arXiv：cs.AI· Sunny Gupta, Amit Sethi·· 22 小时前
对曲率启发的标量特征缩放用于域泛化的受控评估
A Controlled Evaluation of Curvature Inspired Scalar Feature Scaling for Domain Generalization
AI 导读
论文对代码中称为 HyperDG 的实现做了受控评估：它在训练时用可学习的正标量重新缩放欧氏编码器特征，推理时对未缩放特征使用普通线性分类器，并未实现 Lorentz/Poincaré 表示、测地线预测或 SAM 内循环。
正文
Abstract: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 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 $\pm 1$ 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.
| Comments: | Accepted at TMLR, 9 pages, 1 figures |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computer Vision and Pattern Recognition (cs.CV) |
| ACM classes: | I.2.6; C.1.4; D.1.3; I.5.1; H.3.4; I.2.10; I.4.0; I.4.1; I.4.2; I.4.6; I.4.7; I.4.8; I.4.9; I.4.10; I.5.1; I.5.2; I.5.4; J.2; I.2.11; I.2.10 |
| Cite as: | arXiv:2610.18227 [cs.LG] |
| (or arXiv:2610.18227v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.18227 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Sunny Gupta [view email]
[v1]
Tue, 13 Oct 2026 11:56:18 UTC (65 KB)
来源：arXiv：cs.AI · arxiv.org