Markov Constraint as Large Language Model Surrogate

TL;DR

This paper introduces NgramMarkov, a novel Markov constraint variant that leverages large language models to improve text generation efficiency and quality in constraint programming, enabling larger corpora and lower n-gram sizes.

Contribution

It proposes a new Markov constraint that integrates LLM probabilities, reducing candidate sentences and enhancing computational efficiency in text generation tasks.

Findings

Generated text aligns with LLM perplexity measures.

Significant reduction in candidate sentences and computation time.

Enabled use of 4-grams instead of 5-grams in a real-world problem.

Abstract

This paper presents NgramMarkov, a variant of the Markov constraints. It is dedicated to text generation in constraint programming (CP). It involves a set of n-grams (i.e., sequence of n words) associated with probabilities given by a large language model (LLM). It limits the product of the probabilities of the n-gram of a sentence. The propagator of this constraint can be seen as an extension of the ElementaryMarkov constraint propagator, incorporating the LLM distribution instead of the maximum likelihood estimation of n-grams. It uses a gliding threshold, i.e., it rejects n-grams whose local probabilities are too low, to guarantee balanced solutions. It can also be combined with a "look-ahead" approach to remove n-grams that are very unlikely to lead to acceptable sentences for a fixed-length horizon. This idea is based on the MDDMarkovProcess constraint propagator, but without explicitly using an MDD (Multi-Valued Decision Diagram). The experimental results show that the generated text is valued in a similar way to the LLM perplexity function. Using this new constraint dramatically reduces the number of candidate sentences produced, improves computation times, and allows larger corpora or smaller n-grams to be used. A real-world problem has been solved for the first time using 4-grams instead of 5-grams.