Rational Tuning of LLM Cascades via Probabilistic Modeling

TL;DR

This paper introduces a probabilistic model for optimizing the performance of cascaded large language models (LLMs), improving error-cost trade-offs and sample efficiency in tuning their confidence thresholds.

Contribution

It presents a novel Markov-copula probabilistic model for joint LLM cascade performance, enabling rational threshold tuning and outperforming Bayesian optimization.

Findings

4.3% average improvement in error-cost trade-offs

10.2% improvement with limited training data

Enhanced sample efficiency in cascade tuning

Abstract

Understanding the reliability of large language models (LLMs) has recently garnered significant attention. Given LLMs' propensity to hallucinate, as well as their high sensitivity to prompt design, it is already challenging to predict the performance of an individual LLM. However, the problem becomes more complex for compound LLM systems such as cascades, where in addition to each model's standalone performance, we must understand how the error rates of different models interact. In this paper, we present a probabilistic model for the joint performance distribution of a sequence of LLMs, which enables a framework for rationally tuning the confidence thresholds of a LLM cascade using continuous optimization. Compared to selecting confidence thresholds using Bayesian optimization, our parametric Markov-copula model yields more favorable error-cost trade-offs, improving the area under the error-cost curve by 4.3% on average for cascades with $k\geq 3$ models. In the low-sample regime with $n \leq 30$ training examples, the performance improvement widens to 10.2%, suggesting that our framework's inductive assumptions about the interactions between the error rates of different LLMs enhance sample efficiency. Overall, our Markov-copula model provides a rational basis for tuning LLM cascade performance and points to the potential of probabilistic methods in analyzing systems of LLMs.