Scaled Legendre HiPPO operator
Mathematical Methods AIMech:HiPPOLegS DRAFT
Aliases: HiPPO-LegS
The HiPPO projection operator using the uniform measure over the full elapsed interval from zero to the current time, with scaled-Legendre coefficients evolving under explicitly time-dependent linear memory dynamics.
Identity Notes & Concept Scope
HiPPO-LegS is the scaled-Legendre instantiation of the broader HiPPO framework. Its time-dependent operator differs from a fixed state matrix used to initialize a later S4 model and from the fixed-width translated-Legendre window.
Claims & Grounded Evidence
1 Claim
Mechanism
#sequence-mechanism
Use the normalized uniform measure on [0,t] and the corresponding Legendre basis. For positive time, the coefficient derivative is minus A times the current coefficient vector divided by t, plus B times the current signal divided by t; the source specifies a lower-triangular A and a fixed B and derives discrete recurrences from these dynamics.
⚠️ Curated Limitations & Negative Results
- The displayed differential formula contains 1/t and applies for positive t; an executable initialization at the time origin is not supplied by this record.
- Equation 4 illustrates an Euler discretization; the paper also uses bilinear and zero-order-hold schemes. The operator's approximation properties do not guarantee arbitrary downstream-network accuracy.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:MathematicalFunction
Mathematical Function
|
broad_match | This specific scaled-Legendre projection maps signal history to a coefficient-valued function. It is a mathematical operator, not itself a complete neural network or external memory store. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
original-paper
|
Albert Gu, Tri Dao, Stefano Ermon, Atri Rudra, Christopher Ré
|
primary paper
full_text
|
sha256:e99e0063517a…
|
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/HiPPOLegS.yaml