Paper · arXiv 2503.11224
Technologies on Effectiveness and Efficiency: A Survey of State Spaces Models
Xingtai Lv, Youbang Sun, Kaiyan Zhang, Shang Qu, Xuekai Zhu, Yuchen Fan, Yi Wu, Ermo Hua, Xinwei Long, Ning Ding, Bowen Zhou
This survey provides a comprehensive overview of State Space Models (SSMs), their mathematical foundations, and their applications, emphasizing their efficiency and effectiveness compared to transformer-based models.
Abstract
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.