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

• URL: http://arxiv.org/abs/2407.15504v1
• Date: Mon, 22 Jul 2024 09:40:13 GMT
• Title: Fundamental Limits of Prompt Compression: A Rate-Distortion Framework for Black-Box Language Models
• Authors: Adway Girish, Alliot Nagle, Marco Bondaschi, Michael Gastpar, Ashok Vardhan Makkuva, Hyeji Kim,
• Abstract summary: We formalize the problem of prompt compression for large language models (LLMs) We present a framework to unify token-level prompt compression methods which create hard prompts for black-box models. We show that there is a large gap between the performance of current prompt compression methods and the optimal strategy.
• Score: 21.025001473355996
• License: http://creativecommons.org/licenses/by/4.0/
• 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 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.

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