Deep models often fail to generalize well in test domains when the data distribution differs from that in the training domain. Among numerous approaches to address this Out-of-Distribution (OOD) generalization problem, there has been a growing surge of interest in exploiting Adversarial Training (AT) to improve OOD performance. Recent works have revealed that the robust model obtained by conducting sample-wise AT also retains transferability to biased test domains. In this paper, we empirically show that sample-wise AT has limited improvement on OOD performance. Specifically, we find that AT can only maintain performance at smaller scales of perturbation while Universal AT (UAT) is more robust to larger-scale perturbations. This provides us with clues that adversarial perturbations with universal (low dimensional) structures can enhance the robustness against large data distribution shifts that are common in OOD scenarios. Inspired by this, we propose two AT variants with low-rank structures to train OOD-robust models. Extensive experiments on DomainBed benchmark show that our proposed approaches outperform Empirical Risk Minimization (ERM) and sample-wise AT.

The purpose of this study is to evaluate the validity of measuring grammatical diversity with a specifically designed Lexical Diversity Assessment Tool (LDAT). A secondary objective is to use LDAT to determine if the level of difficulty assigned to English as a Second Language (ESL) texts corresponds to increases in grammatical, lexical, and temporal diversity. Other methods of lexical diversity assessment, such as type-token ratio (TTR), have been used with varying accuracy in an effort to determine the complexity or level of texts. We analyzed 120 ESL texts independently assigned by their sources to one of four levels (Beginner, Lower-intermediate, Upper-intermediate, and Advanced). We demonstrated that LDAT significantly reflected the grammatical diversity within these texts. While the findings conflicted with the prediction that grammatical and lexical diversity would increase with assigned level, we concluded that the implementation of LDAT in text design could provide reliable assessments of grammatical diversity.