# The Probabilities Also Matter: A More Faithful Metric for Faithfulness of Free-Text Explanations in Large Language Models

arXiv: https://arxiv.org/abs/2404.03189 · HTML: https://mlsanity.com/paper/2404.03189/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 56 references that are in the map.
- First posted on arXiv 4 Apr 2024.

## Builds on (most cited first, 29 of 29)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Towards Faithfully Interpretable NLP Systems: How should we define and evaluate faithfulness?](https://mlsanity.com/paper/2004.03685/) (2020)
- [ERASER: A Benchmark to Evaluate Rationalized NLP Models](https://mlsanity.com/paper/1911.03429/) (2019)
- [e-SNLI: Natural Language Inference with Natural Language Explanations](https://mlsanity.com/paper/1812.01193/) (2018)
- [Explain Yourself! Leveraging Language Models for Commonsense Reasoning](https://mlsanity.com/paper/1906.02361/) (2019)
- [Selection-Inference: Exploiting Large Language Models for Interpretable Logical Reasoning](https://mlsanity.com/paper/2205.09712/) (2022)
- [The Alignment Problem from a Deep Learning Perspective](https://mlsanity.com/paper/2209.00626/) (2022)
- [Measuring Association Between Labels and Free-Text Rationales](https://mlsanity.com/paper/2010.12762/) (2020)
- [Faithful Reasoning Using Large Language Models](https://mlsanity.com/paper/2208.14271/) (2022)
- [Teach Me to Explain: A Review of Datasets for Explainable Natural Language Processing](https://mlsanity.com/paper/2102.12060/) (2021)
- [Goal Misgeneralization: Why Correct Specifications Aren't Enough For Correct Goals](https://mlsanity.com/paper/2210.01790/) (2022)
- [Question Decomposition Improves the Faithfulness of Model-Generated Reasoning](https://mlsanity.com/paper/2307.11768/) (2023)
- [Faithfulness Tests for Natural Language Explanations](https://mlsanity.com/paper/2305.18029/) (2023)
- [On Interpretability of Artificial Neural Networks: A Survey](https://mlsanity.com/paper/2001.02522/) (2020)
- [On Measuring Faithfulness or Self-consistency of Natural Language Explanations](https://mlsanity.com/paper/2311.07466/) (2023)
- [Preventing Language Models From Hiding Their Reasoning](https://mlsanity.com/paper/2310.18512/) (2023)
- [Interpretability and Explainability: A Machine Learning Zoo Mini-tour](https://mlsanity.com/paper/2012.01805/) (2020)
- [SemEval-2020 Task 4: Commonsense Validation and Explanation](https://mlsanity.com/paper/2007.00236/) (2020)
- [Honesty Is the Best Policy: Defining and Mitigating AI Deception](https://mlsanity.com/paper/2312.01350/) (2023)
- [Challenges with unsupervised LLM knowledge discovery](https://mlsanity.com/paper/2312.10029/) (2023)
- [Interpretable by Design: Learning Predictors by Composing Interpretable Queries](https://mlsanity.com/paper/2207.00938/) (2022)
- [Explaining Chest X-ray Pathologies in Natural Language](https://mlsanity.com/paper/2207.04343/) (2022)
- [The Struggles of Feature-Based Explanations: Shapley Values vs. Minimal Sufficient Subsets](https://mlsanity.com/paper/2009.11023/) (2020)
- [HuSpaCy: an industrial-strength Hungarian natural language processing toolkit](https://mlsanity.com/paper/2201.01956/) (2022)

## Built on by (most cited first, 29 of 29)

- [Chain-of-Thought Reasoning In The Wild Is Not Always Faithful](https://mlsanity.com/paper/2503.08679/) (2025)
- [FaithEval: Can Your Language Model Stay Faithful to Context, Even If "The Moon is Made of Marshmallows"](https://mlsanity.com/paper/2410.03727/) (2024)
- [A Primer on the Inner Workings of Transformer-based Language Models](https://mlsanity.com/paper/2405.00208/) (2024)
- [Measuring Chain of Thought Faithfulness by Unlearning Reasoning Steps](https://mlsanity.com/paper/2502.14829/) (2025)
- [DarkBench: Benchmarking Dark Patterns in Large Language Models](https://mlsanity.com/paper/2503.10728/) (2025)
- [FaithCoT-Bench: Benchmarking Instance-Level Faithfulness of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2510.04040/) (2025)
- [RAGEN-2: Reasoning Collapse in Agentic RL](https://mlsanity.com/paper/2604.06268/) (2026)
- [How does Chain of Thought Think? Mechanistic Interpretability of Chain-of-Thought Reasoning with Sparse Autoencoding](https://mlsanity.com/paper/2507.22928/) (2025)
- [LLMs Can Covertly Sandbag on Capability Evaluations Against Chain-of-Thought Monitoring](https://mlsanity.com/paper/2508.00943/) (2025)
- [Towards Faithful Natural Language Explanations: A Study Using Activation Patching in Large Language Models](https://mlsanity.com/paper/2410.14155/) (2024)
- [A Positive Case for Faithfulness: LLM Self-Explanations Help Predict Model Behavior](https://mlsanity.com/paper/2602.02639/) (2026)
- [Biases in the Blind Spot: Detecting What LLMs Fail to Mention](https://mlsanity.com/paper/2602.10117/) (2026)
- [Fool Me Once? Contrasting Textual and Visual Explanations in a Clinical Decision-Support Setting](https://mlsanity.com/paper/2410.12284/) (2024)
- [Towards Transparent Reasoning: What Drives Faithfulness in Large Language Models?](https://mlsanity.com/paper/2510.24236/) (2025)
- [How Can We Diagnose and Treat Bias in Large Language Models for Clinical Decision-Making?](https://mlsanity.com/paper/2410.16574/) (2024)
- [Aligning What LLMs Do and Say: Towards Self-Consistent Explanations](https://mlsanity.com/paper/2506.07523/) (2025)
- [VisualThink-VLA: Visual Intermediate Reasoning for Effective and Low-Latency Vision-Language-Action Policies](https://mlsanity.com/paper/2605.30011/) (2026)
- [Argumentation for Explainable and Globally Contestable Decision Support with LLMs](https://mlsanity.com/paper/2603.14643/) (2026)
- [Faithfulness Metrics Don't Measure Faithfulness: A Meta-Evaluation with Ground Truth](https://mlsanity.com/paper/2605.25052/) (2026)
- [Argument-Based Consistency in Toxicity Explanations of LLMs](https://mlsanity.com/paper/2506.19113/) (2025)
- [Multi-Step Knowledge Interaction Analysis via Rank-2 Subspace Disentanglement](https://mlsanity.com/paper/2511.01706/) (2025)
- [CAuSE: Decoding Multimodal Classifiers using Faithful Natural Language Explanation](https://mlsanity.com/paper/2512.06814/) (2025)
- [Cross-Examiner: Evaluating Consistency of Large Language Model-Generated Explanations](https://mlsanity.com/paper/2503.08815/) (2025)
- [NeuroFaith: Evaluating LLM Self-Explanation Faithfulness via Internal Representation Alignment](https://mlsanity.com/paper/2506.09277/) (2025)
- [WeNLEX: Weakly Supervised Natural Language Explanations for Multilabel Chest X-ray Classification](https://mlsanity.com/paper/2603.18752/) (2026)
- [Faithfulness Serum: Mitigating the Faithfulness Gap in Textual Explanations of LLM Decisions via Attribution Guidance](https://mlsanity.com/paper/2604.14325/) (2026)
- [Training Large Language Models for Self-Explanation Faithfulness](https://mlsanity.com/paper/2607.21090/) (2026)
- [Correct Diagnosis, Better Feedback: A Symbolic-Verifier for Faithful LLM Tutoring Feedback in Logic Proofs](https://mlsanity.com/paper/2609.22553/) (2026)
- [Does a model's stated reason for rejecting a candidate do any work?](https://mlsanity.com/paper/2609.30151/) (2026)

## Abstract (arXiv)

In order to oversee advanced AI systems, it is important to understand their underlying decision-making process. When prompted, large language models (LLMs) can provide natural language explanations or reasoning traces that sound plausible and receive high ratings from human annotators. However, it is unclear to what extent these explanations are faithful, i.e., truly capture the factors responsible for the model's predictions. In this work, we introduce Correlational Explanatory Faithfulness (CEF), a metric that can be used in faithfulness tests based on input interventions. Previous metrics used in such tests take into account only binary changes in the predictions. Our metric accounts for the total shift in the model's predicted label distribution, more accurately reflecting the explanations' faithfulness. We then introduce the Correlational Counterfactual Test (CCT) by instantiating CEF on the Counterfactual Test (CT) from Atanasova et al. (2023). We evaluate the faithfulness of free-text explanations generated by few-shot-prompted LLMs from the Llama2 family on three NLP tasks. We find that our metric measures aspects of faithfulness which the CT misses.