Prediction-Powered Ranking of Large Language Models (2402.17826v3)

Abstract: LLMs are often ranked according to their level of alignment with human preferences -- a model is better than other models if its outputs are more frequently preferred by humans. One of the popular ways to elicit human preferences utilizes pairwise comparisons between the outputs provided by different models to the same inputs. However, since gathering pairwise comparisons by humans is costly and time-consuming, it has become a common practice to gather pairwise comparisons by a strong LLM -- a model strongly aligned with human preferences. Surprisingly, practitioners cannot currently measure the uncertainty that any mismatch between human and model preferences may introduce in the constructed rankings. In this work, we develop a statistical framework to bridge this gap. Given a (small) set of pairwise comparisons by humans and a large set of pairwise comparisons by a model, our framework provides a rank-set -- a set of possible ranking positions -- for each of the models under comparison. Moreover, it guarantees that, with a probability greater than or equal to a user-specified value, the rank-sets cover the true ranking consistent with the distribution of human pairwise preferences asymptotically. Using pairwise comparisons made by humans in the LMSYS Chatbot Arena platform and pairwise comparisons made by three strong LLMs, we empirically demonstrate the effectivity of our framework and show that the rank-sets constructed using only pairwise comparisons by the strong LLMs are often inconsistent with (the distribution of) human pairwise preferences.

• The paper introduces a statistical framework that quantifies uncertainty in LLM rankings using confidence ellipsoids and rank-sets from pairwise comparisons.
• It employs a hybrid approach combining human and model-generated comparisons to calculate unbiased estimates of model preference probabilities.
• The framework offers practical insights with robust coverage guarantees and an open-source implementation for efficient LLM evaluation.

Uncertainty Quantification in Ranking LLMs with Human and Model Pairwise Comparisons

Introduction

The evaluation of LLMs has conventionally focused on their alignment with human preferences, a paradigm which pivots on ranking models based on pairwise comparisons. The aspect of practicality under this evaluation lens, however, suffers due to the extensive human resource and time requirements. To mitigate this, utilizing a well-aligned strong LLM for generating pairwise comparisons has emerged as a common practice. Nevertheless, the reliability of rankings derived through such automated comparisons remains questionable due to potential discrepancies with human judgement and the statistical uncertainty inherent in finite comparison samples. This paper introduces a statistical framework that addresses these concerns by quantifying uncertainty in model rankings through the concept of rank-sets, which encapsulate the potential ranking positions of models given both human and automated pairwise comparisons.

Statistical Framework

The cornerstone of this framework is the integration of prediction-powered inference to construct confidence ellipsoids that encapsulate the true probabilities of a model being preferred, thereby facilitating the formation of rank-sets. These rank-sets offer a probabilistic guarantee to cover the actual model rankings as per human preferences. The framework's novelty lies in offering a computational mechanism to account for uncertainties without stringent assumptions about preference distributions and model alignments, marking a significant advancement in the assessment of LLMs' standings.

Methodology

Employing a combination of human and model-generated pairwise comparisons, the framework first calculates an unbiased estimate of models' preference probabilities. These estimates feed into the creation of a confidence ellipsoid that probabilistically encompasses the true preference probabilities, from which rank-sets are derived. For each LLM, the rank-set is computed by evaluating distances to hyperplanes that equate models' probabilities of being preferred, allowing an enumeration of potential ranking positions within statistically grounded confidence bounds.

Theoretical Contributions

The formal analysis underpinning the framework ensures that the calculated rank-sets possess coverage guarantees, meaning they are statistically expected to contain the true model rankings according to human preferences. This is a pivotal accomplishment that imbues the rank-sets with a robust measure of credibility and reliability, addressing the inherent uncertainties associated with model evaluations based on preferences.

Practical Implications and Future Directions

The implementation of this framework can substantially refine the process of LLM evaluation by incorporating a systematic consideration of uncertainty. The practical aspect is further strengthened by the provision of an open-source implementation, facilitating its accessibility and applicability in various domains where LLM ranking is essential. Looking ahead, the research introduces several pathways for exploration, such as the verification of the framework with empirical data, the extension of coverage guarantees under finite sample scenarios, and adjustments for inputs' distribution shifts.

Conclusions

The proposed statistical framework significantly enriches the landscape of LLM evaluation by quantifying ranking uncertainty through rank-sets. It embodies a methodologically sound approach that harmonizes the dual objectives of leveraging the efficiency of model-generated comparisons and ensuring fidelity to human preferences. As LLMs continue to evolve and find applications across an expanding spectrum of tasks, methodologies that provide nuanced insights into model rankings will remain indispensable, underscoring the pertinence of this research.