Precision cancer diagnosis relies on identifying driver genes, yet distinguishing these from passenger mutations in high-dimensional transcriptomics remains challenging. Gene prioritization in high-dimensional transcriptomic data conventionally relies on variance-based filtering, under the assumption that biologically important genes exhibit high expression variability. However, accumulating evidence suggests that structurally influential genes may exert disproportionate effects on cellular programs despite modest marginal variance.
We introduce a manifold-based framework that quantifies gene importance through geometric sensitivity analysis. By training a nonlinear embedding with manifold regularization, we define a gradient-based sensitivity measure that captures how perturbations along individual gene dimensions propagate through the learned representation space. Applied to TCGA breast cancer transcriptomics (N=526, G=17,800), our approach identified structurally influential genes including ASCL2, NAPRT1, and OR10AG1, which ranked beyond the top 15,000 genes by variance yet exhibited high geometric leverage. Survival stratification based on manifold-sensitive genes achieved log-rank p=0.0048, compared to p=0.157 for PCA-based approaches. Ablation studies confirmed that performance gains arise from structural alignment rather than model complexity. These findings demonstrate that geometry-aware gene prioritization can reveal functionally important features that are systematically suppressed by variance-based filtering.