Adversarial Data Augmentation for Single Domain Generalization via Lyapunov Exponent-Guided Optimization

Single Domain Generalization (SDG) aims to develop models capable of generalizing to unseen target domains using only one source domain, a task complicated by substantial domain shifts and limited data diversity. Existing SDG approaches primarily rely on data augmentation techniques, which struggle to effectively adapt training dynamics to accommodate large domain shifts. To address this, we propose LEAwareSGD, a novel Lyapunov Exponent (LE)guided optimization approach inspired by dynamical systems theory. By leveraging LE measurements to modulate the learning rate, LEAwareSGD encourages model training near the edge of chaos, a critical state that optimally balances stability and adaptability. This dynamic adjustment allows the model to explore a wider parameter space and capture more generalizable features, ultimately enhancing the model's generalization capability. Extensive experiments on PACS, OfficeHome, and DomainNet demonstrate that LEAwareSGD yields substantial generalization gains, achieving up to 9.47% improvement on PACS in low-data regimes. These results underscore the effectiveness of training near the edge of chaos for enhancing model generalization capability in SDG tasks.

To further validate the effectiveness of our proposed LEAwareSGD optimizer, we conducted a comparison with four widely used optimization approaches, including Adam [14], AdamW [20], RMSprop [30], and SGD [26], on the PACS and OfficeHome datasets. As shown in Table 4, our proposed optimizer achieves the highest average accuracy of 69.46%, surpassing all other optimizers on the PACS dataset. In contrast, widely used optimizers such