The closed-loop adaptation law is stable only when the adaptation gain is small relative to behavioural responsiveness¶
Claim · All claims
Evidence · 1 study · theoreticalr3·q1
Currency · newest study 2026 · not yet checked against its sources · not reviewed by a person · recheck by 2029: tool and model accuracy changes quickly
Subclaims¶
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q1 i? With a first-order lag on intensity and Lipschitz behavioural response, the closed loop is a contraction whenever the product of the adaptation coefficient and the two Lipschitz constants is below one, yielding a unique equilibrium. → Gupta 2026
Evidence¶
Gupta 2026¶
Gupta, L. R., Kaur, K., Ram, D. S., & Parani, P. (2026). Behaviorally Adaptive Visual Diversion for Inclusive and Resilient Digital Assessment Delivery. arXiv preprint, under review at IEEE Transactions on Learning Technologies. https://arxiv.org/abs/2608.03531 doi:10.48550/arxiv.2608.03531
q1 · i? · theoretical · r3
Analytical derivation (Equations 9a-9b, Theorem 5) using the Banach fixed-point theorem: the lag rate-limits intensity so a behavioural jump produces a ramp rather than a step, making the flash-rate constraint enforceable at the intensity level.
"If g is Lipschitz with constant Lg and the behavioural response to on-screen intensity is Lipschitz with constant LB, the closed loop is a contraction whenever β Lg LB < 1"
Discussion¶
Related Claims¶
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Page metadata
| Field | Value |
|---|---|
type |
claim |
id |
bavd-closed-loop-stability-contraction-condition |
title |
The closed-loop adaptation law is stable only when the adaptation gain is small relative to behavioural responsiveness |
description |
The closed-loop adaptation law is stable only when the adaptation gain is small relative to behavioural responsiveness |
status |
review |
evidence_strength |
weak |
newest_evidence |
2026 |
recheck_by |
2029 |
generated |
by process:wiki-ingest on 2026-10-10 |
trust |
unverified — no one has confirmed this page's content |
sources |
1 — gupta-2026 |
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