  We introduce a formal information-theoretic framework for image captioning by
regarding it as a representation learning task. Our framework defines three key
objectives: task sufficiency, minimal redundancy, and human interpretability.
Building upon this foundation, we propose a novel Pyramid of Captions (PoCa)
method, which constructs caption pyramids by generating localized captions for
zoomed-in image patches and integrating them with global caption information
using large language models. This approach leverages intuition that the
detailed examination of local patches can reduce error risks and address
inaccuracies in global captions, either by correcting the hallucination or
adding missing details. Based on our theoretical framework, we formalize this
intuition and provide formal proof demonstrating the effectiveness of PoCa
under certain assumptions. Empirical tests with various image captioning models
and large language models show that PoCa consistently yields more informative
and semantically aligned captions, maintaining brevity and interpretability.
