LLM-Relative Kolmogorov Complexity Measures Prompt Value

A recent preprint on arXiv (2608.16438) presents a computational framework aimed at assessing the worth of prompts utilized by large language models (LLMs). The researchers contend that as LLMs increasingly generate or handle valuable outputs, the focus shifts to the significance of inputs—such as prompts, hints, critiques, problem statements, or partial solutions—that steer the model. They classify an input as valuable if it facilitates the model's generation of the desired artifact by either enhancing sampling probability or minimizing processing time. The paper introduces a concept of probabilistic Levin–Kolmogorov complexity relative to LLMs, substituting the traditional universal Turing machine with the LLM itself. This framework, known as pKt, provides a formal metric for evaluating prompt value based on computational complexity. The theoretical work falls under the domains of computer science and artificial intelligence, potentially influencing the valuation of prompts in AI-assisted creative and scientific endeavors.