# Evaluating the Robustness of Interpretability Methods through Explanation Invariance and Equivariance

arXiv: https://arxiv.org/abs/2304.06715 · HTML: https://mlsanity.com/paper/2304.06715/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 64 of its 104 references that are in the map.
- First posted on arXiv 13 Apr 2023.

## Builds on (most cited first, 30 of 64)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Captum: A unified and generic model interpretability library for PyTorch](https://mlsanity.com/paper/2009.07896/) (2020)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)

## Built on by (most cited first, 14 of 14)

- [A Primer on the Inner Workings of Transformer-based Language Models](https://mlsanity.com/paper/2405.00208/) (2024)
- [How Interpretable Are Interpretable Graph Neural Networks?](https://mlsanity.com/paper/2406.07955/) (2024)
- [Interpretability Can Be Actionable](https://mlsanity.com/paper/2605.11161/) (2026)
- [Towards Adversarial Robustness via Debiased High-Confidence Logit Alignment](https://mlsanity.com/paper/2408.06079/) (2024)
- [One Wave To Explain Them All: A Unifying Perspective On Feature Attribution](https://mlsanity.com/paper/2410.01482/) (2024)
- [Robustness of Explainable Artificial Intelligence in Industrial Process Modelling](https://mlsanity.com/paper/2407.09127/) (2024)
- [EvoSpeak: Large Language Models for Interpretable Genetic Programming-Evolved Heuristics](https://mlsanity.com/paper/2510.02686/) (2025)
- [ProtoSiTex: Learning Semi-Interpretable Prototypes for Multi-label Text Classification](https://mlsanity.com/paper/2510.12534/) (2025)
- [φ-Table: A Statistical Explanation for Global SHAP](https://mlsanity.com/paper/2512.07578/) (2025)
- [Consistent Evidence, Robust Recognition: Faithful Attribution Regularization under Geometric Transformations](https://mlsanity.com/paper/2607.23835/) (2026)
- [Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks](https://mlsanity.com/paper/2607.26344/) (2026)
- [LAWFUL: Law-Aligned Witness for Faithful Use of Latents](https://mlsanity.com/paper/2607.28672/) (2026)
- [Signal or Noise? Auditing Rotation-Induced Saliency Drift in Medical and Aerial Imaging](https://mlsanity.com/paper/2609.02224/) (2026)
- [Hidden Activations are not Enough I: Knowledge Matrices as Higher Representations](https://mlsanity.com/paper/2609.34166/) (2026)

## Abstract (arXiv)

Interpretability methods are valuable only if their explanations faithfully describe the explained model. In this work, we consider neural networks whose predictions are invariant under a specific symmetry group. This includes popular architectures, ranging from convolutional to graph neural networks. Any explanation that faithfully explains this type of model needs to be in agreement with this invariance property. We formalize this intuition through the notion of explanation invariance and equivariance by leveraging the formalism from geometric deep learning. Through this rigorous formalism, we derive (1) two metrics to measure the robustness of any interpretability method with respect to the model symmetry group; (2) theoretical robustness guarantees for some popular interpretability methods and (3) a systematic approach to increase the invariance of any interpretability method with respect to a symmetry group. By empirically measuring our metrics for explanations of models associated with various modalities and symmetry groups, we derive a set of 5 guidelines to allow users and developers of interpretability methods to produce robust explanations.