A Controlled Evaluation of Curvature Inspired Scalar Feature Scaling for Domain Generalization

Sunny Gupta, Amit Sethi

Domain-specific curvature is an appealing idea for domain generalization (DG), but curvature learning can denote substantially different computations. This paper evaluates one deliberately narrow implementation: the code calls it HyperDG, but it rescales Euclidean encoder features during training by learned positive scalars and uses an ordinary linear classifier on unscaled Euclidean features at inference. It does not implement a Lorentz or Poincaré representation, geodesic prediction, or a Sharpness-Aware Minimization inner loop. We audit the executed objective and evaluate six conditions on PACS, VLCS, Office Home, and TerraIncognita. The completed design contains 384 runs: six conditions, four held-out targets, and four run seeds per dataset. Checkpoints are selected using only the three source-validation environments. Inference first averages paired seed differences within each held-out target; targets, rather than 16 seed-by-target observations, are the per-dataset clusters. The full implementation's equal-dataset macro point estimate is 1.61 percentage points below native DomainBed ERM (95% clustered CI [-3.17, -0.04]). All four dataset point estimates favor ERM, but an…