Peipei Yuan

Xuelin Zhang, Peipei Yuan

Bilevel optimization and bilevel minimax optimization have recently emerged as unifying frameworks for a range of machine-learning tasks, including hyperparameter optimization and reinforcement learning. The existing literature focuses on empirical efficiency and convergence guarantees, leaving a critical theoretical gap in understanding how well these algorithms generalize. To bridge this gap, we provide the first systematic generalization analysis for first-order gradient-based bilevel minimax solvers with lower-level minimax problems. Specifically, by leveraging algorithmic stability arguments, we derive fine-grained generalization bounds for three representative algorithms, including single-timescale stochastic gradient descent-ascent, and two variants of two-timescale stochastic gradient descent-ascent. Our results reveal a precise trade-off among algorithmic stability, generalization gaps, and practical settings. Furthermore, extensive empirical evaluations corroborate our theoretical insights on realistic optimization tasks with bilevel minimax structures.

Peipei Yuan, Zijing Xie, Shuo Ye et al.

Generative artificial intelligence holds significant potential for abuse, and generative image detection has become a key focus of research. However, existing methods primarily focused on detecting a specific generative model and emphasizing the localization of synthetic regions, while neglecting the interference caused by image size and style on model learning. Our goal is to reach a fundamental conclusion: Is the image real or generated? To this end, we propose a diffusion model-based generative image detection framework termed Hierarchical Retrospection Refinement~(HRR). It designs a multi-scale style retrospection module that encourages the model to generate detailed and realistic multi-scale representations, while alleviating the learning biases introduced by dataset styles and generative models. Additionally, based on the principle of correntropy sparse additive machine, a feature refinement module is designed to reduce the impact of redundant features on learning and capture the intrinsic structure and patterns of the data, thereby improving the model's generalization ability. Extensive experiments demonstrate the HRR framework consistently delivers significant performance improvements, outperforming state-of-the-art methods in generated image detection task.

Yanfang Tao, Peipei Yuan, Biqin Song

Learning with Fredholm kernel has attracted increasing attention recently since it can effectively utilize the data information to improve the prediction performance. Despite rapid progress on theoretical and experimental evaluations, its generalization analysis has not been explored in learning theory literature. In this paper, we establish the generalization bound of least square regularized regression with Fredholm kernel, which implies that the fast learning rate O(l^{-1}) can be reached under mild capacity conditions. Simulated examples show that this Fredholm regression algorithm can achieve the satisfactory prediction performance.