Information Bottleneck Dominates Adversarial Training for Ancestry-Invariant Polygenic Risk Prediction: Dimensionality, Not Gradient Reversal, Controls the Fairness-Accuracy Tradeoff

In adversarial representation learning for fair prediction, the gradient reversal coefficient ({lambda}) is widely treated as the primary control for sensitive-attribute invariance. We show this assumption is wrong. Using a dual-stream architecture for cross-ancestry polygenic risk score (PRS) prediction, we demonstrate that latent dimensionality -- the information bottleneck -- accounts for 8-27 x more variance in ancestry leakage than adversarial strength. Varying{lambda} across a 20 x range changes leakage by only 2.2 percentage points; varying dimensionality across a 16 x range changes it by 46.6 pp. At dimension 8 with no adversarial training ({lambda} = 0), ancestry leakage is 32.9% (chance = 20%): the bottleneck alone achieves near-invariance. The adversary architecture (linear vs deep MLP) is equally irrelevant (0.6 pp range). We validate this finding across two unrelated domains -- genomic ancestry invariance (6 clinical traits, 1000 Genomes, n = 2,504) and EEG subject invariance (pretrained HFTP + Braindecode dual-domain model, 20 subjects) -- observing consistent dimensionality dominance (12.7:1 ratio in EEG). For the genomic application, Stream 1 encodes population structure via DCT-II frequencydomain features (136 coefficients); Stream 2 encodes phenotype signal from top PRS SNPs (PCA to 128 dimensions). The architecture works equally well with standard genomic PCA as the ancestry stream (R2 = 0.217 vs 0.222), confirming the contribution is architectural, not encoding-specific. African-ancestry PRS reconstruction R2 improves on all six traits (e.g., +5.1 pp for coronary artery disease). Linear models achieve higher aggregate R2 but fail catastrophically on cross-ancestry transfer (R2 = - 12.45 for African-ancestry CAD). We emphasize that we predict PRS (a computed score), not disease phenotypes; validation on biobank-scale phenotype data is ongoing. These results suggest the adversarial fairness community has been over-investing in adversary engineering relative to simple capacity control. Practitioners should select latent dimensionality first to set the information budget for the fairness-accuracy tradeoff, then optionally use adversarial training for marginal refinement.