State Space Models
A guide to structured memory and complex dynamics in deep learning
Open Edition · 2026
Changelog
- [Jun 2026] First public preview. Foundations and Structured State Spaces & S4 chapters available.
Cite this book
@book{santoni2026ssm,
author = {Santoni, Cosmo},
title = {State Space Models: A guide to structured memory and complex dynamics in deep learning},
year = {2026},
note = {Open Edition},
doi = {10.5281/zenodo.20736327},
url = {https://ssm.guide}
}
Table of contents
- 1 Introduction
- 2 State as Memory
- 3 Continuous-Time Linear State Spaces
- 4 Discretisation
- 5 Recurrence, Convolution, and Toeplitz Maps
- 6 Transfer Functions and Kernel Generation
- 7 The Memory Problem
- 8 HiPPO
- 9 Structured State Matrices
- 10 The S4 Kernel Algorithm
- 11 Diagonal State Spaces: DSS, S4D, and S5