  While LLMs can provide reasoned explanations along with their answers, the
nature and quality of those explanations are still poorly understood. In
response, our goal is to define a detailed way of characterizing the
explanation capabilities of modern models and to create a nuanced,
interpretable explanation evaluation tool that can generate such
characterizations automatically, without relying on expensive API calls or
human annotations. Our approach is to (a) define the new task of explanation
critiquing - identifying and categorizing any main flaw in an explanation and
providing suggestions to address the flaw, (b) create a sizeable,
human-verified dataset for this task, and (c) train an open-source, automatic
critique model (called Digital Socrates) using this data. Through quantitative
and qualitative analysis, we demonstrate how Digital Socrates is useful for
revealing insights about student models by examining their reasoning chains,
and how it can provide high-quality, nuanced, automatic evaluation of those
model explanations for the first time. Digital Socrates thus fills an important
gap in evaluation tools for understanding and improving the explanation
behavior of models.
