Finite Certificates for In-Context Determinacy and a Threshold Theory of Emergence in Language Models
arXiv:2606.07623v1 Announce Type: new Abstract: This paper develops a model-theoretic framework for verifying context-conditioned language-model behavior by replacing benchmark labels with finite semantic certificates. The first problem is finite determinacy: when do examples in a context force the answer to a query without changing model parameters? In finite-field linear task families, we prove an exact row-space criterion, compute the residual hypothesis count, derive full and query-local identification curves, and show that extracting a smallest forcing subcontext is NP-complete even for b
This research provides a framework for understanding and verifying language model behavior at a critical juncture where AI models are becoming increasingly complex and autonomous, necessitating new methods for safety and interpretability.
A strategic reader should care because improving the verifiability and determinacy of AI models accelerates their deployability in sensitive, high-value applications, ultimately impacting R&D and regulatory landscapes.
The ability to use 'finite semantic certificates' replaces traditional benchmarking for context-conditioned model behavior, marking a methodological shift in how AI reliability and emergent properties are assessed.
- · AI Safety Researchers
- · AI Development Platforms
- · High-Compliance Industries
- · Academic AI Research
- · Black Box AI Approaches
- · Unregulated AI Systems
The ability to formally verify AI model outputs under specific contexts improves trust and enables broader adoption of advanced AI systems.
Increased verification capabilities could lead to more robust regulatory frameworks and industry standards for AI, accelerating market maturation.
This could foster competition toward 'provably safe' or 'certifiably determinate' AI models, leading to a new standard in AI product development.
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Read at arXiv cs.LG