  Implicit knowledge hidden within the explicit table cells, such as data
insights, is the key to generating a high-quality table summary. However,
unveiling such implicit knowledge is a non-trivial task. Due to the complex
nature of structured tables, it is challenging even for large language models
(LLMs) to mine the implicit knowledge in an insightful and faithful manner. To
address this challenge, we propose a novel table reasoning framework
Question-then-Pinpoint. Our work focuses on building a plug-and-play table
reasoner that can self-question the insightful knowledge and answer it by
faithfully pinpointing evidence on the table to provide explainable guidance
for the summarizer. To train a reliable reasoner, we collect table knowledge by
guiding a teacher LLM to follow the coarse-to-fine reasoning paths and refine
it through two quality enhancement strategies to selectively distill the
high-quality knowledge to the reasoner. Extensive experiments on two table
summarization datasets, including our newly proposed InsTaSumm, validate the
general effectiveness of our framework.
