# PCS: Perceived Confidence Scoring of Black Box LLMs with Metamorphic Relations

arXiv: https://arxiv.org/abs/2502.07186 · HTML: https://mlsanity.com/paper/2502.07186/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 53 references that are in the map.
- First posted on arXiv 11 Feb 2025.

## Builds on (most cited first, 30 of 35)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [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)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Fake News Detection on Social Media: A Data Mining Perspective](https://mlsanity.com/paper/1708.01967/) (2017)
- [FakeNewsNet: A Data Repository with News Content, Social Context and Spatialtemporal Information for Studying Fake News on Social Media](https://mlsanity.com/paper/1809.01286/) (2018)
- [Sentiment Analysis in the Era of Large Language Models: A Reality Check](https://mlsanity.com/paper/2305.15005/) (2023)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [Judging the Judges: Evaluating Alignment and Vulnerabilities in LLMs-as-Judges](https://mlsanity.com/paper/2406.12624/) (2024)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [A Systematic Survey and Critical Review on Evaluating Large Language Models: Challenges, Limitations, and Recommendations](https://mlsanity.com/paper/2407.04069/) (2024)
- [Uncertainty Estimation and Quantification for LLMs: A Simple Supervised Approach](https://mlsanity.com/paper/2404.15993/) (2024)
- [Metamorphic Testing: A New Approach for Generating Next Test Cases](https://mlsanity.com/paper/2002.12543/) (2020)
- [LLM Comparative Assessment: Zero-shot NLG Evaluation through Pairwise Comparisons using Large Language Models](https://mlsanity.com/paper/2307.07889/) (2023)
- [SPUQ: Perturbation-Based Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2403.02509/) (2024)
- [Can Unconfident LLM Annotations Be Used for Confident Conclusions?](https://mlsanity.com/paper/2408.15204/) (2024)
- [From Understanding to Utilization: A Survey on Explainability for Large Language Models](https://mlsanity.com/paper/2401.12874/) (2024)
- [Decoding Biases: Automated Methods and LLM Judges for Gender Bias Detection in Language Models](https://mlsanity.com/paper/2408.03907/) (2024)
- [Examining LLMs' Uncertainty Expression Towards Questions Outside Parametric Knowledge](https://mlsanity.com/paper/2311.09731/) (2023)
- [Hidden flaws behind expert-level accuracy of multimodal GPT-4 vision in medicine](https://mlsanity.com/paper/2401.08396/) (2024)
- [The Effectiveness of LLMs as Annotators: A Comparative Overview and Empirical Analysis of Direct Representation](https://mlsanity.com/paper/2405.01299/) (2024)
- [Language Models Do Hard Arithmetic Tasks Easily and Hardly Do Easy Arithmetic Tasks](https://mlsanity.com/paper/2406.02356/) (2024)
- [METAL: Metamorphic Testing Framework for Analyzing Large-Language Model Qualities](https://mlsanity.com/paper/2312.06056/) (2023)
- [Drowzee: Metamorphic Testing for Fact-Conflicting Hallucination Detection in Large Language Models](https://mlsanity.com/paper/2405.00648/) (2024)
- [Large Language Model Confidence Estimation via Black-Box Access](https://mlsanity.com/paper/2406.04370/) (2024)
- [Calibration of Large Language Models on Code Summarization](https://mlsanity.com/paper/2404.19318/) (2024)
- [Prompt-and-Align: Prompt-Based Social Alignment for Few-Shot Fake News Detection](https://mlsanity.com/paper/2309.16424/) (2023)

## Abstract (arXiv)

Zero-shot LLMs are now also used for textual classification tasks, e.g., sentiment and bias detection in a sentence or article. However, their performance can be suboptimal in such data annotation tasks. We introduce a novel technique that evaluates an LLM's confidence for classifying a textual input by leveraging Metamorphic Relations (MRs). The MRs generate semantically equivalent yet textually divergent versions of the input. Following the principles of Metamorphic Testing (MT), the mutated versions are expected to have annotation labels similar to the input. By analyzing the consistency of an LLM's responses across these variations, we compute a perceived confidence score (PCS) based on the frequency of the predicted labels. PCS can be used for both single and multiple LLM settings (e.g., when multiple LLMs are vetted in a majority-voting setup). Empirical evaluation shows that our PCS-based approach improves the performance of zero-shot LLMs by 9.3% in textual classification tasks. When multiple LLMs are used in a majority-voting setup, we obtain a performance boost of 5.8% with PCS.