Technologies on Effectiveness and Efficiency: A Survey of State Spaces
  Models
Authors: name: Xingtai Lv, name: Youbang Sun, name: Kaiyan Zhang, name: Shang Qu, name: Xuekai Zhu, name: Yuchen Fan, name: Yi Wu, name: Ermo Hua, name: Xinwei Long, name: Ning Ding, name: Bowen Zhou

State Space Models (SSMs) have emerged as a promising alternative to the
popular transformer-based models and have been increasingly gaining attention.
Compared to transformers, SSMs excel at tasks with sequential data or longer
contexts, demonstrating comparable performances with significant efficiency
gains. In this survey, we provide a coherent and systematic overview for SSMs,
including their theoretical motivations, mathematical formulations, comparison
with existing model classes, and various applications. We divide the SSM series
into three main sections, providing a detailed introduction to the original
SSM, the structured SSM represented by S4, and the selective SSM typified by
Mamba. We put an emphasis on technicality, and highlight the various key
techniques introduced to address the effectiveness and efficiency of SSMs. We
hope this manuscript serves as an introduction for researchers to explore the
theoretical foundations of SSMs.