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Diagonal structured state space model

Model Families AIMech:S4D DRAFT

Aliases: S4D

A diagonal state-space sequence-model family that computes its discretized convolution kernel by a Vandermonde product, with explicit choices of discretization, state-matrix constraint and initialization.

Identity Notes & Concept Scope S4D is the family defined by Gu and colleagues, distinguished from S4's diagonal-plus-low-rank construction. The paper separates the earlier DSS configuration and the S4D-LegS, S4D-Inv and S4D-Lin initialization choices rather than treating all diagonal models as identical.

Claims & Grounded Evidence

1 Claim

Mechanism #sequence-mechanism

Discretize a diagonal continuous-time state model using bilinear or zero-order-hold rules. Kernel entries are sums of output and input coefficients multiplied by powers of the discretized diagonal state entries. Constrain the continuous state eigenvalue real parts using the chosen parameterization and initialize their spectrum according to the selected variant.

supports Source: On the Parameterization and Initialization of Diagonal State Space Models · Locator: Sections 3.1–3.4 and 4, equations 6–9 and Table 1, PDF/printed pp. 4–6

⚠️ Curated Limitations & Negative Results

Algebraic diagonalizability does not guarantee numerically stable representation or successful optimization; initialization and discretization remain explicit choices.
S4D-LegS convergence to the corresponding S4 dynamics is an infinite-state-size statement, not exact equality of all finite S4D and S4 models.
The inverse-law spectral asymptotics are presented as Conjecture 4, not a proved theorem. No universal performance advantage is asserted.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:Model` Model	broad_match	This is a parameterized family of linear sequence models; Model is broader and does not conflate the core with the nonlinear architectures built from it.

Evidence Sources & Primary Literature

1 Source

Source ID	Publication / Document	Type / Access	Reference & Checksum
`original-paper`	On the Parameterization and Initialization of Diagonal State Space Models Albert Gu, Ankit Gupta, Karan Goel, Christopher Ré	primary paper full_text	ID: doi:10.52202/068431-2607 sha256:95b3596262fa…

Curation Provenance

Curator: Codex

Method: ai_assisted

Model: GPT-6

Created: 2026-10-11T04:33:01Z

Updated: 2026-10-11T04:33:01Z

Source File: data/curated/S4D.yaml