Finite Certificates for In-Context Determinacy and a Threshold Theory of Emergence in Language Models
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 binary outputs. The second problem is threshold emergence: when does an apparent benchmark jump reflect a semantic transition rather than a discon...
| Authors | Faruk Alpay, Hamdi Alakkad |
|---|---|
| Primary category | cs.LG |
| Published | 30 May 2026 |
| Last updated at source | 30 May 2026 |
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