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S4 (Structured State Spaces)

2021
Computer Science (theoretical)Machine Learning TheoryFrameworkfoundational

Efficient diagonal-plus-low-rank parameterization of state space sequence models, the first to make the LSSL/HiPPO line of models practical at scale (Gu, Goel & Ré, "Efficiently Modeling Long Sequences with Structured State Spaces," ICLR 2022). Mamba's own selective SSM layer (S6) is described as "S4 models with a selection mechanism."

Originators

  • Gu, A.
  • Goel, K.
  • Ré, C.

Landmark Paper

W3209374680 ↗
Not retracted (OpenAlex)

Checked 2026-09-19 — interim signal only, see docs/BASIC_ROADMAP.md Phase 10

Connections

  • is component of H3 (Hungry Hungry Hippos)
    basis: reasoned

    Mamba Appendix B.2: "H3 (Dao, Fu, Saab, et al. 2023) is motivated by combining S4 with linear attention... the first to generalize this formulation of linear attention to more general recurrences" -- H3's architecture is explicitly built on top of S4 as its inner SSM layer (confirmed in Table 6: "H3 ... SSM Layer: S4").