# A Differential Geometric View and Explainability of GNN on Evolving Graphs

arXiv: https://arxiv.org/abs/2403.06425 · HTML: https://mlsanity.com/paper/2403.06425/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 43 references that are in the map.
- First posted on arXiv 11 Mar 2024.

## Builds on (most cited first, 30 of 31)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Inductive Representation Learning on Temporal Graphs](https://mlsanity.com/paper/2002.07962/) (2020)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [On Explainability of Graph Neural Networks via Subgraph Explorations](https://mlsanity.com/paper/2102.05152/) (2021)
- [Representation Learning for Dynamic Graphs: A Survey](https://mlsanity.com/paper/1905.11485/) (2019)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [XGNN: Towards Model-Level Explanations of Graph Neural Networks](https://mlsanity.com/paper/2006.02587/) (2020)
- [PGM-Explainer: Probabilistic Graphical Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2010.05788/) (2020)
- [Higher-Order Explanations of Graph Neural Networks via Relevant Walks](https://mlsanity.com/paper/2006.03589/) (2020)
- [Universal Statistics of Fisher Information in Deep Neural Networks: Mean Field Approach](https://mlsanity.com/paper/1806.01316/) (2018)
- [The Riemannian Geometry of Deep Generative Models](https://mlsanity.com/paper/1711.08014/) (2017)
- [DIG: A Turnkey Library for Diving into Graph Deep Learning Research](https://mlsanity.com/paper/2103.12608/) (2021)
- [On the distance between two neural networks and the stability of learning](https://mlsanity.com/paper/2002.03432/) (2020)
- [How to Build a Graph-Based Deep Learning Architecture in Traffic Domain: A Survey](https://mlsanity.com/paper/2005.11691/) (2020)
- [Large-Scale Distributed Second-Order Optimization Using Kronecker-Factored Approximate Curvature for Deep Convolutional Neural Networks](https://mlsanity.com/paper/1811.12019/) (2018)
- [Learning Dynamics via Graph Neural Networks for Human Pose Estimation and Tracking](https://mlsanity.com/paper/2106.03772/) (2021)
- [On the Variance of the Fisher Information for Deep Learning](https://mlsanity.com/paper/2107.04205/) (2021)
- [f-GANs in an Information Geometric Nutshell](https://mlsanity.com/paper/1707.04385/) (2017)
- [Interpreting and Disentangling Feature Components of Various Complexity from DNNs](https://mlsanity.com/paper/2006.15920/) (2020)
- [Lower Bounds on the Generalization Error of Nonlinear Learning Models](https://mlsanity.com/paper/2103.14723/) (2021)

## Built on by (most cited first, 4 of 4)

- [CoDy: Counterfactual Explainers for Dynamic Graphs](https://mlsanity.com/paper/2403.16846/) (2024)
- [Introducing Diminutive Causal Structure into Graph Representation Learning](https://mlsanity.com/paper/2406.08709/) (2024)
- [ST-TGExplainer: Disentangling Stability and Transition Patterns for Temporal GNN Interpretability](https://mlsanity.com/paper/2605.19822/) (2026)
- [Towards the Explainability of Temporal Graph Networks via Memory Backtracking and Topological Attribution](https://mlsanity.com/paper/2607.07716/) (2026)

## Abstract (arXiv)

Graphs are ubiquitous in social networks and biochemistry, where Graph Neural Networks (GNN) are the state-of-the-art models for prediction. Graphs can be evolving and it is vital to formally model and understand how a trained GNN responds to graph evolution. We propose a smooth parameterization of the GNN predicted distributions using axiomatic attribution, where the distributions are on a low-dimensional manifold within a high-dimensional embedding space. We exploit the differential geometric viewpoint to model distributional evolution as smooth curves on the manifold. We reparameterize families of curves on the manifold and design a convex optimization problem to find a unique curve that concisely approximates the distributional evolution for human interpretation. Extensive experiments on node classification, link prediction, and graph classification tasks with evolving graphs demonstrate the better sparsity, faithfulness, and intuitiveness of the proposed method over the state-of-the-art methods.