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Uncertainty-Aware Answer Selection for Improved Reasoning in Multi-LLM Systems

Aakriti Agrawal, Rohith Aralikatti, Anirudh Satheesh, Souradip Chakraborty, Amrit Singh Bedi, Furong Huang

TL;DR

This work tackles the problem of selecting the best answer across multiple heterogeneous LLMs without relying on costly external verifiers or extensive sampling. It introduces a calibrated log-likelihood framework that aggregates per-token probabilities across models, using a teacher-forcing based single forward pass to compute a model-agnostic score and thereby identify the most confident, and likely correct, response. A generalization to incorporate any uncertainty measure via $M_c(C\mid p) = \frac{1}{N} \sum_{i=1}^N M_i(C\mid p)$ makes the method flexible for various uncertainty signals. Empirically, the approach yields notable improvements on GSM8K, MMLU, and ARC datasets in both debate and best-of-N settings, outperforming random tie-breaking and matching or surpassing single-model baselines under equal call counts. Overall, the calibrated, ensemble-based scoring enables efficient and reliable multi-LLM reasoning by leveraging model diversity without external judges or heavy sampling.

Abstract

Large Language Models (LLMs) have demonstrated exceptional capabilities, yet selecting the most reliable response from multiple LLMs remains a challenge, particularly in resource-constrained settings. Existing approaches often depend on costly external verifiers, human evaluators, or self-consistency techniques that require multiple samples from a single model. While multi-LLM systems produce more diverse responses than single models and thus have greater potential, they often underperform compared to single LLM self-consistency. We propose a principled, novel and computationally efficient method to select the best response from multiple different LLMs using a calibrated log-likelihood score, implicitly leveraging the inherent knowledge and confidence of these models. Our method demonstrates improvements of approx. 4%, 3%, and 5% across both debate (multi-round LLM discussions) and non-debate (Best-of-N with multiple LLMs) settings on GSM8K, MMLU (6 subsets), and ARC datasets respectively.

Uncertainty-Aware Answer Selection for Improved Reasoning in Multi-LLM Systems

TL;DR

This work tackles the problem of selecting the best answer across multiple heterogeneous LLMs without relying on costly external verifiers or extensive sampling. It introduces a calibrated log-likelihood framework that aggregates per-token probabilities across models, using a teacher-forcing based single forward pass to compute a model-agnostic score and thereby identify the most confident, and likely correct, response. A generalization to incorporate any uncertainty measure via makes the method flexible for various uncertainty signals. Empirically, the approach yields notable improvements on GSM8K, MMLU, and ARC datasets in both debate and best-of-N settings, outperforming random tie-breaking and matching or surpassing single-model baselines under equal call counts. Overall, the calibrated, ensemble-based scoring enables efficient and reliable multi-LLM reasoning by leveraging model diversity without external judges or heavy sampling.

Abstract

Large Language Models (LLMs) have demonstrated exceptional capabilities, yet selecting the most reliable response from multiple LLMs remains a challenge, particularly in resource-constrained settings. Existing approaches often depend on costly external verifiers, human evaluators, or self-consistency techniques that require multiple samples from a single model. While multi-LLM systems produce more diverse responses than single models and thus have greater potential, they often underperform compared to single LLM self-consistency. We propose a principled, novel and computationally efficient method to select the best response from multiple different LLMs using a calibrated log-likelihood score, implicitly leveraging the inherent knowledge and confidence of these models. Our method demonstrates improvements of approx. 4%, 3%, and 5% across both debate (multi-round LLM discussions) and non-debate (Best-of-N with multiple LLMs) settings on GSM8K, MMLU (6 subsets), and ARC datasets respectively.

Paper Structure

This paper contains 32 sections, 18 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Uncertainty-Aware Answer Selection
  3. Calibrated Log-Likelihood Metric
  4. Our Calibrated Metric with any Uncertainty Method:
  5. Why Does Calibrated Log-Likelihood Improve Multi-LLM Performance?
  6. Computational Cost of the Proposed Approach.
  7. Experimental Setup and Results
  8. Tie-breaking Using Calibrated Metrics Outperforms Random Tie-breaking
  9. All Calibrated Metrics Provide Similar Performance
  10. Conclusion
  11. Limitation
  12. Acknowledgments
  13. Related Works
  14. Multi-LLM Systems:
  15. Single LLM Self-Improvement:
  16. ...and 17 more sections

Figures (2)

  • Figure 1: Diagram illustrating our proposed calibrated log-likelihood based metric for answer selection in a multi-LLM system. The multi-LLM system shows a debate setting which goes on for $K$ rounds. When $K=1$, it is best-of-N setting when answers are independently sampled from each LLM and best answer is selected without exposing the answer to the other LLMs. The best answer is chosen based on calibrated log-likelihood scoring. Our-approach outperforms random selection when there is no clear majority answer.
  • Figure 2: Histogram of log‐likelihood scores, showing the distribution for correct (blue) versus incorrect (orange) responses. The histogram is plotted over responses sampled from round 3 of the LLM-debate experiment from the GSM8K dataset.