arXiv Machine Learning By Faruk Alpay, Hamdi Alakkad

Finite Certificates for In-Context Determinacy and a Threshold Theory of Emergence in Language Models

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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.

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arXiv AI
Aug 25

Measuring in-context algorithmic reasoning in language models against an exact Bayes-optimal reference

The paper introduces F-ICL, a benchmark that measures in‑context algorithmic reasoning in language models by exhaustively enumerating 86 million valid programs of length ≤13 on a Turing‑complete machine and computing the exact posterior under a bounded Levin–Solomonoff prior. Unlike typical benchmarks, F‑ICL provides a distributional reference rather than just answers, allowing the evaluation of models’ inductive priors. Across 105 configurations of models ranging from 0.8 B to 675 B parameters, models achieve up to 92 % accuracy, yet many still deviate from the Bayes‑optimal reference, and the study derives theoretical bounds on cumulative loss for predictors with positive prior weight on the reference.

By Luan Ozelim, Hector Zenil