# GOAt: Explaining Graph Neural Networks via Graph Output Attribution

arXiv: https://arxiv.org/abs/2401.14578 · HTML: https://mlsanity.com/paper/2401.14578/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 33 references that are in the map.
- First posted on arXiv 26 Jan 2024.

## Builds on (most cited first, 25 of 25)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [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)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [On Explainability of Graph Neural Networks via Subgraph Explorations](https://mlsanity.com/paper/2102.05152/) (2021)
- [PGM-Explainer: Probabilistic Graphical Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2010.05788/) (2020)
- [Layer-wise Relevance Propagation for Neural Networks with Local Renormalization Layers](https://mlsanity.com/paper/1604.00825/) (2016)
- [Explainability Techniques for Graph Convolutional Networks](https://mlsanity.com/paper/1905.13686/) (2019)
- [Interpreting Graph Neural Networks for NLP With Differentiable Edge Masking](https://mlsanity.com/paper/2010.00577/) (2020)
- [Higher-Order Explanations of Graph Neural Networks via Relevant Walks](https://mlsanity.com/paper/2006.03589/) (2020)
- [Generative Causal Explanations for Graph Neural Networks](https://mlsanity.com/paper/2104.06643/) (2021)
- [CF-GNNExplainer: Counterfactual Explanations for Graph Neural Networks](https://mlsanity.com/paper/2102.03322/) (2021)
- [Learning and Evaluating Graph Neural Network Explanations based on Counterfactual and Factual Reasoning](https://mlsanity.com/paper/2202.08816/) (2022)
- [Robust Counterfactual Explanations on Graph Neural Networks](https://mlsanity.com/paper/2107.04086/) (2021)
- [Global Explainability of GNNs via Logic Combination of Learned Concepts](https://mlsanity.com/paper/2210.07147/) (2022)
- [RelEx: A Model-Agnostic Relational Model Explainer](https://mlsanity.com/paper/2006.00305/) (2020)
- [GStarX: Explaining Graph Neural Networks with Structure-Aware Cooperative Games](https://mlsanity.com/paper/2201.12380/) (2022)
- [Explaining Convolutional Neural Networks using Softmax Gradient Layer-wise Relevance Propagation](https://mlsanity.com/paper/1908.04351/) (2019)
- [Task-Agnostic Graph Explanations](https://mlsanity.com/paper/2202.08335/) (2022)
- [DEGREE: Decomposition Based Explanation For Graph Neural Networks](https://mlsanity.com/paper/2305.12895/) (2023)
- [Towards Faithful and Consistent Explanations for Graph Neural Networks](https://mlsanity.com/paper/2205.13733/) (2022)

## Built on by (most cited first, 10 of 10)

- [From Nodes to Narratives: Explaining Graph Neural Networks with LLMs and Graph Context](https://mlsanity.com/paper/2508.07117/) (2025)
- [EiG-Search: Generating Edge-Induced Subgraphs for GNN Explanation in Linear Time](https://mlsanity.com/paper/2405.01762/) (2024)
- [GnnXemplar: Exemplars to Explanations -- Natural Language Rules for Global GNN Interpretability](https://mlsanity.com/paper/2509.18376/) (2025)
- [Model-Level GNN Explanations via Rule-to-Graph Readout for Logit Reconstruction](https://mlsanity.com/paper/2503.09051/) (2025)
- [AdversariaL attacK sAfety aLIgnment(ALKALI): Safeguarding LLMs through GRACE: Geometric Representation-Aware Contrastive Enhancement- Introducing Adversarial Vulnerability Quality Index (AVQI)](https://mlsanity.com/paper/2506.08885/) (2025)
- [ARM-Explainer -- Explaining and improving graph neural network predictions for the maximum clique problem using node features and association rule mining](https://mlsanity.com/paper/2511.22866/) (2025)
- [FSX: Message Flow Sensitivity Enhanced Structural Explainer for Graph Neural Networks](https://mlsanity.com/paper/2601.14730/) (2026)
- [Improving Adversarial Robustness of Attribution via Implicit Regularization](https://mlsanity.com/paper/2605.29983/) (2026)
- [CIExplainer++: Generating Causal and Interpretable Explanations for Graph Neural Networks](https://mlsanity.com/paper/2606.20747/) (2026)
- [GraphSelect for Budgeted Representation Selection in Multimodal Graph Inference](https://mlsanity.com/paper/2609.33561/) (2026)

## Abstract (arXiv)

Understanding the decision-making process of Graph Neural Networks (GNNs) is crucial to their interpretability. Most existing methods for explaining GNNs typically rely on training auxiliary models, resulting in the explanations remain black-boxed. This paper introduces Graph Output Attribution (GOAt), a novel method to attribute graph outputs to input graph features, creating GNN explanations that are faithful, discriminative, as well as stable across similar samples. By expanding the GNN as a sum of scalar products involving node features, edge features and activation patterns, we propose an efficient analytical method to compute contribution of each node or edge feature to each scalar product and aggregate the contributions from all scalar products in the expansion form to derive the importance of each node and edge. Through extensive experiments on synthetic and real-world data, we show that our method not only outperforms various state-ofthe-art GNN explainers in terms of the commonly used fidelity metric, but also exhibits stronger discriminability, and stability by a remarkable margin.