Baiyuan Chen

Baiyuan Chen

Robustness is a critical aspect of machine learning models. Existing robustness evaluation approaches often lack theoretical generality or rely heavily on empirical assessments, limiting insights into the structural factors contributing to robustness. Moreover, theoretical robustness analysis is not applicable for direct comparisons between models. To address these challenges, we propose $\textit{TopoLip}$, a metric based on layer-wise analysis that bridges topological data analysis and Lipschitz continuity for robustness evaluation. TopoLip provides a unified framework for both theoretical and empirical robustness comparisons across different architectures or configurations, and it reveals how model parameters influence the robustness of models. Using TopoLip, we demonstrate that attention-based models typically exhibit smoother transformations and greater robustness compared to convolution-based models, as validated through theoretical analysis and adversarial tasks. Our findings establish a connection between architectural design, robustness, and topological properties.

Baiyuan Chen, Shinji Ito, Masaaki Imaizumi

Transformers have demonstrated exceptional performance across a wide range of domains. While their ability to perform reinforcement learning in-context has been established both theoretically and empirically, their behavior in non-stationary environments remains less understood. In this study, we address this gap by showing that transformers can achieve nearly optimal dynamic regret bounds in non-stationary settings. We prove that transformers are capable of approximating strategies used to handle non-stationary environments and can learn the approximator in the in-context learning setup. Our experiments further show that transformers can match or even outperform existing expert algorithms in such environments.

Baiyuan Chen

This paper presents an innovative enhancement to the Sphere as Prior Generative Adversarial Network (SP-GAN) model, a state-of-the-art GAN designed for point cloud generation. A novel method is introduced for point cloud generation that elevates the structural integrity and overall quality of the generated point clouds by incorporating topological priors into the training process of the generator. Specifically, this work utilizes the K-means algorithm to segment a point cloud from the repository into clusters and extract centroids, which are then used as priors in the generation process of the SP-GAN. Furthermore, the discriminator component of the SP-GAN utilizes the identical point cloud that contributed the centroids, ensuring a coherent and consistent learning environment. This strategic use of centroids as intuitive guides not only boosts the efficiency of global feature learning but also substantially improves the structural coherence and fidelity of the generated point clouds. By applying the K-means algorithm to generate centroids as the prior, the work intuitively and experimentally demonstrates that such a prior enhances the quality of generated point clouds.