# MARGIN: Runtime Confidence Calibration for Multi-Agent Foundation Model Coordination

arXiv: https://arxiv.org/abs/2605.22949 · HTML: https://mlsanity.com/paper/2605.22949/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 21 May 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 21 of 21)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [Should we be going MAD? A Look at Multi-Agent Debate Strategies for LLMs](https://mlsanity.com/paper/2311.17371/) (2023)
- [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025)
- [Thermometer: Towards Universal Calibration for Large Language Models](https://mlsanity.com/paper/2403.08819/) (2024)
- [Large Language Models Miss the Multi-Agent Mark](https://mlsanity.com/paper/2505.21298/) (2025)
- [Your Pre-trained LLM is Secretly an Unsupervised Confidence Calibrator](https://mlsanity.com/paper/2505.16690/) (2025)

## Built on by (most cited first, 1 of 1)

- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)

## Abstract (arXiv)

When a coordinator compares answers from heterogeneous foundation models, self-reported confidence may have different meanings across responders and changing workloads. This paper presents MARGIN (Multi-Agent Runtime Grading via Incremental Normalisation), a runtime calibration method that learns model-specific confidence corrections from observed answer outcomes without retraining the models or requiring a held-out calibration set. MARGIN tracks recent accuracy and stated confidence within confidence bands, uses their ratio to correct reported confidence, and blends sparse-band corrections toward a model-level estimate. The corrected scores weight candidate answers in a collective decision. Evaluation covers code generation, question answering, and mathematics, using an 18-model pool and a nine-model subset for distribution-shift experiments. On BigCodeBench, model-mean confidence is negatively related to accuracy; among correct/incorrect response pairs, choosing the more confident responder performs below chance. Against five online calibration baselines receiving identical feedback and retaining their learned state across each transition, MARGIN achieves lower post-shift expected calibration error than all five in two code-generation transitions and than four in a question-answering transition; the remaining question-answering comparison is inconclusive. In separate code-generation coordination experiments, calibration improves the ranking of correct responses and increases answer-selection accuracy by 4.3 and 14.0 percentage points on two of three benchmarks relative to uncalibrated confidence weighting. These results support model-specific runtime calibration for coordination under changing workloads when correctness feedback is available for the participating responders.