Dataset-Dependent Utility of Discrete Ricci Curvature for Transition-Region Ranking in Single-Cell Lineage Graphs

Abstract

Discrete Ricci curvature is an appealing descriptor for single-cell trajectory graphs, but its practical value depends on task validity, graph-topology controls, and whether the biological target is a local transition region or a broader fate decision. We present a controlled empirical study of when curvature features add information to single-cell lineage graphs after repairing unsupported task definitions and preserving strong graph baselines. Paul15 is used as a benchmark-repair and boundary-setting dataset: on the repaired annotation-informed branch-region proxy, graph-plus-Forman and graph-plus-Ollivier improve modestly over graph topology alone (exact AUPRC 0.652 and 0.635 versus 0.607). Pancreas provides the clearest positive transition-region ranking result. On a Fev+ endocrine transition-region benchmark, graph-plus-Ollivier reaches exact AUPRC 0.761 versus 0.669 for the graph-feature stack (five-split canonical evaluation, paired mean +0.092, 95% CI [0.076, 0.114]), and a restricted preterminal endocrine fate task improves under both curvature hybrids. The primary evaluation is transductive node ranking; graph-attachment analyses provide supporting out-of-sample robustness checks. Zebrafish provides a realism check: branch-region ranking again benefits from a hybrid model, with graph-plus-Forman strongest (0.704 versus 0.593 for graph topology), whereas a valid early Notochord versus Prechordal Plate task is graph-topology dominated on the canonical graph. Supplementary checks, including a stricter zebrafish sample-token holdout, biologically grounded bottleneck proxy, negative controls, and pairwise transfer, sharpen the same conclusion without expanding the claim set. Curvature can add useful, dataset-dependent hybrid signal for lineage transition-region tasks, but curvature-only models are weak and graph topology remains essential and sometimes sufficient.