  In the post-deep learning era, the Transformer architecture has demonstrated
its powerful performance across pre-trained big models and various downstream
tasks. However, the enormous computational demands of this architecture have
deterred many researchers. To further reduce the complexity of attention
models, numerous efforts have been made to design more efficient methods. Among
them, the State Space Model (SSM), as a possible replacement for the
self-attention based Transformer model, has drawn more and more attention in
recent years. In this paper, we give the first comprehensive review of these
works and also provide experimental comparisons and analysis to better
demonstrate the features and advantages of SSM. Specifically, we first give a
detailed description of principles to help the readers quickly capture the key
ideas of SSM. After that, we dive into the reviews of existing SSMs and their
various applications, including natural language processing, computer vision,
graph, multi-modal and multi-media, point cloud/event stream, time series data,
and other domains. In addition, we give statistical comparisons and analysis of
these models and hope it helps the readers to understand the effectiveness of
different structures on various tasks. Then, we propose possible research
points in this direction to better promote the development of the theoretical
model and application of SSM. More related works will be continuously updated
on the following GitHub:
https://github.com/Event-AHU/Mamba_State_Space_Model_Paper_List.
