Contextuality from Single-State Representations: An Information-Theoretic Principle for Adaptive Intelligence

2026-02-20 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Advanced, extended

Summary

Research from SOBIN Institute LLC demonstrates that adaptive systems reusing a fixed internal state space across multiple contexts incur an irreducible information-theoretic cost when using classical probabilistic representations. This cost, quantified as $H(M)\geq I(C;O\mid S)>0$, signifies that contextual dependence cannot be mediated solely through the internal state without additional contextual information $M$. The study defines "single-state representation" as a fixed internal state space $\mathcal{S}$ not indexed by context, and "interventions" as context-modifying transformations on $\mathcal{S}$. A constructive example illustrates how incompatible marginal distributions under single-state constraints necessitate this additional information. Nonclassical probabilistic frameworks, by relaxing the assumption of a single global probability space, avoid this obstruction, suggesting contextuality is a general representational constraint rather than a quantum-specific phenomenon.

Key takeaway

For AI Researchers designing adaptive systems with fixed internal state spaces, this work highlights a fundamental trade-off: classical probabilistic models will inherently incur an information-theoretic cost to manage contextual dependence. You should explore nonclassical probabilistic frameworks, not for their physical interpretations, but for their structural ability to maintain consistency across interventions without expanding representational resources, thereby offering a more economical approach to context sensitivity.

Key insights

Single-state classical representations incur an irreducible information cost when handling contextual dependence.

Principles

• Contextuality is a general representational constraint.
• Fixed internal state reuse creates information-theoretic costs.
• Nonclassical probability avoids this cost by relaxing global joint representability.

Method

The study formalizes single-state representations and interventions, then proves an information-theoretic obstruction $H(M)\geq I(C;O\mid S)$ for classical probabilistic models, illustrating it with a minimal constructive example.

In practice

• Consider nonclassical probability for bounded adaptive systems.
• Account for information costs in classical single-state designs.

Topics

• Contextuality
• Single-State Representations
• Information Theory
• Adaptive Intelligence
• Nonclassical Probability

Best for: AI Researcher, AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.