The Value of a Prompt: An LLM-Relative Kolmogorov-Complexity Approach

Excerpt

arXiv:2608.16438v1 Announce Type: new Abstract: In a world where valuable artifacts are increasingly created, completed, or processed by LLMs, the central economic question is not only what the LLM can produce, but what \emph{value} remains in the inputs (i.e., the prompts) we provide to it. Given a prompt, hint, critique, problem statement, or partial solution that helps an LLM produce an artifact $z$---a proof, program, design, or scientific hypothesis---how should we measure the value of that