Domain generalization (DG) aims to learn models that can generalize well to unseen domains by training only on a set of source domains. Sharpness-Aware Minimization (SAM) has been a popular approach for this, aiming to find flat minima in the total loss landscape. However, we show that minimizing the total loss sharpness does not guarantee sharpness across individual domains. In particular, SAM can converge to fake flat minima, where the total loss may exhibit flat minima, but sharp minima are present in individual domains. Moreover, the current perturbation update in gradient ascent steps is ineffective in directly updating the sharpness of individual domains. Motivated by these findings, we introduce a novel DG algorithm, Decreased-overhead Gradual Sharpness-Aware Minimization (DGSAM), that applies gradual domain-wise perturbation to reduce sharpness consistently across domains while maintaining computational efficiency. Our experiments demonstrate that DGSAM outperforms state-of-the-art DG methods, achieving improved robustness to domain shifts and better performance across various benchmarks, while reducing computational overhead compared to SAM.

Time series modeling and analysis has become critical in various domains. Conventional methods such as RNNs and Transformers, while effective for discrete-time and regularly sampled data, face significant challenges in capturing the continuous dynamics and irregular sampling patterns inherent in real-world scenarios. Neural Differential Equations (NDEs) represent a paradigm shift by combining the flexibility of neural networks with the mathematical rigor of differential equations. This paper presents a comprehensive review of NDE-based methods for time series analysis, including neural ordinary differential equations, neural controlled differential equations, and neural stochastic differential equations. We provide a detailed discussion of their mathematical formulations, numerical methods, and applications, highlighting their ability to model continuous-time dynamics. Furthermore, we address key challenges and future research directions. This survey serves as a foundation for researchers and practitioners seeking to leverage NDEs for advanced time series analysis.