Contextual Information Allocation in Shared-State Cognitive Models: An Information-Theoretic Bound

arXiv:2602.16716v4 Announce Type: replace-cross Abstract: Context-sensitive behavior can be modeled by enriching an internal state, by allowing a response rule to access context directly, or by preserving a shared state while introducing an auxiliary criterion or control variable. This paper isolates an information-theoretic constraint on the third architecture. Let $C$ denote context, $S$ a candidate internal or latent state, $O$ an observable response, and $M$ an auxiliary variable such that $O\perp C\mid(S,M)$. Then \[ I(C;O\mid S)\le I(C;M\mid S)\le H(M\mid S). \] Once a shared state has been specified, residual context dependence in behavior therefore lower-bounds both the context information and the conditional entropy that an auxiliary context-mediating mechanism must carry. The bound is representation-relative rather than a measure of state-space size or a universal contextuality measure. A worked recognition-memory example shows how the quantity can be computed for payoff-induced criterion shifts and compared across alternative representational allocations. Ontological contextuality and quantum probability are treated as a separate specialization rather than as prerequisites for the cognitive interpretation. More broadly, the framework provides a basis for analyzing context-memory-control trade-offs in cognitive models and artificial agents that must maintain coherent behavior across changing contexts under bounded internal representations.

Abstract:Context-sensitive behavior can be modeled by enriching an internal state, by allowing a response rule to access context directly, or by preserving a shared state while introducing an auxiliary criterion or control variable. This paper isolates an information-theoretic constraint on the third architecture. Let $C$ denote context, $S$ a candidate internal or latent state, $O$ an observable response, and $M$ an auxiliary variable such that $O\perp C\mid(S,M)$. Then \[ I(C;O\mid S)\le I(C;M\mid S)\le H(M\mid S). \] Once a shared state has been specified, residual context dependence in behavior therefore lower-bounds both the context information and the conditional entropy that an auxiliary context-mediating mechanism must carry. The bound is representation-relative rather than a measure of state-space size or a universal contextuality measure. A worked recognition-memory example shows how the quantity can be computed for payoff-induced criterion shifts and compared across alternative representational allocations. Ontological contextuality and quantum probability are treated as a separate specialization rather than as prerequisites for the cognitive interpretation. More broadly, the framework provides a basis for analyzing context-memory-control trade-offs in cognitive models and artificial agents that must maintain coherent behavior across changing contexts under bounded internal representations.

Version 4: The manuscript was substantially revised to emphasize contextual information allocation in shared-state cognitive models. We strengthened the information-theoretic result, added tightness conditions and a worked recognition-memory example, clarified its distinction from contextuality measures, and expanded discussion of cognitive modeling and AI-agent context-memory-control trade-offs

Artificial Intelligence (cs.AI); Information Theory (cs.IT); Quantum Physics (quant-ph)

arXiv:2602.16716 [cs.AI]

(or arXiv:2602.16716v4 [cs.AI] for this version)

From: Song-Ju Kim Dr. [view email] [v1] Tue, 3 Feb 2026 19:20:10 UTC (11 KB) [v2] Sat, 21 Feb 2026 02:25:37 UTC (11 KB) [v3] Wed, 15 Apr 2026 10:37:25 UTC (12 KB) [v4] Tue, 22 Sep 2026 19:18:02 UTC (14 KB)

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Contextual Information Allocation in Shared-State Cognitive Models: An Information-Theoretic Bound

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