  Vision transformers (ViTs) have emerged as a significant area of focus,
particularly for their capacity to be jointly trained with large language
models and to serve as robust vision foundation models. Yet, the development of
trustworthy explanation methods for ViTs has lagged, particularly in the
context of post-hoc interpretations of ViT predictions. Existing sub-image
selection approaches, such as feature-attribution and conceptual models, fall
short in this regard. This paper proposes five desiderata for explaining ViTs
-- faithfulness, stability, sparsity, multi-level structure, and parsimony --
and demonstrates the inadequacy of current methods in meeting these criteria
comprehensively. We introduce a variational Bayesian explanation framework,
dubbed ProbAbilistic Concept Explainers (PACE), which models the distributions
of patch embeddings to provide trustworthy post-hoc conceptual explanations.
Our qualitative analysis reveals the distributions of patch-level concepts,
elucidating the effectiveness of ViTs by modeling the joint distribution of
patch embeddings and ViT's predictions. Moreover, these patch-level
explanations bridge the gap between image-level and dataset-level explanations,
thus completing the multi-level structure of PACE. Through extensive
experiments on both synthetic and real-world datasets, we demonstrate that PACE
surpasses state-of-the-art methods in terms of the defined desiderata.
