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Linear State-Space Layer (LSSL)

2021
Computer Science (theoretical)Machine Learning TheoryArchitecture Componentfoundational

Deep-learning layer unifying recurrent, convolutional, and continuous-time models under one linear state-space formulation (Gu, Johnson, Goel, Saab, Dao, Rudra & Ré, "Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers," NeurIPS 2021). Mamba's own Theorem 1 is stated as a direct improvement of this paper's Lemma 3.1.

Originators

  • Gu, A.
  • Johnson, I.
  • Goel, K.
  • Saab, K.
  • Dao, T.
  • Rudra, A.
  • Ré, C.

Landmark Paper

W3212492847 ↗
Not retracted (OpenAlex)

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

Connections

  • evolved into S4 (Structured State Spaces)
    basis: reasoned

    Mamba's own reference list bundles S4's citation as "Gu, Goel, and Ré 2022; Gu, Johnson, Goel, et al. 2021" -- S4 is presented as the efficient, practical formalization of LSSL's original linear state-space layer, same authorship carrying the idea forward.

  • is component of Mamba
    basis: reasoned

    Section 3.5.1: "Theorem 1 is an improvement of Gu, Johnson, Goel, et al. (2021, Lemma 3.1) generalizing to the ZOH discretization and input-dependent gates" -- Mamba's central theoretical result is stated as a direct extension of LSSL's own proven lemma, not just a shared research lineage.