In recent years, there has been a growing interest in integrating linear
state-space models (SSM) in deep neural network architectures of foundation
models. This is exemplified by the recent success of Mamba, showing better
performance than the state-of-the-art Transformer architectures in language
tasks. Foundation models, like e.g. GPT-4, aim to encode sequential data into a
latent space in order to learn a compressed representation of the data. The
same goal has been pursued by control theorists using SSMs to efficiently model
dynamical systems. Therefore, SSMs can be naturally connected to deep sequence
modeling, offering the opportunity to create synergies between the
corresponding research areas. This paper is intended as a gentle introduction
to SSM-based architectures for control theorists and summarizes the latest
research developments. It provides a systematic review of the most successful
SSM proposals and highlights their main features from a control theoretic
perspective. Additionally, we present a comparative analysis of these models,
evaluating their performance on a standardized benchmark designed for assessing
a model's efficiency at learning long sequences.

近年来，将线性状态空间模型（SSM）整合到深度神经网络架构的基础模型中的兴趣日益增长。该论文对控制理论家介绍了 SSM 基于架构，并总结了最新的研究进展，对最成功的 SSM 提案进行了系统回顾，从控制理论的角度突出了它们的主要特点。此外，我们针对用于评估模型在学习长序列方面效率的标准基准进行了这些模型的性能比较分析。