Invariance Principle Meets Vicinal Risk Minimization

TL;DR

This work tackles out-of-distribution generalization by integrating invariance with vicinal data augmentation. It introduces a domain-shared Semantic Data Augmentation (SDA) module and a Variance Risk Minimization (VRM) framework, forming Vicinal Invariant Risk Minimization (VIRM) to expand inter-domain feature overlap while preserving label consistency. The authors provide a Rademacher-complexity based generalization bound and demonstrate state-of-the-art performance on four challenging DG benchmarks (PACS, VLCS, OfficeHome, TerraIncognita). Through ablations and visualizations, they show that domain-shared SDA increases feature overlap and that VREx on original features yields the best DG performance while maintaining label-consistency in augmented samples. The approach offers a principled and effective path for robust OOD generalization in vision tasks with large domain diversity.

Abstract

Deep learning models excel in computer vision tasks but often fail to generalize to out-of-distribution (OOD) domains. Invariant Risk Minimization (IRM) aims to address OOD generalization by learning domain-invariant features. However, IRM struggles with datasets exhibiting significant diversity shifts. While data augmentation methods like Mixup and Semantic Data Augmentation (SDA) enhance diversity, they risk over-augmentation and label instability. To address these challenges, we propose a domain-shared Semantic Data Augmentation (SDA) module, a novel implementation of Variance Risk Minimization (VRM) designed to enhance dataset diversity while maintaining label consistency. We further provide a Rademacher complexity analysis, establishing a tighter generalization error bound compared to baseline methods. Extensive evaluations on OOD benchmarks, including PACS, VLCS, OfficeHome, and TerraIncognita, demonstrate consistent performance improvements over state-of-the-art domain generalization methods.

Figures (4)

• Figure 1: 2D classification example illustrating domain generalization failed. The dashed lines indicate generalization failure predictors.
• Figure 2: (a) and (b) Example of generalized failure in 2D classification when features do not satisfy support overlap leading to model generalization failure; (c) Example of generalized success in 2D classification using semantic data augmentation to generate new samples.
• Figure 3: Kernel density estimation of feature distributions across domains on the VLCS dataset (Category: Car).
• Figure 4: Visualization of feature distributions using UMAP on the VLCS dataset (training set: VLS, test set: C).

Theorems & Definitions (13)

• Definition 1: IRM
• Definition 2: VRM
• Definition 3: VIRM
• Lemma 1
• Lemma 2
• Theorem 1
• Lemma 1
• Proof 1: Lower Bound of \ref{['lemma:bound']}
• Proof 2: Upper Bound of \ref{['lemma:bound']}
• Lemma 2