Fundamental Limits of Prompt Compression: A Rate-Distortion Framework for Black-Box Language Models

Alliot Nagle, Adway Girish, Marco Bondaschi, Michael Gastpar, Ashok Vardhan Makkuva, Hyeji Kim

Keywords: information theory, prompt compression, LLMs, optimization

TL;DR: We formalize and study fundamental limits of prompt compression for large language models via a rate-distortion framework.

Abstract: We formalize the problem of prompt compression for large language models (LLMs) and present a framework to unify token-level prompt compression methods which create hard prompts for black-box models. We derive the distortion-rate function for this setup as a linear program, and provide an efficient algorithm to compute this fundamental limit via the dual of the linear program. Using the distortion-rate function as the baseline, we study the performance of existing compression schemes on a synthetic dataset consisting of prompts generated from a Markov chain, natural language queries, and their respective answers. Our empirical analysis demonstrates the criticality of query-aware prompt compression, where the compressor has knowledge of the downstream task/query for the black-box LLM. We show that there is a large gap between the performance of current prompt compression methods and the optimal strategy, and propose Adaptive QuerySelect, a query-aware, variable-rate adaptation of a prior work to close the gap. We extend our experiments to a small natural language dataset to further confirm our findings on our synthetic dataset.

Primary Area: Other (please use sparingly, only use the keyword field for more details)

Submission Number: 7615