Source vs. Mechanistic Redundancy in Pointwise Partial Information Decomposition

We introduce a framework for pointwise partial information decomposition (PID) that estimates sample- and distribution-level redundancy, uniqueness, and synergy between two modalities and a target. We define an $I_{\min }$-inspired pointwise redundancy measure that is computed directly from predictive models, avoiding explicit high-dimensional input-density estimation. We further introduce a supervised Gács–Körner-inspired objective for learning target-predictive shared representations across modalities. This enables us to decompose predictive redundancy into source redundancy, arising from information shared between the modalities, and mechanistic redundancy, arising when distinct modality-specific mechanisms provide overlapping predictive information. Across analytically tractable synthetic benchmarks, controlled multimodal tasks, and clinical data, the framework improves pointwise estimation accuracy, recovers known source–mechanistic structure, and yields interpretable multimodal information-sharing patterns.