Contextuality from Single-State Representations: An Information-Theoretic Principle for Adaptive Intelligence
arXiv:2602.16716v1 Announce Type: new Abstract: Adaptive systems often operate across multiple contexts while reusing a fixed internal state space due to constraints on memory, representation, or physical resources. Such single-state reuse is ubiquitous in natural and artificial intelligence, yet its fundamental representational consequences remain poorly understood. We show that contextuality is not a peculiarity of quantum mechanics, but an inevitable consequence of single-state reuse in classical probabilistic representations. Modeling contexts as interventions acting on a shared internal state, we prove that any classical model reproducing contextual outcome statistics must incur an irreducible information-theoretic cost: dependence on context cannot be mediated solely through the internal state. We provide a minimal constructive example that explicitly realizes this cost and clarifies its operational meaning. We further explain how nonclassical probabilistic frameworks avoid this
arXiv:2602.16716v1 Announce Type: new Abstract: Adaptive systems often operate across multiple contexts while reusing a fixed internal state space due to constraints on memory, representation, or physical resources. Such single-state reuse is ubiquitous in natural and artificial intelligence, yet its fundamental representational consequences remain poorly understood. We show that contextuality is not a peculiarity of quantum mechanics, but an inevitable consequence of single-state reuse in classical probabilistic representations. Modeling contexts as interventions acting on a shared internal state, we prove that any classical model reproducing contextual outcome statistics must incur an irreducible information-theoretic cost: dependence on context cannot be mediated solely through the internal state. We provide a minimal constructive example that explicitly realizes this cost and clarifies its operational meaning. We further explain how nonclassical probabilistic frameworks avoid this obstruction by relaxing the assumption of a single global joint probability space, without invoking quantum dynamics or Hilbert space structure. Our results identify contextuality as a general representational constraint on adaptive intelligence, independent of physical implementation.
Executive Summary
This article presents a novel information-theoretic principle that explains the inevitability of contextuality in adaptive systems with single-state reuse. By modeling contexts as interventions on a shared internal state, the authors prove that classical models reproducing contextual outcome statistics incur an irreducible information-theoretic cost. This finding has significant implications for our understanding of adaptive intelligence and its fundamental representational constraints. The authors also demonstrate how nonclassical probabilistic frameworks, such as those used in quantum mechanics, avoid this obstruction without invoking quantum dynamics. This research contributes to the growing body of work on the intersection of information theory, probabilistic modeling, and cognitive science.
Key Points
- ▸ Contextuality is not a peculiarity of quantum mechanics, but an inevitable consequence of single-state reuse in classical probabilistic representations.
- ▸ Classical models reproducing contextual outcome statistics incur an irreducible information-theoretic cost.
- ▸ Nonclassical probabilistic frameworks, such as those used in quantum mechanics, avoid this obstruction without invoking quantum dynamics.
Merits
Strength
The article presents a novel and well-motivated information-theoretic principle that sheds new light on the fundamental representational constraints of adaptive intelligence.
Demerits
Limitation
The article assumes a specific mathematical framework, which may limit its applicability to other areas of study.
Expert Commentary
This article represents a significant contribution to the field of information theory and its applications in cognitive science. The authors' use of a novel information-theoretic principle to explain the inevitability of contextuality in adaptive systems is a masterful demonstration of the power of mathematical modeling in understanding complex phenomena. While the article assumes a specific mathematical framework, its findings have far-reaching implications for the development of adaptive artificial intelligence systems and our understanding of the fundamental representational constraints of adaptive intelligence.
Recommendations
- ✓ Future research should explore the applicability of this information-theoretic principle to other areas of study, such as decision-making under uncertainty and information-theoretic principles in cognitive science.
- ✓ The findings of this article should be taken into account in the design of intelligent systems and policies that rely on adaptive intelligence, to ensure that they are cognizant of the fundamental representational constraints of adaptive intelligence.
