arXiv Machine Learning

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.

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
arXiv AI
2d ago

Measuring the Microtask Eligibility Gap: When Is an Off-the-Shelf SLM Enough for an Agent Harness?

The paper introduces a benchmark for evaluating whether off‑the‑shelf small language models (SLMs) can reliably perform microtasks that support a large language model (LLM) planner, such as auto‑approving shell commands, writing memory, selecting tools, and ranking past turns. Using fixed prompts and confidence‑interval‑aware eligibility thresholds, the authors test several Qwen3 models (0.6/1.7/4/8 B) in FP16 with no tuning and find that none of the 16 configurations meet the eligibility criteria. Quantization to 4‑bit precision further degrades performance, with the eligibility gap tracking model size rather than precision, and the issue persists across different models (e.g., Llama‑3.x) and prompt variations.

By Jundong Hu, Shekar Ramachandran
arXiv AI
Jun 16

The Faithfulness Gap: Certifying Semantic Equivalence Between Natural-Language and Formal Mathematical Statements

arXiv:2606. 16541v1 Announce Type: new Abstract: Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by \emph{faithfulness}: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended.

By Noor Islam S. Mohammad, Tamim Sheikh