Sharpness-aware minimization (SAM) is widely recognized for enhancing the generalization performance of deep neural networks. However, recent works have challenged the statement that flatness implies generalization, demonstrating that it is insufficient as the indicator of generalization. In this paper, we reveal an insightful phenomenon: among minima of similar sharpness, stochastic optimization algorithms tend to prefer those with lower nonuniformity. We define nonuniformity by both the magnitude and structure of the gradient noise, and show that it fundamentally differs from sharpness and plays a critical role in generalization. Specifically, we first theoretically prove that the expected generalization gap of models trained via stochastic optimization algorithm is positively correlated with nonuniformity (the magnitude of the gradient noise). Empirically, we show that nonuniformity exhibits a stronger correlation with generalization than sharpness, especially in Transformer models. Furthermore, we demonstrate that the nonuniformity (the structure of the gradient noise) more effectively guides the algorithm towards sparser solutions and exhibits better generalization performance than sharpness-based methods in the high-dimensional sparse regression problem. Finally, extensive experiments on various datasets and models confirm the advantages of nonuniformity for generalization: (1) optimization guided by nonuniformity achieves better generalization compared to those achieved through flatness (including standard training, transfer learning, hyperparameter sensitivity and robustness to label noise); (2) model architecture (such as depth and width) is closely related to nonuniformity.

Automatic modulation classification (AMC) in complex electromagnetic environments is essential for ensuring reliable spectrum surveillance. However, most existing AMC algorithms primarily rely on the data engineer and focus on improving accuracy under high signal-to-noise ratio (SNR) conditions, making it difficult to maintain robust and accurate performance in real-world unstable SNR scenarios. In order to address this challenge, a knowledge-guided spatial-temporal fusion network for low-SNR modulation recognition is proposed, named STFNet. Firstly, aiming at the instability of the model classification caused by the single input mode, the enhanced constellation diagram and the I/Q signal are simultaneously introduced as the inputs of the STFNet. Furthermore, the STFNet is designed as a dual-path adaptive multimodal fusion architecture to simultaneously exploit the spatial features of the enhanced constellation diagram and the temporal features of the I/Q signal. Secondly, an AMC-specific transfer learning (AMC-TL) strategy is introduced to enhance the global robustness of spatial representations through contrastive learning. More importantly, a domain knowledge-guided mixture of experts (DKG-MoE) is proposed to incorporate traditional features into the expert routing process, which improves temporal recognition accuracy. Then, an adaptive modality attention (AMA) module is developed to balance the accuracy under high SNR and the robustness under low SNR. Finally, extensive experiments on four benchmark datasets demonstrate that the proposed method achieves a 4.13% accuracy improvement under low SNR conditions (-20 dB ∼ 0 dB) and outperforms all state-of-the-art (SOTA) methods in overall average accuracy (65.57%). The code is publicly available at https://github.com/yoho78/STFNet.