Contextuality Inevitable in Single-State AI

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📄Read original on ArXiv AI

💡Proves contextuality unavoidable in classical AI states—key constraint for adaptive intelligence.

⚡ 30-Second TL;DR

What changed

Contextuality arises inevitably from single-state reuse across contexts

Why it matters

Reveals fundamental limits of classical representations in adaptive AI, potentially inspiring nonclassical approaches for more efficient intelligence.

What to do next

Download arXiv:2602.16716v1 and replicate the minimal constructive example in Python.

Who should care:Researchers & Academics

🧠 Deep Insight

Web-grounded analysis with 6 cited sources.

🔑 Key Takeaways

•Contextuality emerges inevitably from reusing fixed internal states across multiple contexts in adaptive AI systems due to resource constraints like memory limits.[1]
•Classical probabilistic models incur an irreducible information-theoretic cost to reproduce contextual outcome statistics, as context dependence cannot be fully mediated by the internal state.[1][2]
•A minimal constructive example in the paper demonstrates and operationalizes this information cost, clarifying its practical implications for AI representations.[1]

🛠️ Technical Deep Dive

The proof models contexts as interventions on a shared internal state in classical probabilistic representations, showing unavoidable contextuality from single-state reuse.[1]
Contextual statistics require either embedding context into the state or external labels with nonzero mutual information, quantifying the cost.[1][2]
Nonclassical models relax the global joint probability assumption, accommodating contextual operations efficiently.[1]

🔮 Future ImplicationsAI analysis grounded in cited sources

This principle highlights fundamental representational limits in resource-constrained adaptive AI, potentially guiding designs toward nonclassical frameworks to minimize info costs in contextual reasoning and intelligence.

⏳ Timeline

2026-01

arXiv:2601.20167 published by Song-Ju Kim, introducing contextuality as info-theoretic obstruction to classical probability in single-state models.[2]

2026-02

arXiv:2602.16716 submitted on Feb 3 by Song-Ju Kim, proving contextuality inevitable in adaptive intelligence from single-state reuse with minimal example.[1]

📎 Sources (6)

Factual claims are grounded in the sources below. Forward-looking analysis is AI-generated interpretation.

Adaptive systems reuse fixed internal states across contexts due to resource limits, leading to inevitable contextuality in classical probabilistic models. The paper proves an irreducible information-theoretic cost for reproducing contextual statistics. Nonclassical frameworks avoid this without quantum mechanics by lacking a global joint probability space.

Key Points

1.Contextuality arises inevitably from single-state reuse across contexts
2.Classical models incur irreducible info cost for contextual outcomes
3.Minimal example realizes and operationalizes the cost
4.Nonclassical probs bypass via no global joint probability space

Impact Analysis

Reveals fundamental limits of classical representations in adaptive AI, potentially inspiring nonclassical approaches for more efficient intelligence.

Technical Details

Contexts modeled as interventions on shared internal state. Proof: context dependence cannot be solely mediated by internal state in classical setups.

#contextuality #information-theory #single-state #probabilistic-modelsarxiv

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