arxiv: 2604.20082 · v1 · submitted 2026-04-22 · 💻 cs.LG

Recognition: unknown

Concept Graph Convolutions: Message Passing in the Concept Space

Lucie Charlotte Magister , Pietro Lio

Authors on Pith no claims yet

Pith reviewed 2026-05-10 00:12 UTC · model grok-4.3

classification 💻 cs.LG

keywords graph neural networksinterpretabilityconcept-based explanationsmessage passinggraph convolutionsexplainable AInode representations

0 comments

The pith

Graph neural networks can perform message passing directly on node concepts to reveal how reasoning evolves across layers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces the Concept Graph Convolution, a new layer designed to operate on node-level concepts extracted from latent representations. Prior explanation techniques only interpreted final outputs after message passing, leaving the process itself opaque. By combining raw features with these concepts and weighting messages through both structural edges and attention, the layer supports competitive accuracy on graph tasks while exposing concept changes step by step. A pure concept-space variant is also defined for cases that prioritize interpretability.

Core claim

The central claim is that message passing can be redefined to act on a mixture of raw node features and extracted concepts using structural and attention-based edge weights, so that the evolution of concepts across convolutional steps becomes directly observable while task performance stays competitive with standard graph convolutions.

What carries the argument

The Concept Graph Convolution layer, which integrates node-level concepts with raw features for message passing via structural and attention edge weights to enable process-level interpretability.

If this is right

Task accuracy remains competitive with conventional graph convolutions.
Users gain direct visibility into how concepts change and interact across each convolutional step.
The pure concept variant allows the entire convolution to run inside concept space alone.
Explanations now cover the message-passing process rather than only final latent states.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The concept trajectories could serve as a diagnostic tool to locate where a model's reasoning diverges from expected patterns on specific nodes.
Similar concept-space message passing might be tested on non-graph architectures that rely on iterative feature mixing.
If concept evolution proves stable, the layer could support training objectives that explicitly reward coherent concept flow.

Load-bearing premise

Concepts extracted from the network's own latent representations can be meaningfully recombined with raw input features to represent the actual reasoning steps inside the message-passing operation.

What would settle it

Train the layer on a standard benchmark such as Cora or MUTAG and check whether accuracy matches a baseline GCN while the extracted concept trajectories visibly align with the model's final predictions; a clear drop in accuracy or mismatch in concept paths would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.20082 by Lucie Charlotte Magister, Pietro Lio.

**Figure 2.** Figure 2: Concept completeness measured across Concept Graph Convolution (CGC) and pure CGC [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: We plot the learned γ value of Concept Graph Convolution (CGC) and pure CGC layers across the models trained for node classification. 5.0.1 Visualisation of concept-based message passing Finally, we can provide a deeper insight into the model via more elaborate visualizations of how concepts arise. We can visualize the concept found at a given layer and how the concepts are the previous layer contribute to… view at source ↗

**Figure 4.** Figure 4: A concept discovered for the BA-Shapes dataset at the second pure Concept Graph Convolution [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: Concept completeness measured across Concept Graph Convolution (CGC) and pure CGC [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗

**Figure 6.** Figure 6: We measure concept completeness across models with an increasing number of Concept Graph [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗

**Figure 7.** Figure 7: Concept completeness and accuracy measured across training epochs for a model using [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗

**Figure 8.** Figure 8: We plot the learned γ value of Concept Graph Convolution (CGC) and pure CGC layers across the models trained for graph classification. G Reliance on node embeddings versus concept embeddings While the pure CGC layer only operates in the node concept space, the CGC layer also learns a mixing parameter η for determining the mixing of the raw node representations with the concept node representations [PITH_F… view at source ↗

**Figure 9.** Figure 9: We plot the learned η value of Concept Graph Convolution (CGC) and pure CGC layers across the models trained for node and graph classification. H Concept visualisations The CGC layers allow us to visualize concepts discovered at different stages of the receptive fields of a GNN, as we can extract concepts per layer. A benefit of extracting concepts across layers is that 16 [PITH_FULL_IMAGE:figures/full_fi… view at source ↗

**Figure 10.** Figure 10: A concept discovered in the first layer of a model using pure Concept Graph Convolution [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗

**Figure 11.** Figure 11: A concept discovered in the second layer of a model using pure Concept Graph Convolution [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗

**Figure 12.** Figure 12: A concept discovered in the fourth layer of a model using Concept Graph Convolution (CGC) [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗

**Figure 13.** Figure 13: A concept discovered in the fourth layer of a model using [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗

**Figure 14.** Figure 14: A rare concept discovered in the second layer of a model using [PITH_FULL_IMAGE:figures/full_fig_p019_14.png] view at source ↗

**Figure 15.** Figure 15: A concept discovered in the second layer of a model using Concept Graph Convolution (CGC) [PITH_FULL_IMAGE:figures/full_fig_p019_15.png] view at source ↗

**Figure 16.** Figure 16: A concept discovered in the second layer of a model using Concept Graph Convolution [PITH_FULL_IMAGE:figures/full_fig_p020_16.png] view at source ↗

**Figure 17.** Figure 17: A concept discovered for the BA-Community dataset at the third pure Concept Graph [PITH_FULL_IMAGE:figures/full_fig_p020_17.png] view at source ↗

**Figure 18.** Figure 18: A concept discovered for the BA-Grid dataset at the second Concept Graph Convolution [PITH_FULL_IMAGE:figures/full_fig_p021_18.png] view at source ↗

read the original abstract

The trust in the predictions of Graph Neural Networks is limited by their opaque reasoning process. Prior methods have tried to explain graph networks via concept-based explanations extracted from the latent representations obtained after message passing. However, these explanations fall short of explaining the message passing process itself. To this aim, we propose the Concept Graph Convolution, the first graph convolution designed to operate on node-level concepts for improved interpretability. The proposed convolutional layer performs message passing on a combination of raw and concept representations using structural and attention-based edge weights. We also propose a pure variant of the convolution, only operating in the concept space. Our results show that the Concept Graph Convolution allows to obtain competitive task accuracy, while enabling an increased insight into the evolution of concepts across convolutional steps.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper introduces a convolution layer that folds node concepts into message passing rather than explaining after the fact, but the supporting experiments and extraction details are not visible enough to judge the claims.

read the letter

The main new piece here is a graph convolution that runs message passing on a mix of raw node features and pre-extracted concepts, using both structural edges and attention weights. They also give a pure-concept version that drops the raw features entirely. That is a clean architectural shift from the usual post-hoc concept extraction that happens after standard GNN layers have already done their work. If the extraction step is stable, this could let someone watch how concepts change layer by layer instead of only seeing a final explanation. The abstract is direct about the goal and does not overclaim the scope; it stays inside interpretability for GNNs rather than promising broader performance gains. Credit for keeping the proposal simple and for offering the pure-concept variant as an explicit option. The soft spots are mostly about missing pieces. The abstract says the layer gives competitive accuracy plus better insight into concept evolution, yet no equations, no extraction procedure, no baselines, and no error bars are shown. Without those, it is impossible to tell whether the attention weights are surfacing real concept dynamics or just reflecting how the concepts were pulled out of the latents in the first place. The weakest assumption is that node-level concepts extracted from hidden states can be treated as reliable inputs during the forward pass without introducing circularity or instability. If the full paper has solid ablations on extraction methods and shows that accuracy does not drop when concepts are used, that would address the main concern. This is the kind of work that belongs in a reading group on interpretable graph models. A serious editor should send it to review so the methods and results can be checked properly; the idea is clear enough to be worth referee time even if revisions are needed on the experimental side.

Referee Report

2 major / 3 minor

Summary. The manuscript proposes Concept Graph Convolutions (CGC), a new graph convolution layer that performs message passing by combining raw node features with node-level concepts extracted from latent representations. The layer employs both structural edge weights and attention-based weights; a pure-concept variant operating solely in concept space is also introduced. The central claims are that CGC achieves competitive task accuracy on graph benchmarks while providing direct insight into the evolution of concepts across successive convolutional steps, addressing the limitation that prior concept-based explanations only interpret post-message-passing latents.

Significance. If the empirical claims hold, the work offers a meaningful step toward intrinsically interpretable GNNs by embedding concept-based reasoning inside the message-passing operation itself rather than relying on post-hoc analysis. The dual hybrid/pure-concept design is a constructive feature that permits controlled examination of the necessity of raw features. The approach is grounded in standard GNN machinery and does not introduce obvious circularity or unstated assumptions that would invalidate the construction on its face.

major comments (2)

[§3.2] §3.2 (Concept extraction procedure): the stability of the node-level concepts extracted from latent representations is load-bearing for the interpretability claim; without quantitative evidence (e.g., concept consistency across random seeds or layers) it remains unclear whether observed evolution reflects genuine dynamics or extraction artifacts.
[§4.2] §4.2 (Experimental results): the reported competitive accuracy must be supported by direct comparison against the same backbone GNN without the concept layer (i.e., an ablation that isolates the effect of the proposed convolution); the current presentation leaves open whether gains are attributable to the concept mechanism or to other architectural choices.

minor comments (3)

[§3.1] Notation for the attention-based edge weights and the structural weights should be unified and introduced before the first equation that uses them.
[Figure 3] Figure 3 (concept evolution visualization) would benefit from an explicit legend indicating which colors correspond to which extracted concepts and from reporting the number of concepts used.
[Abstract / Introduction] The abstract states 'competitive task accuracy' without naming the datasets or baselines; this should be expanded in the introduction for immediate context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which will help improve the clarity and rigor of our work. We address each major comment below.

read point-by-point responses

Referee: [§3.2] §3.2 (Concept extraction procedure): the stability of the node-level concepts extracted from latent representations is load-bearing for the interpretability claim; without quantitative evidence (e.g., concept consistency across random seeds or layers) it remains unclear whether observed evolution reflects genuine dynamics or extraction artifacts.

Authors: We concur that stability analysis is crucial to substantiate the interpretability benefits. Although the current manuscript focuses on demonstrating the evolution of concepts through visualizations, we will augment the revised version with quantitative metrics for concept stability. Specifically, we will report concept consistency scores across different random seeds and layers using measures such as cosine similarity between concept vectors or adjusted Rand index for clustering stability. This will provide evidence that the observed dynamics are robust rather than extraction artifacts. revision: yes
Referee: [§4.2] §4.2 (Experimental results): the reported competitive accuracy must be supported by direct comparison against the same backbone GNN without the concept layer (i.e., an ablation that isolates the effect of the proposed convolution); the current presentation leaves open whether gains are attributable to the concept mechanism or to other architectural choices.

Authors: We appreciate this point on isolating the contribution of the concept mechanism. The experiments in the manuscript compare CGC against standard GNNs and other concept-based methods, but to directly address this, we will include an ablation study in the revision. This will involve running the exact same backbone network (e.g., the GCN or GAT architecture used) but replacing the CGC layers with standard convolution layers, allowing a direct comparison of task performance with and without the concept-based message passing. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The manuscript introduces Concept Graph Convolution as an architectural design choice that mixes raw node features with extracted concepts via structural and attention weights during message passing. This construction is defined directly by the proposed layer rather than derived from fitted parameters, self-referential equations, or prior self-citations that would force the outcome. Competitive task accuracy and insight into concept evolution are presented as empirical results of the new layer, not as quantities that reduce to the inputs by construction. No load-bearing step matches the enumerated circularity patterns; the approach remains self-contained as a novel GNN variant.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Review is limited to the abstract; detailed parameter counts and assumptions cannot be audited.

axioms (1)

domain assumption Node-level concepts can be reliably extracted from latent representations after message passing
The method builds on prior concept-extraction techniques mentioned in the abstract.

invented entities (1)

Concept Graph Convolution layer no independent evidence
purpose: To enable message passing directly in concept space for interpretability
This is the core proposed component; no independent evidence of its behavior is supplied in the abstract.

pith-pipeline@v0.9.0 · 5418 in / 1160 out tokens · 46900 ms · 2026-05-10T00:12:46.147974+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

49 extracted references · 16 canonical work pages · 3 internal anchors

[1]

The graph neural network model.IEEE transactions on neural networks, 20(1):61–80, 2008

Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, and Gabriele Monfardini. The graph neural network model.IEEE transactions on neural networks, 20(1):61–80, 2008

2008
[2]

Graphxai: a survey of graph neural networks (gnns) for explainable ai (xai).Neural Computing and Applications, 37(17):10949–11000, 2025

Mauparna Nandan, Soma Mitra, and Debashis De. Graphxai: a survey of graph neural networks (gnns) for explainable ai (xai).Neural Computing and Applications, 37(17):10949–11000, 2025. URLhttps://doi.org/10.1007/s00521-025-11054-3

work page doi:10.1007/s00521-025-11054-3 2025
[3]

Graph neural networks.Nature Reviews Methods Primers, 4(1):17, 2024

Gabriele Corso, Hannes Stark, Stefanie Jegelka, Tommi Jaakkola, and Regina Barzilay. Graph neural networks.Nature Reviews Methods Primers, 4(1):17, 2024

2024
[4]

A comprehensive survey on self-interpretable neural networks.Proceedings of the IEEE, 2025

Yang Ji, Ying Sun, Yuting Zhang, Zhigaoyuan Wang, Yuanxin Zhuang, Zheng Gong, Dazhong Shen, Chuan Qin, Hengshu Zhu, and Hui Xiong. A comprehensive survey on self-interpretable neural networks.Proceedings of the IEEE, 2025

2025
[5]

Gcexplainer: Human-in- the-loop concept-based explanations for graph neural networks.arXiv preprint arXiv:2107.11889, 2021

Lucie Charlotte Magister, Dmitry Kazhdan, Vikash Singh, and Pietro Liò. Gcexplainer: Human-in- the-loop concept-based explanations for graph neural networks.arXiv preprint arXiv:2107.11889, 2021

work page arXiv 2021
[6]

Concept distillation in graph neural networks

Lucie Charlotte Magister, Pietro Barbiero, Dmitry Kazhdan, Federico Siciliano, Gabriele Ciravegna, Fabrizio Silvestri, Mateja Jamnik, and Pietro Liò. Concept distillation in graph neural networks. In World Conference on Explainable Artificial Intelligence, pages 233–255. Springer, 2023

2023
[7]

Global explain- ability of gnns via logic combination of learned concepts

Steve Azzolin, Antonio Longa, Pietro Barbiero, Pietro Liò, and Andrea Passerini. Global explain- ability of gnns via logic combination of learned concepts. InInternational Conference on Learning Representations. PMLR, 2023

2023
[8]

Beyond message passing: A symbolic alternative for expressive and interpretable graph learning

Chuqin Geng, Li Zhang, Haolin Ye, Ziyu Zhao, Yuhe Jiang, Tara Saba, Xinyu Wang, and Xujie Si. Beyond message passing: A symbolic alternative for expressive and interpretable graph learning. arXiv preprint arXiv:2602.16947, 2026

work page arXiv 2026
[9]

& Yahav, E

Shaked Brody, Uri Alon, and Eran Yahav. How attentive are graph attention networks?arXiv preprint arXiv:2105.14491, 2021

work page arXiv 2021
[10]

Interpretable and generalizable graph learning via stochastic attention mechanism

Siqi Miao, Mia Liu, and Pan Li. Interpretable and generalizable graph learning via stochastic attention mechanism. InInternational conference on machine learning, pages 15524–15543. PMLR, 2022

2022
[11]

Graph Attention Networks.International Conference on Learning Representations, 2018

Petar Veliˇckovi´c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio. Graph Attention Networks.International Conference on Learning Representations, 2018. URLhttps://openreview.net/forum?id=rJXMpikCZ

2018
[12]

Semi-Supervised Classification with Graph Convolutional Networks

Thomas N. Kipf and Max Welling. Semi-Supervised Classification with Graph Convolutional Networks. In5th International Conference on Learning Representations, ICLR 2017 - Conference Track Proceedings, pages 11313–11320. International Conference on Learning Representations, ICLR, sep 2016. URLhttp://arxiv.org/abs/1609.02907

work page internal anchor Pith review arXiv 2017
[13]

Hamilton, Rex Ying, and Jure Leskovec

William L. Hamilton, Rex Ying, and Jure Leskovec. Inductive representation learning on large graphs. InProceedings of the 31st International Conference on Neural Information Processing Systems, NIPS’17, page 1025–1035, Red Hook, NY , USA, 2017. Curran Associates Inc. ISBN 9781510860964

2017
[14]

How Powerful are Graph Neural Networks?

Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks?arXiv preprint arXiv:1810.00826, 2018

work page internal anchor Pith review arXiv 2018
[15]

Convolutional neural networks on graphs with fast localized spectral filtering

Michaël Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on graphs with fast localized spectral filtering. InProceedings of the 30th International Conference on Neural Information Processing Systems, NIPS’16, page 3844–3852, Red Hook, NY , USA, 2016. Curran Associates Inc. ISBN 9781510838819

2016
[16]

arXiv preprint arXiv:1803.03735 , year=

Kiran K Thekumparampil, Chong Wang, Sewoong Oh, and Li-Jia Li. Attention-based graph neural network for semi-supervised learning.arXiv preprint arXiv:1803.03735, 2018. 10

work page arXiv 2018
[17]

and Oh, A

Dongkwan Kim and Alice Oh. How to find your friendly neighborhood: Graph attention design with self-supervision.arXiv preprint arXiv:2204.04879, 2022

work page arXiv 2022
[18]

Sim- plifying graph convolutional networks

Felix Wu, Amauri Souza, Tianyi Zhang, Christopher Fifty, Tao Yu, and Kilian Weinberger. Sim- plifying graph convolutional networks. InInternational conference on machine learning, pages 6861–6871. Pmlr, 2019

2019
[19]

Revisitingover-smoothingindeepgcns

Chaoqi Yang, Ruijie Wang, Shuochao Yao, Shengzhong Liu, and Tarek Abdelzaher. Revisiting over-smoothing in deep gcns.arXiv preprint arXiv:2003.13663, 2020

work page arXiv 2003
[20]

Relational concept bottleneck models.Advances in Neural Information Processing Systems, 37:77663–77685, 2024

Pietro Barbiero, Francesco Giannini, Gabriele Ciravegna, Michelangelo Diligenti, and Giuseppe Marra. Relational concept bottleneck models.Advances in Neural Information Processing Systems, 37:77663–77685, 2024

2024
[21]

Causal concept graph models: Beyond causal opacity in deep learning

Gabriele Dominici, Pietro Barbiero, Mateo Espinosa Zarlenga, Alberto Termine, Martin Gjoreski, Giuseppe Marra, and Marc Langheinrich. Causal concept graph models: Beyond causal opacity in deep learning. InThe Thirteenth International Conference on Learning Representations, ICLR 2025, Singapore, April 24-28, 2025, 2025

2025
[22]

Is attention explanation? an introduction to the debate

Adrien Bibal, Rémi Cardon, David Alfter, Rodrigo Wilkens, Xiaoou Wang, Thomas François, and Patrick Watrin. Is attention explanation? an introduction to the debate. InProceedings of the 60th Annual Meeting of the Association for Computational Linguistics (volume 1: long papers), pages 3889–3900, 2022

2022
[23]

Attention is not explanation

Sarthak Jain and Byron C Wallace. Attention is not explanation. InProceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers), pages 3543–3556, 2019

2019
[24]

Attention is not not explanation

Sarah Wiegreffe and Yuval Pinter. Attention is not not explanation. InProceedings of the 2019 conference on empirical methods in natural language processing and the 9th international joint conference on natural language processing (EMNLP-IJCNLP), pages 11–20, 2019

2019
[25]

Why attentions may not be interpretable? InProceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining, pages 25–34, 2021

Bing Bai, Jian Liang, Guanhua Zhang, Hao Li, Kun Bai, and Fei Wang. Why attentions may not be interpretable? InProceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining, pages 25–34, 2021

2021
[26]

Attention cannot be an explanation.arXiv preprint arXiv:2201.11194, 2022

Arjun R Akula and Song-Chun Zhu. Attention cannot be an explanation.arXiv preprint arXiv:2201.11194, 2022

work page arXiv 2022
[27]

Ridge regression.Wiley Interdisciplinary Reviews: Computational Statistics, 1 (1):93–100, 2009

Gary C McDonald. Ridge regression.Wiley Interdisciplinary Reviews: Computational Statistics, 1 (1):93–100, 2009

2009
[28]

Bronstein, Joan Bruna, Taco Cohen, and Petar Veliˇckovi´c

Michael M. Bronstein, Joan Bruna, Taco Cohen, and Petar Veliˇckovi´c. Geometric deep learning: Grids, groups, graphs, geodesics, and gauges, 2021. URL https://arxiv.org/abs/2104. 13478

2021
[29]

On Completeness-aware Concept-Based Explanations in Deep Neural Net- works

Chih-Kuan Yeh, Been Kim, Sercan Ö Arık, Chun-Liang Li, Tomas Pfister, and Pradeep Ravikumar. On Completeness-aware Concept-Based Explanations in Deep Neural Net- works. InAdvances in Neural Information Processing Systems 33 (NeurIPS 2020), vol- ume 33, pages 20554–20565, 2020. URL https://papers.nips.cc/paper/2020/hash/ ecb287ff763c169694f682af52c1f309-Ab...

2020
[30]

Wadsworth, 1984

L Breiman, JH Friedman, R Olshen, and CJ Stone.Classification and Regression Trees. Wadsworth, 1984

1984
[31]

Gnnexplainer: Generating explanations for graph neural networks.Advances in neural information processing systems, 32, 2019

Zhitao Ying, Dylan Bourgeois, Jiaxuan You, Marinka Zitnik, and Jure Leskovec. Gnnexplainer: Generating explanations for graph neural networks.Advances in neural information processing systems, 32, 2019

2019
[32]

Parameterized explainer for graph neural network.Advances in neural information processing systems, 33:19620–19631, 2020

Dongsheng Luo, Wei Cheng, Dongkuan Xu, Wenchao Yu, Bo Zong, Haifeng Chen, and Xiang Zhang. Parameterized explainer for graph neural network.Advances in neural information processing systems, 33:19620–19631, 2020

2020
[33]

Pgm-explainer: Probabilistic graphical model explanations for graph neural networks.Advances in neural information processing systems, 33:12225–12235, 2020

Minh Vu and My T Thai. Pgm-explainer: Probabilistic graphical model explanations for graph neural networks.Advances in neural information processing systems, 33:12225–12235, 2020. 11

2020
[34]

Global concept-based interpretability for graph neural networks via neuron analysis

Han Xuanyuan, Pietro Barbiero, Dobrik Georgiev, Lucie Charlotte Magister, and Pietro Liò. Global concept-based interpretability for graph neural networks via neuron analysis. InProceedings of the AAAI conference on artificial intelligence, volume 37, pages 10675–10683, 2023

2023
[35]

Explaining the explainers in graph neural networks: a comparative study.ACM Computing Surveys, 57(5):1–37, 2025

Antonio Longa, Steve Azzolin, Gabriele Santin, Giulia Cencetti, Pietro Lio, Bruno Lepri, and Andrea Passerini. Explaining the explainers in graph neural networks: a comparative study.ACM Computing Surveys, 57(5):1–37, 2025

2025
[36]

Emergence of scaling in random networks.science, 286 (5439):509–512, 1999

Albert-László Barabási and Réka Albert. Emergence of scaling in random networks.science, 286 (5439):509–512, 1999

1999
[37]

Erdos and Alfréd Rényi

Paul L. Erdos and Alfréd Rényi. On the evolution of random graphs.Transactions of the Amer- ican Mathematical Society, 286:257–257, 1984. URL https://api.semanticscholar.org/ CorpusID:6829589

1984
[38]

TUDataset: A collection of benchmark datasets for learning with graphs.arXiv preprint arXiv:2007.08663,

Christopher Morris, Nils M Kriege, Franka Bause, Kristian Kersting, Petra Mutzel, and Marion Neumann. Tudataset: A collection of benchmark datasets for learning with graphs.arXiv preprint arXiv:2007.08663, 2020

work page arXiv 2007
[39]

Protgnn: Towards self- explaining graph neural networks

Zaixi Zhang, Qi Liu, Hao Wang, Chengqiang Lu, and Cheekong Lee. Protgnn: Towards self- explaining graph neural networks. InProceedings of the AAAI Conference on Artificial Intelligence, volume 36, pages 9127–9135, 2022

2022
[40]

Megan: Multi-explanation graph attention network.arXiv preprint arXiv:2211.13236, 2022

Jonas Teufel, Luca Torresi, Patrick Reiser, and Pascal Friederich. Megan: Multi-explanation graph attention network.arXiv preprint arXiv:2211.13236, 2022

work page arXiv 2022
[41]

Explaining gnn explanations with edge gradients

Jesse He, Akbar Rafiey, Gal Mishne, and Yusu Wang. Explaining gnn explanations with edge gradients. InProceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V . 2, pages 884–895, 2025

2025
[42]

Efficient gnn explanation via learning removal-based attribution.Acm Transactions on Knowledge Discovery from Data, 19(2):1–23, 2025

Yao Rong, Guanchu Wang, Qizhang Feng, Ninghao Liu, Zirui Liu, Enkelejda Kasneci, and Xia Hu. Efficient gnn explanation via learning removal-based attribution.Acm Transactions on Knowledge Discovery from Data, 19(2):1–23, 2025

2025
[43]

Concept embedding models: beyond the accuracy-explainability trade-off

Mateo Espinosa Zarlenga, Pietro Barbiero, Gabriele Ciravegna, Giuseppe Marra, Francesco Gian- nini, Michelangelo Diligenti, Zohreh Shams, Frederic Precioso, Stefano Melacci, Adrian Weller, Pietro Lio, and Mateja Jamnik. Concept embedding models: beyond the accuracy-explainability trade-off. InProceedings of the 36th International Conference on Neural Info...

2024
[44]

Stochastic modified equations and adaptive stochastic gradi- ent algorithms

Qianxiao Li, Cheng Tai, and Weinan E. Stochastic modified equations and adaptive stochastic gradi- ent algorithms. In Doina Precup and Yee Whye Teh, editors,Proceedings of the 34th International Conference on Machine Learning, volume 70 ofProceedings of Machine Learning Research, pages 2101–2110. PMLR, 06–11 Aug 2017. URL https://proceedings.mlr.press/v70...

2017
[45]

PyTorch: An Imperative Style, High-Performance Deep Learning Library

Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library.arXiv preprint arXiv:1912.01703, 2019

work page internal anchor Pith review Pith/arXiv arXiv 1912
[46]

Learning deep features for discriminative localization

Bolei Zhou, Aditya Khosla, Agata Lapedriza, Aude Oliva, and Antonio Torralba. Learning deep features for discriminative localization. In2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 2921–2929, 2016. doi:10.1109/CVPR.2016.319

work page doi:10.1109/cvpr.2016.319 2016
[47]

Selvaraju, Michael Cogswell, Ab- hishek Das, Ramakrishna Vedantam, Devi Parikh, and Dhruv Batra

Ramprasaath R. Selvaraju, Michael Cogswell, Abhishek Das, Ramakrishna Vedantam, Devi Parikh, and Dhruv Batra. Grad-cam: Visual explanations from deep networks via gradient-based localiza- tion. In2017 IEEE International Conference on Computer Vision (ICCV), pages 618–626, 2017. doi:10.1109/ICCV .2017.74

work page doi:10.1109/iccv 2017
[48]

End-to-end feature alignment: A simple cnn with intrinsic class attribution.arXiv preprint arXiv:2603.25798, 2026

Parniyan Farvardin and David Chapman. End-to-end feature alignment: A simple cnn with intrinsic class attribution.arXiv preprint arXiv:2603.25798, 2026

work page arXiv 2026
[49]

Interactive exploration of cnn interpretability via coalitional game theory.Scientific Reports, 15(1):9261, 2025

Lei Yang, Lingmeng Lu, Chao Liu, Jian Zhang, Kehua Guo, Ning Zhang, Fangfang Zhou, and Ying Zhao. Interactive exploration of cnn interpretability via coalitional game theory.Scientific Reports, 15(1):9261, 2025. 12 A Dataset statistics Table 3 collates different statistics on the node and graph classification datasets used, such as the number of graphs, a...

2025