Ying Zhu

Hanwei Zhang, Ying Zhu, Dan Wang et al.

State space models (SSMs) with selection mechanisms and hardware-aware architectures, namely Mamba, have recently demonstrated significant promise in long-sequence modeling. Since the self-attention mechanism in transformers has quadratic complexity with image size and increasing computational demands, the researchers are now exploring how to adapt Mamba for computer vision tasks. This paper is the first comprehensive survey aiming to provide an in-depth analysis of Mamba models in the field of computer vision. It begins by exploring the foundational concepts contributing to Mamba's success, including the state space model framework, selection mechanisms, and hardware-aware design. Next, we review these vision mamba models by categorizing them into foundational ones and enhancing them with techniques such as convolution, recurrence, and attention to improve their sophistication. We further delve into the widespread applications of Mamba in vision tasks, which include their use as a backbone in various levels of vision processing. This encompasses general visual tasks, Medical visual tasks (e.g., 2D / 3D segmentation, classification, and image registration, etc.), and Remote Sensing visual tasks. We specially introduce general visual tasks from two levels: High/Mid-level vision (e.g., Object detection, Segmentation, Video classification, etc.) and Low-level vision (e.g., Image super-resolution, Image restoration, Visual generation, etc.). We hope this endeavor will spark additional interest within the community to address current challenges and further apply Mamba models in computer vision.

Wee Chaimanowong, Ying Zhu

Many machine learning models leverage group invariance which is enjoyed with a wide-range of applications. For exploiting an invariance structure, one common approach is known as \emph{frame averaging}. One popular example of frame averaging is the \emph{group averaging}, where the entire group is used to symmetrize a function. Another example is the \emph{canonicalization}, where a frame at each point consists of a single group element which transforms the point to its orbit representative, for example, sorting. Compared to group averaging, canonicalization is more efficient computationally. However, it results in non-differentiablity or discontinuity of the canonicalized function. As a result, the theoretical performance of canonicalization has not been given much attention. In this work, we establish an approximation theory for canonicalization. Specifically, we bound the point-wise and $L^2(\mathbb{P})$ approximation errors as well as the eigenvalue decay rates associated with a canonicalization trick applied to reproducing kernels. We discuss two key insights from our theoretical analyses and why they point to an interesting future research direction on how one can choose a design to fully leverage canonicalization in practice.