# Pareto Optimal Learning for Estimating Large Language Model Errors

arXiv: https://arxiv.org/abs/2306.16564 · HTML: https://mlsanity.com/paper/2306.16564/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 58 references that are in the map.
- First posted on arXiv 28 Jun 2023.

## Builds on (most cited first, 27 of 27)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [Domain-Specific Language Model Pretraining for Biomedical Natural Language Processing](https://mlsanity.com/paper/2007.15779/) (2020)
- [Capabilities of GPT-4 on Medical Challenge Problems](https://mlsanity.com/paper/2303.13375/) (2023)
- [A Prompt Pattern Catalog to Enhance Prompt Engineering with ChatGPT](https://mlsanity.com/paper/2302.11382/) (2023)
- [Snorkel: Rapid Training Data Creation with Weak Supervision](https://mlsanity.com/paper/1711.10160/) (2017)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [Data Programming: Creating Large Training Sets, Quickly](https://mlsanity.com/paper/1605.07723/) (2016)
- [Training Complex Models with Multi-Task Weak Supervision](https://mlsanity.com/paper/1810.02840/) (2018)
- [Fast and Three-rious: Speeding Up Weak Supervision with Triplet Methods](https://mlsanity.com/paper/2002.11955/) (2020)
- [WRENCH: A Comprehensive Benchmark for Weak Supervision](https://mlsanity.com/paper/2109.11377/) (2021)
- [Fine-Tuning Pre-trained Language Model with Weak Supervision: A Contrastive-Regularized Self-Training Approach](https://mlsanity.com/paper/2010.07835/) (2020)
- [Learning from Rules Generalizing Labeled Exemplars](https://mlsanity.com/paper/2004.06025/) (2020)
- [A Brief Report on LawGPT 1.0: A Virtual Legal Assistant Based on GPT-3](https://mlsanity.com/paper/2302.05729/) (2023)
- [End-to-End Weak Supervision](https://mlsanity.com/paper/2107.02233/) (2021)
- [NERO: A Neural Rule Grounding Framework for Label-Efficient Relation Extraction](https://mlsanity.com/paper/1909.02177/) (2019)
- [SAIS: Supervising and Augmenting Intermediate Steps for Document-Level Relation Extraction](https://mlsanity.com/paper/2109.12093/) (2021)
- [Multi-Resolution Weak Supervision for Sequential Data](https://mlsanity.com/paper/1910.09505/) (2019)
- [Deep Probabilistic Logic: A Unifying Framework for Indirect Supervision](https://mlsanity.com/paper/1808.08485/) (2018)
- [Self-supervised self-supervision by combining deep learning and probabilistic logic](https://mlsanity.com/paper/2012.12474/) (2020)

## Built on by (most cited first, 5 of 5)

- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [Understanding the Effects of Iterative Prompting on Truthfulness](https://mlsanity.com/paper/2402.06625/) (2024)
- [A Survey of Calibration Process for Black-Box LLMs](https://mlsanity.com/paper/2412.12767/) (2024)
- [Interactive DualChecker for Mitigating Hallucinations in Distilling Large Language Models](https://mlsanity.com/paper/2408.12326/) (2024)
- [ARISE: Iterative Rule Induction and Synthetic Data Generation for Text Classification](https://mlsanity.com/paper/2502.05923/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) have shown impressive abilities in many applications. When a concrete and precise answer is desired, it is important to have a quantitative estimation of the potential error rate. However, this can be challenging due to the text-in-text-out nature of generative models. We present a method based on Pareto optimization that generates a risk score to estimate the probability of error in an LLM response by integrating multiple sources of information. We prove theoretically that the error estimator optimized in our framework aligns with the LLM and the information sources in an Pareto optimal manner. Experimental results show that the risk scores estimated by our method are well correlated with the true LLM error rate, thus facilitating error correction. By dynamically combining with prompting strategies such as self-verification and information retrieval, we demonstrate the proposed method can be utilized to increase the performance of an LLM, surpassing state-of-the-art task specific models.