Structured state space sequence model
Model Families AIMech:S4 DRAFT
Aliases: S4
A structured linear state-space sequence model whose normal-plus-low-rank state matrix is transformed to diagonal-plus-low-rank form for efficient convolution-kernel computation and recurrent sequence evaluation.
Identity Notes & Concept Scope
S4 denotes Gu, Goel and Ré's specific structured state-space construction, not every state-space model, S4D, an exponential-smoothing model, or Mamba's input-dependent selective state updates. Deep S4 networks compose these linear models with channel mixing and nonlinearities.
Claims & Grounded Evidence
1 Claim
Mechanism
#sequence-mechanism
Bilinear discretization gives recurrent and zero-initial-state convolutional views. A unitary basis change produces a diagonal-plus-low-rank state matrix; Cauchy-kernel evaluations, a low-rank Woodbury correction and an inverse FFT compute the finite convolution kernel.
⚠️ Curated Limitations & Negative Results
- This record follows arXiv v3's original diagonal-minus-PQ* parameterization. Section 3.4 notes possible numerical instability with right-half-plane eigenvalues and points to a later diagonal-minus-PP* revision; stability is not asserted unconditionally.
- The core S4 model is linear. A deep nonlinear S4 network adds channel mixing and nonlinear transformations; kernel computation is not the complete network.
- No universal accuracy, memory or wall-clock advantage is asserted.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:Model
Model
|
broad_match | The local concept is a particular parameterized sequence model. AIO Model is broader; a generic neural-network mapping would conflate its linear state-space core with the nonlinear networks built from it. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
original-paper
|
Albert Gu, Karan Goel, Christopher Ré
|
primary paper
full_text
|
ID: arXiv:2111.00396v3
sha256:872b4ef30231…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T04:26:45Z
Updated: 2026-10-11T04:26:45Z
Source File:
data/curated/S4.yaml