Few-Shot Multimodal Medical Imaging: A Theoretical Framework

Medical imaging relies heavily on large, labeled datasets. But, unfortunately, they are not always easily accessible in clinical settings. Additionally, many practitioners often face various structural obstacles like limited data availability, fragmented data systems, and unbalanced datasets. These barriers often lead to the increased diagnostic uncertainty, underrepresentation of certain conditions, reduced model robustness, and biased diagnostic decisions. In response to these challenges, approaches such as transfer learning, meta-learning, and multimodal fusion have made great strides. However, they still need a solid theoretical justification for why they succeed or fail in situations where data is scarce. To address this gap, we propose a unified theoretical framework that characterizes learning and inference under low-resource medical imaging conditions. We first formalize the learning objective under few-shot conditions and compute sample complexity constraints to estimate the smallest quantity of data needed to achieve clinically reliable accuracy. Then based on ideas from PAC-learning and PAC-Bayesian theory, we explain how multimodal integration encourages generalization and quantifies uncertainty under sparse supervision. We further propose a formal metric for explanation stability, offering interpretability guarantees under low-data conditions. Taken together, the proposed framework establishes a principled foundation for constructing dependable, data-efficient diagnostic systems by jointly characterizing sample efficiency, uncertainty quantification, and interpretability in a unified theoretical setting.