State Space Models

A guide to structured memory and complex dynamics in deep learning.

A mathematical text on the S4–Mamba line of neural state space sequence models. It begins with a continuous-time state space model, discretises it for sampled sequences, gives the state a structured memory, and follows that construction through to selective and matrix-view models.

Read it at https://ssm.guide.

Roadmap

The book is released as chapters are finished. Coming next are Selective State Spaces (the Mamba block), Matrix Views and State Space Duality (Mamba-2), and Modern Refinements (Mamba-3 and attention hybrids).

Contributing

Corrections, clearer explanations, and worked examples are welcome. See CONTRIBUTING.md and CODE_OF_CONDUCT.md.

Citing

@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}
}

Machine-readable metadata is in CITATION.cff.

Licence

© 2026 Cosmo Santoni.

• Text, figures, and equations: CC BY 4.0 — see LICENSE.
• Code: Apache 2.0 — see LICENSE-CODE.