Share to Extrapolate: Learning Reusable Response Components for Single-Cell Perturbation Prediction

Predicting how genetic perturbations change gene expression is central to understanding gene function and cellular regulation. Yet experimental coverage remains limited, requiring generalization to unseen perturbations. Despite advances in perturbation prediction, matching observed conditional distributions alone leaves responses to unseen perturbations underdetermined. With supervision limited to observed perturbations, models can fit the training distributions equally well yet predict different responses to the same unseen perturbation. Similar patterns of gene-expression change across perturbations suggest that shared response components can provide an inductive bias for extrapolation. We introduce CoShare, a graph-routed factorized Delta Flow Matching framework. CoShare decomposes responses relative to the control mean into mean responses and cell-level residuals, learning from unpaired control and perturbed populations. A component router uses multi-source gene graphs and cell-type context to produce a component coefficient vector. This vector weights shared response vectors in the population mean branch and controls adapters combining shared feature transformations in the cellular residual branch. Experiments on Adamson, Norman, and Replogle demonstrate improved prediction of mean responses and cell distributions, including for unseen gene combinations. CoShare reduces Energy Distance over 2,000 highly variable genes by 44.5% on Adamson and 66.2% on Replogle relative to the best baseline for this metric on each benchmark. Ablations support the complementary contributions of mean–residual factorization and graph-routed component reuse.