# Towards a Theory of Faithfulness: Faithful Explanations of Differentiable Classifiers over Continuous Data

arXiv: https://arxiv.org/abs/2205.09620 · HTML: https://mlsanity.com/paper/2205.09620/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 19 May 2022.

## Builds on (most cited first, 13 of 13)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Fooling Neural Network Interpretations via Adversarial Model Manipulation](https://mlsanity.com/paper/1902.02041/) (2019)
- [On the Tractability of SHAP Explanations](https://mlsanity.com/paper/2009.08634/) (2020)
- [Explaining the Explainer: A First Theoretical Analysis of LIME](https://mlsanity.com/paper/2001.03447/) (2020)
- [Model Agnostic Supervised Local Explanations](https://mlsanity.com/paper/1807.02910/) (2018)
- [Towards the Unification and Robustness of Perturbation and Gradient Based Explanations](https://mlsanity.com/paper/2102.10618/) (2021)
- [Gradient-based Analysis of NLP Models is Manipulable](https://mlsanity.com/paper/2010.05419/) (2020)

## Built on by (most cited first, 3 of 3)

- [Argument Attribution Explanations in Quantitative Bipolar Argumentation Frameworks (Technical Report)](https://mlsanity.com/paper/2307.13582/) (2023)
- [Contestability in Quantitative Argumentation](https://mlsanity.com/paper/2507.11323/) (2025)
- [Attribution Explanations for Deep Neural Networks: A Theoretical Perspective](https://mlsanity.com/paper/2508.07636/) (2025)

## Abstract (arXiv)

There is broad agreement in the literature that explanation methods should be faithful to the model that they explain, but faithfulness remains a rather vague term. We revisit faithfulness in the context of continuous data and propose two formal definitions of faithfulness for feature attribution methods. Qualitative faithfulness demands that scores reflect the true qualitative effect (positive vs. negative) of the feature on the model and quanitative faithfulness that the magnitude of scores reflect the true quantitative effect. We discuss under which conditions these requirements can be satisfied to which extent (local vs global). As an application of the conceptual idea, we look at differentiable classifiers over continuous data and characterize Gradient-scores as follows: every qualitatively faithful feature attribution method is qualitatively equivalent to Gradient-scores. Furthermore, if an attribution method is quantitatively faithful in the sense that changes of the output of the classifier are proportional to the scores of features, then it is either equivalent to gradient-scoring or it is based on an inferior approximation of the classifier. To illustrate the practical relevance of the theory, we experimentally demonstrate that popular attribution methods can fail to give faithful explanations in the setting where the data is continuous and the classifier differentiable.