Jiankai Zuo

Jun Yan, Weiquan Huang, Jiankai Zuo et al.

Adversarial training (AT) remains one of the most reliable empirical defenses against adversarial attacks. Its robustness critically depends on how the underlying min-max objective is optimized. In practice, Stochastic Gradient Descent (SGD) optimizer remains the default optimization choice for AT, whereas adaptive optimizers often improve standard training but may yield inferior robustness. Recently, the Muon optimizer, which orthogonalizes matrix-valued updates via an approximate polar decomposition, has achieved notable success in large-scale training at a memory cost comparable to SGD. This raises a security-relevant question: \textit{can orthogonalized optimization improve AT under strong and heterogeneous threat models?} Focusing on this problem, we conduct a comprehensive theoretical and empirical study. Theoretically, we show that Muon imposes a spectral-norm stability ceiling on matrix updates, limiting uncontrolled spectral growth in the training dynamics without explicitly shrinking the learned weights. Empirically, across five architectures and three $\ell_p$ threat models ($\ell_\infty$, $\ell_1$, $\ell_2$) and their union, Muon is competitive with SGD on CNNs and substantially outperforms AdamW on both CNNs and ViTs. These results identify optimizer geometry as a security-relevant factor in adversarial training, while clarifying the empirical regimes in which orthogonalized updates are beneficial. Overall, our findings highlight optimizer design as a security-critical component of AT.

Zihao Yao, Jiankai Zuo, Yaying Zhang

Time series data plays a pivotal role in a wide variety of fields but faces challenges related to privacy concerns. Recently, synthesizing data via diffusion models is viewed as a promising solution. However, existing methods still struggle to capture long-range temporal dependencies and complex channel interrelations. In this research, we aim to utilize the sequence modeling capability of a State Space Model called Mamba to extend its applicability to time series data generation. We firstly analyze the core limitations in State Space Model, namely the lack of consideration for correlated temporal lag and channel permutation. Building upon the insight, we propose Lag Fusion Mamba and Permutation Scanning Mamba, which enhance the model's ability to discern significant patterns during the denoising process. Theoretical analysis reveals that both variants exhibit a unified matrix multiplication framework with the original Mamba, offering a deeper understanding of our method. Finally, we integrate two variants and introduce Diffusion Mamba for Time Series (DiM-TS), a high-quality time series generation model that better preserves the temporal periodicity and inter-channel correlations. Comprehensive experiments on public datasets demonstrate the superiority of DiM-TS in generating realistic time series while preserving diverse properties of data.