SCOR: A Section-Centered Objective for Gene Expression Prediction from Histology

Predicting spatial gene expression from hematoxylin and eosin (H&E) histology is typically optimized with spot-wise regression, even though many spatial observations are grouped within the same tissue section. Viewing the task as grouped regression, conventional mean squared error (MSE) decomposes exactly into within-section residual variation and section-mean residual error. This exposes an implicit objective-design choice: MSE assigns equal weight to error components defined at different levels of the grouped data structure. We introduce the Section-Centered Objective for Regression (SCOR), which retains full weight on within-section residual variation while explicitly controlling the contribution of the section-mean residual component, without changing the histology representation, predictor architecture, or inference procedure. SCOR further admits a profiled regularized section-offset interpretation that gives its weighting parameter a direct shrinkage meaning. Controlled diagnostics show that preserving the section-defined grouping is important for reproducing the benefit: pairwise residual differencing alone is insufficient, and the effect persists beyond local spatial proximity. A fixed-sample analysis further shows that training-section replication modulates its magnitude. With a single fixed objective setting, SCOR improves over MSE on the majority of eight HEST-1K tasks, transfers the same setting without retuning to HER2ST and STNet, and extends to ridge regression. These results identify grouped-error weighting as an overlooked design choice in histology-to-transcriptomics regression.