Articulation Upper Bounds for Language Models

Alexander Spangher, Daniel E. Ho, Diyi Yang, Noah Goodman, Sanmi Koyejo

Language captures only a subset of the perceptions, intuitions and intents that form meaning between speakers. What, then, are the limits of language? We take steps towards measuring this in LLMs as follows: for a set of concepts, we measure how well each concept can be transmitted between two LLMs as their capabilities scale. This requires novel measurement tools: (1) optimal messages: we introduce a prompt optimization algorithm that beats existing algorithms by up to 14% on benchmarks and accurately estimates prompt upper bounds. (2) A transmission measure: the sender is asked to label text; the receiver then tries to recover the sender's prompt, and recovery is measured; we find this correlates strongly with human label error. With these measures, we use observational scaling laws to study how transmissibility of a concept, conveyed with optimal messages, increases as transmitter and receiver capacity grows: does it asymptote below or above a threshold? Measuring 1.2k concepts in eight domains, we find concepts that (a) can be fully articulated; these concepts usually depend on local patterns, e.g. "joke ends with surprise"; (b) might be articulated by future, stronger…