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Linear state-space layer

Layers & Modules AIMech:LinearStateSpaceLayer DRAFT

Aliases: LSSL

A sequence-to-sequence layer defined by discretizing a linear continuous-time state-space system, with a state recurrence and, for zero initial state, an equivalent convolutional representation plus a direct input term.

Identity Notes & Concept Scope LSSL denotes Gu and colleagues' component with state-space parameters and timescale, not the complete deep LSSL network, every recurrent network, or S4's later structured parameterization and kernel algorithm.

Claims & Grounded Evidence

1 Claim

Mechanism #sequence-mechanism

Discretize the state dynamics using a step size to obtain a recurrent state update and linear output map. With zero initial state, powers of the discretized state matrix between input and output projections form the convolution kernel. Separate feature channels use their own broadcast input/output parameters and timescales; complete networks add further layers and connections.

supports Source: Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers · Locator: Section 2 equations 3–5 and Sections 3.1–3.3, equations 6–7, PDF/printed pp. 4–6

⚠️ Curated Limitations & Negative Results

The simple convolution expression assumes zero initial state; a nonzero starting state contributes an additional term.
The layer is linear; nonlinear expressive power of stacked networks is not a property of a single standalone LSSL. Efficient recurrent updates and kernel construction depend on the selected state-matrix structure.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:Layer` Layer	broad_match	The source defines a sequence-representation transformation with a standard layer interface and separately composes complete networks. AIO Layer is the broader component class.

Evidence Sources & Primary Literature

1 Source

Source ID	Publication / Document	Type / Access	Reference & Checksum
`original-paper`	Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers Albert Gu, Isys Johnson, Karan Goel, Khaled Saab, Tri Dao, Atri Rudra, Christopher Ré	primary paper full_text	sha256:32c1802b55e5…

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/LinearStateSpaceLayer.yaml