真，即仅针对单个决策。对于可信赖的XAI应用（尤其是高风险决策场景），需要更全局的模型理解。近期提出的概念方法虽具潜力，但并未确保与模型实际推理过程的绑定。为解决此问题，我们提出多维概念发现(MCD)作为现有方法的扩展，该框架在概念层面实现完备性关系约束。本方法以广义线性子空间作为概念基础，既无需强制概念可解释性，也无需重训练模型组件。我们采用稀疏子空间聚类发现优化概念，充分挖掘多维子空间的潜力。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——展示样本中概念的激活位置，通过原型样本实现概念刻画；(2)概念相关性热力图——将模型决策分解为各概念的贡献量。两种工具协同作用，能够实现对模型推理过程的精细理解，并通过完备性关系保证与模型的实际关联。这为构建更可信赖的概念驱动型XAI奠定基础。实验证明MCD相较于受约束更强的概念定义具有显著优越性。