A new arXiv paper puts a number on something anyone who uses AI chatbots already senses: some prompts are worth more than others.
Researchers writing on arXiv this week proposed a way to measure exactly how much a prompt, hint, critique, or partial solution is worth to a large language model. They adapt Kolmogorov complexity and Levin's search-time complexity - older ideas from theoretical computer science for measuring how hard information is to produce - by swapping the classical "universal Turing machine" for the LLM itself. The resulting metric, which they call probabilistic Levin-Kolmogorov complexity, scores a prompt in bits: a prompt worth b bits makes the target output roughly 2^b times easier to obtain, whether that shows up as higher success probability, less computation spent searching for the answer, or some tradeoff between the two. The authors also show this value is efficiently estimable, unlike the classical notion of algorithmic mutual information it borrows from, which is famously incomputable, and that under a reproduction experiment, b bits of prompt value corresponds to a roughly 2^b times higher median token cost to reproduce the output without the prompt.
If it holds up, this gives a rigorous, model-relative yardstick for judging how much a piece of context actually contributes to an output, instead of relying on intuition. That has a commercial edge too: as more products start charging for "context" or "system prompts" as line items separate from raw model access, someone eventually has to justify what that context is worth, not just how many tokens it consumes.
It is an elegant piece of math dressed up as an economic argument, but for now it is just that - a paper. Turning "bits of prompt value" into something a product team can compute cheaply and trust at scale is a separate, harder problem the paper does not claim to have solved.