xin-icl-likelihood-ratio-convergence
IN premise — summaries/2026/08/24/xie-2021-icl-bayesian-sR-references.md
Created 2026-08-25T02:58:57+00:00
The core theoretical result states that lim_{n→∞} p(S_n | θ) / p(S_n | θ*) = 0 for θ ≠ θ*, meaning prompt likelihood concentrates on the correct concept as example count grows.
Summary
As the number of example prompts grows, the data becomes so strongly in favor of the true underlying concept that every alternative hypothesis becomes essentially indistinguishable from impossible. This means the system is guaranteed to converge on the correct interpretation given enough evidence, rather than lingering in uncertainty between competing explanations.