# Interpretable Geometric Deep Learning via Learnable Randomness Injection

arXiv: https://arxiv.org/abs/2210.16966 · HTML: https://mlsanity.com/paper/2210.16966/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 68 of its 108 references that are in the map.
- First posted on arXiv 30 Oct 2022.

## Builds on (most cited first, 30 of 68)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (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)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1710.11063/) (2017)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)

## Built on by (most cited first, 27 of 27)

- [Encoding Time-Series Explanations through Self-Supervised Model Behavior Consistency](https://mlsanity.com/paper/2306.02109/) (2023)
- [Does Invariant Graph Learning via Environment Augmentation Learn Invariance?](https://mlsanity.com/paper/2310.19035/) (2023)
- [A Survey on Explainability of Graph Neural Networks](https://mlsanity.com/paper/2306.01958/) (2023)
- [TempME: Towards the Explainability of Temporal Graph Neural Networks via Motif Discovery](https://mlsanity.com/paper/2310.19324/) (2023)
- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Towards Robust Fidelity for Evaluating Explainability of Graph Neural Networks](https://mlsanity.com/paper/2310.01820/) (2023)
- [Reconsidering Faithfulness in Regular, Self-Explainable and Domain Invariant GNNs](https://mlsanity.com/paper/2406.15156/) (2024)
- [How Interpretable Are Interpretable Graph Neural Networks?](https://mlsanity.com/paper/2406.07955/) (2024)
- [Beyond Topological Self-Explainable GNNs: A Formal Explainability Perspective](https://mlsanity.com/paper/2502.02719/) (2025)
- [Learning High-Order Relationships of Brain Regions](https://mlsanity.com/paper/2312.02203/) (2023)
- [Factorized Explainer for Graph Neural Networks](https://mlsanity.com/paper/2312.05596/) (2023)
- [Recent Advances in Malware Detection: Graph Learning and Explainability](https://mlsanity.com/paper/2502.10556/) (2025)
- [How Faithful are Self-Explainable GNNs?](https://mlsanity.com/paper/2308.15096/) (2023)
- [SoREX: Towards Self-Explainable Social Recommendation with Relevant Ego-Path Extraction](https://mlsanity.com/paper/2510.00080/) (2025)
- [GNN Explanations that do not Explain and How to find Them](https://mlsanity.com/paper/2601.20815/) (2026)
- [FAIR AI Models in High Energy Physics](https://mlsanity.com/paper/2212.05081/) (2022)
- [GeSS: Benchmarking Geometric Deep Learning under Scientific Applications with Distribution Shifts](https://mlsanity.com/paper/2310.08677/) (2023)
- [RISE: Radius of Influence based Subgraph Extraction for 3D Molecular Graph Explanation](https://mlsanity.com/paper/2505.02247/) (2025)
- [Joint Feature and Differentiable  k -NN Graph Learning using Dirichlet Energy](https://mlsanity.com/paper/2305.12396/) (2023)
- [Discovering robust biomarkers of psychiatric disorders from resting-state functional MRI via graph neural networks: A systematic review](https://mlsanity.com/paper/2405.00577/) (2024)
- [Towards Understanding Sensitive and Decisive Patterns in Explainable AI: A Case Study of Model Interpretation in Geometric Deep Learning](https://mlsanity.com/paper/2407.00849/) (2024)
- [Transformers from Diffusion: A Unified Framework for Neural Message Passing](https://mlsanity.com/paper/2409.09111/) (2024)
- [Explanation-Preserving Augmentation for Semi-Supervised Graph Representation Learning](https://mlsanity.com/paper/2410.12657/) (2024)
- [XAI for Point Cloud Data using Perturbations based on Meaningful Segmentation](https://mlsanity.com/paper/2507.22020/) (2025)
- [Learning Invariant Graph Representations Through Redundant Information](https://mlsanity.com/paper/2512.06154/) (2025)
- [PAC Learnability under Explanation-Preserving Graph Perturbations](https://mlsanity.com/paper/2402.05039/) (2024)
- [Exploring Concept Subspace for Self-explainable Text-Attributed Graph Learning](https://mlsanity.com/paper/2604.11986/) (2026)

## Abstract (arXiv)

Point cloud data is ubiquitous in scientific fields. Recently, geometric deep learning (GDL) has been widely applied to solve prediction tasks with such data. However, GDL models are often complicated and hardly interpretable, which poses concerns to scientists who are to deploy these models in scientific analysis and experiments. This work proposes a general mechanism, learnable randomness injection (LRI), which allows building inherently interpretable models based on general GDL backbones. LRI-induced models, once trained, can detect the points in the point cloud data that carry information indicative of the prediction label. We also propose four datasets from real scientific applications that cover the domains of high-energy physics and biochemistry to evaluate the LRI mechanism. Compared with previous post-hoc interpretation methods, the points detected by LRI align much better and stabler with the ground-truth patterns that have actual scientific meanings. LRI is grounded by the information bottleneck principle, and thus LRI-induced models are also more robust to distribution shifts between training and test scenarios. Our code and datasets are available at urlhttps://github.com/Graph-COM/LRI.