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

**Authors:** Jonathan Crabbé, Mihaela van der Schaar  
**arXiv:** [2304.06715](https://arxiv.org/abs/2304.06715)  
**Date:** 2023-04-13  
**Summary page:** https://www.summarizepaper.com/en/paper/2304.06715v1/

## Key points

- Interpretability methods are crucial for understanding complex machine learning models.
- Explanation invariance and equivariance are necessary to ensure accurate explanations of these models.
- Two metrics, invariance and equivariance scores, can measure the robustness of interpretability methods with respect to model symmetry groups.
- The authors provide theoretical robustness guarantees for some popular interpretability methods and a systematic approach to increase their invariance with respect to a symmetry group.
- Empirical measurements of the metrics were conducted on various modalities and symmetry groups, leading to five guidelines for producing robust explanations:
- Use multiple symmetries when aggregating explanations
- Ensure interpretations are consistent across different samples within a dataset
- Evaluate interpretability methods on diverse datasets with varying levels of complexity
- Test interpretability methods on models trained with different hyperparameters or architectures
- Use domain-specific knowledge when designing interpretation tasks
- Following these guidelines can lead to more reliable interpretations that accurately capture the underlying mechanisms driving complex machine learning models.

## Summary

Interpretability methods are essential for understanding the inner workings of complex machine learning models. To ensure that any explanation accurately explains this type of model, it needs to be in agreement with its invariance property. The authors formalize this intuition through the notion of explanation invariance and equivariance by leveraging the formalism from geometric deep learning. They derive two metrics to measure the robustness of any interpretability method with respect to the model symmetry group: invariance and equivariance scores. The authors also introduce theoretical robustness guarantees for some popular interpretability methods and a systematic approach to increase their invariance with respect to a symmetry group. The authors empirically measure their metrics for explanations of models associated with various modalities and symmetry groups and derive a set of five guidelines to allow users and developers of interpretability methods to produce robust explanations. These guidelines include using multiple symmetries when aggregating explanations, ensuring that interpretations are consistent across different samples within a dataset, evaluating interpretability methods on diverse datasets with varying levels of complexity, testing interpretability methods on models trained with different hyperparameters or architectures, and using domain-specific knowledge when designing interpretation tasks. Overall, this work provides insights into how researchers can evaluate the robustness of interpretability methods and improve their performance by considering specific properties of machine learning models such as their symmetry groups. By following these guidelines, users can produce more reliable interpretations that accurately capture the underlying mechanisms driving complex machine learning models.