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

arXiv: https://arxiv.org/abs/2610.18227 · HTML: https://mlsanity.com/paper/2610.18227/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 17 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 14 of 14)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Learning Fine-grained Domain Generalization via Hyperbolic State Space Hallucination](https://mlsanity.com/paper/2504.08020/) (2025)
- [Curvature Learning for Generalization of Hyperbolic Neural Networks](https://mlsanity.com/paper/2508.17232/) (2025)
- [HypCBC: Domain-Invariant Hyperbolic Cross-Branch Consistency for Generalizable Medical Image Analysis](https://mlsanity.com/paper/2602.03264/) (2026)

## Abstract (arXiv)

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 Poincar'e 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 exact four-dataset sign-flip test gives p = .125 and Holm-adjusted p = .250; we therefore claim no adjusted evidence of a difference. The cleaner domain-specificity contrast, separate learned source scales without their variance penalty versus one shared learned source scale, is -0.13 pp (95% CI [-0.53, 0.27]). Its 90% CI lies within a revision-stage ± 1 pp smallest effect of practical interest (TOST p = .003), supporting equivalence only for the source-selected suite macro, not every dataset, target, or final-step endpoint. The study thus supplies a bounded negative result for this scalar training package; it does not test or refute genuine hyperbolic representation learning.