Before the Critic: Outcome-Free Audit of Finite Reference Laws for Interpretability-Based Discovery
Minji Kim ⋅ Weiman Yuan ⋅ Sunho Park ⋅ Xin M Zhou ⋅ Tae H Hwang
Abstract
Assessing whether a pathology foundation-model representation retains protein-relevant association beyond measured RNA and spatial context requires constructing the corresponding conditional comparison. In the finite-matching design studied here, a critic would compare observed image--protein pairs with negative pairs made from other locations. If those negatives change variables meant to be held fixed, the critic can separate the distributions for the wrong reason. We therefore audit the negative construction before fitting the critic or inspecting the planned image representation and protein outcome. The observational target is $I(X;Y\mid Z,W)$, where $X$ is an H\&E representation, $Y$ is a panel-measured protein, $Z$ is an eight-component RNA representation, and $W$ is RNA-only neighborhood context. A frozen Gaussian sanity check shows that omitting $W$ from the reference law introduces the context term $I(W;Y\mid Z)$. We then test a prespecified spatial construction on one public Xenium renal cell carcinoma section from a single donor (4{,}829 patches). After an H\&E tissue-coverage rule fixed the cohort, matching and gate decisions used RNA-derived quantities and coordinates only. A joint assignment with source-reuse limits and a follow-on independent per-anchor minimum-distance diagnostic were evaluated across two context representations, three radii, and five RNA calipers. All 30 independent settings failed both context gates: the best median-distance ratio was 0.765 (required $\leq0.75$), and the best improved-anchor fraction was 0.551 (required $\geq0.70$); $Z$-balance, coverage, and structural gates passed. We stopped before H\&E embedding extraction, protein-outcome analysis, critic fitting, or real-data CMI estimation. This rejects one frozen construction, not the biological hypothesis or CMI in general.
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