# Normalized AOPC: Fixing Misleading Faithfulness Metrics for Feature Attribution Explainability

arXiv: https://arxiv.org/abs/2408.08137 · HTML: https://mlsanity.com/paper/2408.08137/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 49 references that are in the map.
- First posted on arXiv 15 Aug 2024.

## Builds on (most cited first, 30 of 33)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [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)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [Beam Search Strategies for Neural Machine Translation](https://mlsanity.com/paper/1702.01806/) (2017)
- [A Survey of the State of Explainable AI for Natural Language Processing](https://mlsanity.com/paper/2010.00711/) (2020)
- [Evaluating and Aggregating Feature-based Model Explanations](https://mlsanity.com/paper/2005.00631/) (2020)
- [One Explanation Does Not Fit All: A Toolkit and Taxonomy of AI Explainability Techniques](https://mlsanity.com/paper/1909.03012/) (2019)
- [Pathologies of Neural Models Make Interpretations Difficult](https://mlsanity.com/paper/1804.07781/) (2018)
- [Towards Faithful Model Explanation in NLP: A Survey](https://mlsanity.com/paper/2209.11326/) (2022)
- [The elephant in the interpretability room: Why use attention as explanation when we have saliency methods?](https://mlsanity.com/paper/2010.05607/) (2020)
- [The Out-of-Distribution Problem in Explainability and Search Methods for Feature Importance Explanations](https://mlsanity.com/paper/2106.00786/) (2021)
- [How does this interaction affect me? Interpretable attribution for feature interactions](https://mlsanity.com/paper/2006.10965/) (2020)
- [Learning Variational Word Masks to Improve the Interpretability of Neural Text Classifiers](https://mlsanity.com/paper/2010.00667/) (2020)
- [DecompX: Explaining Transformers Decisions by Propagating Token Decomposition](https://mlsanity.com/paper/2306.02873/) (2023)
- [On the Sensitivity and Stability of Model Interpretations in NLP](https://mlsanity.com/paper/2104.08782/) (2021)
- [An Empirical Study on Explanations in Out-of-Domain Settings](https://mlsanity.com/paper/2203.00056/) (2022)
- [Logic Traps in Evaluating Attribution Scores](https://mlsanity.com/paper/2109.05463/) (2021)
- [Enjoy the Salience: Towards Better Transformer-based Faithful Explanations with Word Salience](https://mlsanity.com/paper/2108.13759/) (2021)
- [Incorporating Attribution Importance for Improving Faithfulness Metrics](https://mlsanity.com/paper/2305.10496/) (2023)
- [The Solvability of Interpretability Evaluation Metrics](https://mlsanity.com/paper/2205.08696/) (2022)
- [Improving Interpretability via Explicit Word Interaction Graph Layer](https://mlsanity.com/paper/2302.02016/) (2023)

## Built on by (most cited first, 10 of 10)

- [Mechanistic Evidence for Faithfulness Decay in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2602.11201/) (2026)
- [Correcting Gradient-Based Circuit Localization via Interaction-Aware Backpropagation](https://mlsanity.com/paper/2505.17630/) (2025)
- [Local MDI+: Local Feature Importances for Tree-Based Models](https://mlsanity.com/paper/2506.08928/) (2025)
- [DLBacktrace: A Model Agnostic Explainability for any Deep Learning Models](https://mlsanity.com/paper/2411.12643/) (2024)
- [Robust Explanations for User Trust in Enterprise NLP Systems](https://mlsanity.com/paper/2604.12069/) (2026)
- [Probabilistic Attribution For Large Language Models](https://mlsanity.com/paper/2605.21726/) (2026)
- [Quantifying Retriever-Generator Alignment in RAG with Local Explanations](https://mlsanity.com/paper/2601.21803/) (2026)
- [Tree-of-Evidence: Efficient "System 2" Search for Faithful Multimodal Grounding](https://mlsanity.com/paper/2604.07692/) (2026)
- [Efficient KernelSHAP Explanations for Patch-based 3D Medical Image Segmentation](https://mlsanity.com/paper/2604.11775/) (2026)
- [Geometry-Adaptive Explainer for Faithful Dictionary-Based Interpretability under Distribution Shift](https://mlsanity.com/paper/2605.21849/) (2026)

## Abstract (arXiv)

Deep neural network predictions are notoriously difficult to interpret. Feature attribution methods aim to explain these predictions by identifying the contribution of each input feature. Faithfulness, often evaluated using the area over the perturbation curve (AOPC), reflects feature attributions' accuracy in describing the internal mechanisms of deep neural networks. However, many studies rely on AOPC to compare faithfulness across different models, which we show can lead to false conclusions about models' faithfulness. Specifically, we find that AOPC is sensitive to variations in the model, resulting in unreliable cross-model comparisons. Moreover, AOPC scores are difficult to interpret in isolation without knowing the model-specific lower and upper limits. To address these issues, we propose a normalization approach, Normalized AOPC (NAOPC), enabling consistent cross-model evaluations and more meaningful interpretation of individual scores. Our experiments demonstrate that this normalization can radically change AOPC results, questioning the conclusions of earlier studies and offering a more robust framework for assessing feature attribution faithfulness. Our code is available at https://github.com/JoakimEdin/naopc.