Pith. sign in

REVIEW 2 major objections 5 minor 60 references

Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks

T0 review · 2 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read For a symmetric graph, no single top-k explanation can be minimal, neutral, and unique unless a minimal valid explanation is fixed by the automorphism group; reports that name one interchangeable edge are arbitrary tie-breaks.

desk verdict The combinatorial core is correct and machine-checked, but the paper's headline claim that the trilemma's obstruction is common is not actually verified — the measured effect is a top-k reporting artifact, not the trigger condition. read the letter →

arxiv 2607.26344 v1 pith:HKS3WMR2 submitted 2026-07-28 cs.LG cs.AI

Xin Xu , Siru Tao , Kaizhen Tan This is my paper · ORCID
classification cs.LGcs.AI
keywords graphneuralnetworksexplainabilityautomorphismstop-kexplanationsequivariancesymmetrynon-canonicitymutagenicity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that when a graph has a nontrivial automorphism—two interchangeable nitro groups in a molecule, say—a top-k explanation of a graph neural network cannot simultaneously be single-valued, minimal, and symmetry-respecting, unless one minimal valid explanation is fixed by the whole automorphism group. Message passing is exactly permutation equivariant, so any attribution derived from the model's outputs ties the interchangeable elements to the last bit; only the reporting step breaks the tie, by array order. The paper proves this as a trilemma, gives a parameter-free combinatorial criterion that decides from the graph and mask alone whether a given exact-k budget must split an orbit, and verifies the criterion against a mechanical model-equivalence check on 21,298 decisions with no exceptions. It measures the phenomenon as common: 93.4% of Mutagenicity graphs admit relevant nontrivial automorphisms, and at k=10, 24.0% of 25 MUTAG molecules with two interchangeable nitro groups surface exactly one, with the automorphic alternative accepted by the model in every such case. A practical consequence is that reporting whole orbits instead of individual edges removes the arbitrariness at negligible cost.

What carries the argument

Theorem 1 (the conditional trilemma) is the load-bearing object: single-valued, minimal, and neutral cannot coexist exactly when no minimal valid explanation is fixed by the automorphism group. Proposition 1 (exact equivariance) supplies the premise by showing message passing makes model outputs and hence validity exactly invariant under automorphisms. Proposition 4 and Corollary 2 convert the trilemma into a graph-only decision rule for exact-k reports: a report is neutral exactly when the cut severs no edge orbit, and a neutral score-optimal report exists exactly when the leftover budget is a sum of complete orbit sizes from the tied block. This criterion is mechanised as a machine-checked

What would settle it

Take any symmetric graph where the paper's criterion predicts a severed orbit at some budget. Form the top-k subgraph, apply the automorphism to it, feed both as hard masks to the frozen model, and compare the predicted-class logits. If the outputs differ by more than one float32 unit in the last place—the paper's observed tolerance—then the automorphic alternative is not equally valid, contradicting the paper's claim that every severed orbit is arbitrary. A second, structural falsifier would be any instance with no automorphism-fixed minimal valid explanation for which a single-valued, minima

Watch

Extended reading notes

Core claim

The central claim is Theorem 1: for an input graph G with automorphism group H, a selection rule that returns exactly one minimal valid explanation and respects symmetry exists exactly when the set of minimal valid explanations contains a member fixed by H. Since message passing is exactly permutation equivariant, every validity criterion built from the model's outputs is exactly H-invariant; therefore, when no minimal explanation survives the symmetry, any single top-k report must choose among model-equivalent alternatives, and the choice is arbitrary. For exact-k reports, a combinatorial condition decides whether every score-optimal report of that size severs an orbit; the paper finds seve

Load-bearing premise

The argument collapses if validity is not a function of the frozen model's outputs: if a human or chemical definition of 'valid explanation' distinguishes two automorphic substructures, Proposition 1's exact invariance no longer transfers to the set of valid explanations, and the trilemma need not bite.

Editorial extensions

If this is right

  • Any equivariant explainer's top-k output on a symmetric input can name one member of an orbit the model scores identically; the displayed edge is a convention, not evidence.
  • A stability score of 1 does not certify canonicity: tie-breaking by array index attains it, while an orbit-sampling rule that produces equally faithful outputs scores lower.
  • Reporting whole orbits instead of single edges removes the arbitrariness, at about 0.11 ms per molecule and 0.43 extra edges on MUTAG.
  • The common dismissal of symmetric inputs as measure-zero is wrong on graphs: 93.4% of Mutagenicity instances carry relevant nontrivial automorphisms, so the obstruction is routine.
  • Common synthetic benchmarks understate the phenomenon because their generator attaches motifs through a vertex its own automorphism moves; re-attaching through a fixed apex restores symmetry.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the formal kernel is really a statement about a permutation acting on a finite set, the non-canonicity likely transfers beyond GNNs to any equivariant scoring procedure that must emit one representative from a tied orbit.
  • A testable extension would audit transformer-style graph models: since their receptive fields are coarser, the relevant equivalence relation is coarser still, likely producing larger orbits and more frequent severed budgets—the paper leaves this untested.
  • The paper's orbit-aware reporting suggests a redefinition of explanation-evaluation metrics: treating orbit members as equivalent would make the stability gap disappear by construction, whereas current fidelity and sparsity metrics on single masks cannot express the symmetry.
  • The 24.0% rate rests on 25 molecules and the paper reports a wide interval; a replication on larger molecular datasets with many interchangeable functional groups would tighten the estimate.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper studies top-k explanations of GNNs on graphs with nontrivial automorphisms. Because message passing is permutation equivariant, any validity criterion built from model outputs is invariant under Aut(G); hence rules for selecting explanation subgraphs face exact ties. The central theoretical result (Theorem 1) is a conditional trilemma: a single-valued, minimal, and neutral selection rule exists exactly when the set of minimal valid explanations contains an element fixed by the full automorphism group. For the exact-k reporting used in practice, Propositions 4 and Corollary 2 give a graph-only subset-sum criterion for whether every score-optimal report of a given size must sever an edge orbit. The combinatorial core is mechanised in Lean 4 with no axiom dependencies. Empirically, the paper measures the incidence of automorphisms in several datasets, validates the criterion against a mechanical model-equivalence check on 21,298 decisions, documents attribution-level ties versus top-k-level severing on 25 nitro-pair MUTAG molecules, and proposes an orbit-aware reporting algorithm.

Significance. The exact-k reporting obstruction is a real and practically relevant phenomenon. It is convincingly isolated: for equivariant explainers, attribution is tied exactly, and the top-k report can still select one orbit representative with no model-based reason. The paper's strengths include a machine-checked combinatorial kernel, a parameter-free check that needs only Aut(G) and the mask, very large empirical agreement under its stated tolerance, and a fully scripted/reproducible pipeline. The paper also honestly labels the mechanical check as a consistency check rather than an independent prediction. The main caveat is that the broader 'obstruction is common' claim in the abstract relies on equating the presence of automorphisms and top-k severing with the trilemma trigger Min(S)^H=empty, which is never verified. That overreach does not invalidate the exact-k contribution, but it needs repair.

major comments (2)
  1. [The Trilemma / Corollary 1] The paper states after Corollary 1 that 'the instances measured below are exactly those where [Min(S)^H=empty] holds.' This is not established anywhere. The empirical results (Tables 1, 3, 5, 6) concern exact-k reporting under a sigma-invariant mask (Proposition 4 / Corollary 2), not the nonexistence of an H-fixed minimal valid explanation. A symmetric graph can have an H-fixed minimal sufficient subgraph while a top-1 report severs an orbit; the trilemma then does not trigger even though top-k is non-neutral. The abstract's 'the obstruction is common' therefore conflates the exact-k reporting obstruction with the conditional trilemma. To keep the claim, define a concrete Valid criterion, compute or bound Min(S) for the datasets/instances, and verify Min(S)^H is empty, or soften the abstract and conclusion to claim only the exact-k reporting obstruction.
  2. [Robustness across Architectures / Appendix Table 4] The abstract claims that the criterion 'agrees with a mechanical model-equivalence check without exception' over all 21,298 decisions. Appendix Table 4 reports agreement of 99.4-99.8% for several rows (e.g., PROTEINS GNNExplainer 99.4%). The main text's 100.0% is under a relative tolerance, and under an absolute tolerance the figure drops to 99.83%. State which tolerance Table 4's 'agree' column uses, which decisions are included in the 21,298 total, and why the appendix rates are not exceptions. Without this, the 'without exception' claim is ambiguous and potentially overstated.
minor comments (5)
  1. [Theory / Proposition 3] The neutrality definition treats sigma.G as equal to G at the point where Proposition 3 concludes hat-sigma(Phi(G))=Phi(G). With concrete node-indexed tensors, sigma.G is a different input. State explicitly whether graphs are considered up to relabeling, and how a rule is extended equivariantly to all relabeled inputs in the converse direction.
  2. [Table 2] The terms 'manufactured' and 'intrinsic' pairs are used in Table 2 but defined only in the text. Add a short definition to the caption or a Symbol/Definition block.
  3. [Abstract / Results] The abstract says attribution scores are equal 'to the last bit', while the body reports an integrated-gradient asymmetry of about 2e-9. Report the actual maximum ULP distance or say 'to floating-point accumulation noise'.
  4. [When a Report Severs an Orbit / GNNExplainer] The sentence 'The disparity is manufactured wholly by the reporting step' is accurate for the exactly equivariant explainers, but not for GNNExplainer, whose optimised attribution itself is non-equivariant (ratios up to 2.93x). Qualify the sentence so it does not appear to apply to the GNNExplainer rows of Table 3.
  5. [Appendix A / Abstract] The Lean development mechanises Proposition 4's orbit-set lemma, but Corollary 2's subset-sum condition does not appear to be part of the Lean files. State precisely which part of the exact-k criterion is machine-checked, so the abstract's 'criterion, mechanised in Lean 4' is not overread.

Circularity Check

1 steps flagged · score 2.0 of 10

Central trilemma is self-contained; only the mechanical-equivalence validation is a consistency check entailed by Proposition 1.

  1. other [Results, 'Validation of the criterion'; Limitations]
    "form the top-k set, form its image under each automorphism, feed both to the frozen model as hard masks, and compare outputs. ... The validation of Proposition 4 is a consistency check, so given Proposition 1 its role is to establish that nothing outside the criterion is at work rather than to predict something new."

    The mechanical check compares f(G,E_k) with f(G,σ(E_k)). By Proposition 1, f(G,σ·m)=f(G,m) for every automorphism and every mask, so the two outputs are identical by construction whenever the reported top-k severs an orbit. Thus the 100% agreement between the criterion and the mechanical check is entailed by the same equivariance that defines the criterion's validity set; it cannot fail and provides no independent empirical confirmation of Proposition 4. The paper itself labels this a consistency check, which limits the severity, but the abstract's 'agrees ... without exception' presents a construction as a validation.

full rationale

The central derivation is not circular. Theorem 1 is a self-contained equivalence proved from Proposition 1 and the definition of neutrality; Proposition 4 and Corollary 2 are combinatorial statements about orbit decompositions and are additionally mechanised in Lean 4 with no axiom dependencies. No parameters are fitted, and no load-bearing self-citation is used: the cited symmetry results are external and the paper disclaims novelty for the group-theoretic part. The only circularity-adjacent element is the mechanical model-equivalence validation, which is a consistency check entailed by Proposition 1 and explicitly described as such in the Limitations. Since the trilemma's truth does not rest on that check, the overall circularity score is low.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The theoretical criterion itself is parameter-free; the empirical pipeline introduces two hand-set thresholds (a tolerance and an accuracy floor) and relies on standard assumptions about message-passing equivariance, model-output validity, and exact automorphism computation. No new physical or mathematical entities are postulated.

free parameters (2)
  • model-equivalence relative tolerance = 1e-4
    Chosen by hand for the mechanical check; the headline counts of arbitrariness depend on it. Under an absolute tolerance of 1e-5, 4 of 884 decisions differ by one float32 ulp (Appendix D).
  • training accuracy floor = 0.7
    Configurations below 0.7 training accuracy are discarded; this selection affects which trained models are explained and measured, though not the theoretical result.
assumptions (4)
  • domain assumption Message-passing layers are permutation-equivariant functions of the neighbourhood multiset.
    Used throughout and proved as Proposition 1; it is standard for the tested GCN/GIN/GAT architectures but not assumed for arbitrary networks.
  • domain assumption Validity is a function of the frozen model's outputs and is therefore automorphism-invariant.
    Central to Theorem 1; stated in the Preliminaries as 'Any validity criterion built from f's outputs ... is therefore exactly σ-invariant.' This excludes human- or domain-defined validity criteria.
  • domain assumption Graph automorphism groups are computed exactly by nauty/pynauty.
    The empirical incidence and the remedy rely on exact Aut(G) computation; nauty is standard and trusted but not formally verified.
  • domain assumption The valid set S is upward-closed for the orbit-reporting remedy.
    The paper notes this holds for sufficiency-style criteria but not for every Valid; Algorithm 1's guarantee that orbit closure remains valid depends on it.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks." pith.science (2026). https://pith.science/paper/HKS3WMR2

@misc{pith2026260726344,
  author       = {Pith},
  title        = {Pith review of: Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HKS3WMR2}},
  note         = {Machine review of arXiv:2607.26344}
}
read the original abstract

A gradient-based GNN explainer given a molecule with two chemically equivalent nitro groups assigns them attribution scores that are equal to the last bit. It cannot do otherwise: message passing is exactly permutation equivariant, so any automorphism of the input leaves every attribution invariant. Yet the standard report, the top-k edges, names one of the two, and which one is settled by the order of an array. We show this is a structural obstruction rather than an implementation slip. When no minimal valid explanation is fixed by the input's automorphism group, no rule can be single-valued, minimal and symmetry-respecting at once. For the exact-k reports used in practice we give a parameter-free criterion, mechanised in Lean 4 with no axiom dependencies, that decides from the graph alone whether every score-optimal report of that size must split an orbit. Across 21298 instance-budget decisions the criterion agrees with a mechanical model-equivalence check without exception, and no severing case we found admitted a neutral alternative. The obstruction is common. Nontrivial automorphisms occur in 93.4% of Mutagenicity, the dataset the seminal explainability papers use, so the measure-zero dismissal of symmetric inputs, sound on the continuous domains it was made for, collapses here. At the sparsity budget those papers report, 24.0% of molecules with two interchangeable nitro groups (6 of 25) surface exactly one of them, every one arbitrary under mechanical verification. A model's blindness also manufactures symmetry: every MUTAG molecule contains atoms chemistry separates and the network provably cannot, and a matched control shows the resolution is set by what the model reads rather than how it is parameterised. Reporting orbits removes the arbitrariness at 0.11 ms and 0.43 extra edges per graph.

Figures

Figures reproduced from arXiv: 2607.26344 by the authors.

Figure 1
Figure 1. 1,4-dinitrobenzene, a MUTAG molecule whose [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. The three relations of Proposition 2, coarsest out [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. The criterion’s signature on Tree-Grid, computed from the graph alone before any model is consulted. Shaded budgets [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

60 extracted references · 3 linked inside Pith

  1. [1]

    Ying, Zhitao and Bourgeois, Dylan and You, Jiaxuan and Zitnik, Marinka and Leskovec, Jure , booktitle =

  2. [2]

    Advances in Neural Information Processing Systems , volume =

    Parameterized Explainer for Graph Neural Network , author =. Advances in Neural Information Processing Systems , volume =

  3. [3]

    Proceedings of the 38th International Conference on Machine Learning , year =

    On Explainability of Graph Neural Networks via Subgraph Explorations , author =. Proceedings of the 38th International Conference on Machine Learning , year =

  4. [4]

    Proceedings of the 34th International Conference on Machine Learning , year =

    Axiomatic Attribution for Deep Networks , author =. Proceedings of the 34th International Conference on Machine Learning , year =

  5. [5]

    Advances in Neural Information Processing Systems , volume =

    Evaluating the Robustness of Interpretability Methods through Explanation Invariance and Equivariance , author =. Advances in Neural Information Processing Systems , volume =

  6. [6]

    NeurIPS Workshop on Symmetry and Geometry in Neural Representations , year =

    Symmetry Breaking and Equivariant Neural Networks , author =. NeurIPS Workshop on Symmetry and Geometry in Neural Representations , year =

  7. [7]

    Physical Review Research , volume =

    Finding Symmetry Breaking Order Parameters with Euclidean Neural Networks , author =. Physical Review Research , volume =

  8. [8]

    Proceedings of the 41st International Conference on Machine Learning , year =

    Equivariant Frames and the Impossibility of Continuous Canonicalization , author =. Proceedings of the 41st International Conference on Machine Learning , year =

Show all 60 references
  1. [9]

    International Conference on Learning Representations , year =

    On the Equivalence between Positional Node Embeddings and Structural Graph Representations , author =. International Conference on Learning Representations , year =

  2. [11]

    Kosan, Mert and Verma, Samidha and Armgaan, Burouj and Pahwa, Khushbu and Singh, Ambuj and Medya, Sourav and Ranu, Sayan , booktitle =

  3. [12]

    Amara, Kenza and Ying, Rex and Zhang, Zitao and Han, Zhihao and Shan, Yinan and Brandes, Ulrik and Schemm, Sebastian and Zhang, Ce , booktitle =

  4. [13]

    Scientific Data , volume =

    Evaluating Explainability for Graph Neural Networks , author =. Scientific Data , volume =

  5. [14]

    and Wattenhofer, Roger , booktitle =

    Faber, Lukas and Moghaddam, Amin K. and Wattenhofer, Roger , booktitle =. When Comparing to Ground Truth is Wrong: On Evaluating

  6. [15]

    Reconsidering Faithfulness in Regular, Self-Explainable and Domain Invariant

    Azzolin, Steve and Longa, Antonio and Barbiero, Pietro and Li. Reconsidering Faithfulness in Regular, Self-Explainable and Domain Invariant. International Conference on Learning Representations , year =

  7. [17]

    Proceedings of the 42nd International Conference on Machine Learning , year =

    On Explaining Equivariant Graph Networks via Improved Relevance Propagation , author =. Proceedings of the 42nd International Conference on Machine Learning , year =

  8. [18]

    , booktitle =

    Duval, Alexandre and Malliaros, Fragkiskos D. , booktitle =

  9. [19]

    Proceedings of the 41st International Conference on Machine Learning , year =

    Explaining Graph Neural Networks via Structure-aware Interaction Index , author =. Proceedings of the 41st International Conference on Machine Learning , year =

  10. [20]

    Exploiting Symmetries in

    Bleukx, Ignace and Verhaeghe, H. Exploiting Symmetries in. Proceedings of the AAAI Conference on Artificial Intelligence , year =

  11. [21]

    and Piperno, Adolfo , journal =

    McKay, Brendan D. and Piperno, Adolfo , journal =. Practical Graph Isomorphism,

  12. [22]

    Journal of Medicinal Chemistry , volume =

    Structure-Activity Relationship of Mutagenic Aromatic and Heteroaromatic Nitro Compounds , author =. Journal of Medicinal Chemistry , volume =

  13. [23]

    Fast Graph Representation Learning with

    Fey, Matthias and Lenssen, Jan Eric , booktitle =. Fast Graph Representation Learning with

  14. [24]

    International Conference on Learning Representations , year =

    Semi-Supervised Classification with Graph Convolutional Networks , author =. International Conference on Learning Representations , year =

  15. [25]

    International Conference on Learning Representations , year =

    How Powerful are Graph Neural Networks? , author =. International Conference on Learning Representations , year =

  16. [26]

    and Lenssen, Jan Eric and Rattan, Gaurav and Grohe, Martin , booktitle =

    Morris, Christopher and Ritzert, Martin and Fey, Matthias and Hamilton, William L. and Lenssen, Jan Eric and Rattan, Gaurav and Grohe, Martin , booktitle =. Weisfeiler and

  17. [27]

    International Conference on Learning Representations , year =

    Strategies for Pre-training Graph Neural Networks , author =. International Conference on Learning Representations , year =

  18. [28]

    Bioinformatics , volume =

    Protein Function Prediction via Graph Kernels , author =. Bioinformatics , volume =

  19. [29]

    and Gomes, Joseph and Geniesse, Caleb and Pappu, Aneesh S

    Wu, Zhenqin and Ramsundar, Bharath and Feinberg, Evan N. and Gomes, Joseph and Geniesse, Caleb and Pappu, Aneesh S. and Leswing, Karl and Pande, Vijay , booktitle =

  20. [30]

    and Bause, Franka and Kersting, Kristian and Mutzel, Petra and Neumann, Marion , booktitle =

    Morris, Christopher and Kriege, Nils M. and Bause, Franka and Kersting, Kristian and Mutzel, Petra and Neumann, Marion , booktitle =

  21. [31]

    Journal of Medicinal Chemistry , volume =

    Derivation and Validation of Toxicophores for Mutagenicity Prediction , author =. Journal of Medicinal Chemistry , volume =

  22. [32]

    Agarwal, C.; Queen, O.; Lakkaraju, H.; and Zitnik, M. 2023. Evaluating Explainability for Graph Neural Networks. Scientific Data, 10(1): 144

    2023

  23. [33]

    Amara, K.; Ying, R.; Zhang, Z.; Han, Z.; Shan, Y.; Brandes, U.; Schemm, S.; and Zhang, C. 2022. GraphFramEx : Towards Systematic Evaluation of Explainability Methods for Graph Neural Networks. In Proceedings of the First Learning on Graphs Conference

    2022

  24. [34]

    Azzolin, S.; Longa, A.; Barbiero, P.; Li \`o , P.; and Passerini, A. 2025. Reconsidering Faithfulness in Regular, Self-Explainable and Domain Invariant GNNs . In International Conference on Learning Representations

    2025

  25. [35]

    Bleukx, I.; Verhaeghe, H.; Bogaerts, B.; and Guns, T. 2025. Exploiting Symmetries in MUS Computation. In Proceedings of the AAAI Conference on Artificial Intelligence

    2025

  26. [36]

    M.; Ong, C

    Borgwardt, K. M.; Ong, C. S.; Sch\"onauer, S.; Vishwanathan, S. V. N.; Smola, A. J.; and Kriegel, H.-P. 2005. Protein Function Prediction via Graph Kernels. Bioinformatics, 21(suppl\_1): i47--i56

    2005

  27. [37]

    T.; Nguyen, V

    Bui, N.; Nguyen, H. T.; Nguyen, V. A.; and Ying, R. 2024. Explaining Graph Neural Networks via Structure-aware Interaction Index. In Proceedings of the 41st International Conference on Machine Learning

    2024

  28. [38]

    Crabb \'e , J.; and van der Schaar, M. 2023. Evaluating the Robustness of Interpretability Methods through Explanation Invariance and Equivariance. In Advances in Neural Information Processing Systems, volume 36

    2023

  29. [39]

    K.; Lopez de Compadre, R

    Debnath, A. K.; Lopez de Compadre, R. L.; Debnath, G.; Shusterman, A. J.; and Hansch, C. 1991. Structure-Activity Relationship of Mutagenic Aromatic and Heteroaromatic Nitro Compounds. Journal of Medicinal Chemistry, 34(2): 786--797

    1991

  30. [40]

    Duval, A.; and Malliaros, F. D. 2021. GraphSVX : Shapley Value Explanations for Graph Neural Networks. In Machine Learning and Knowledge Discovery in Databases (ECML PKDD)

    2021

  31. [41]

    Dym, N.; Lawrence, H.; and Siegel, J. W. 2024. Equivariant Frames and the Impossibility of Continuous Canonicalization. In Proceedings of the 41st International Conference on Machine Learning

    2024

  32. [42]

    K.; and Wattenhofer, R

    Faber, L.; Moghaddam, A. K.; and Wattenhofer, R. 2021. When Comparing to Ground Truth is Wrong: On Evaluating GNN Explanation Methods. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining

    2021

  33. [43]

    Fey, M.; and Lenssen, J. E. 2019. Fast Graph Representation Learning with PyTorch Geometric . In ICLR Workshop on Representation Learning on Graphs and Manifolds

    2019

  34. [44]

    Hu, W.; Liu, B.; Gomes, J.; Zitnik, M.; Liang, P.; Pande, V.; and Leskovec, J. 2020. Strategies for Pre-training Graph Neural Networks. In International Conference on Learning Representations

    2020

  35. [45]

    Kaba, S.-O.; and Ravanbakhsh, S. 2023. Symmetry Breaking and Equivariant Neural Networks. In NeurIPS Workshop on Symmetry and Geometry in Neural Representations. ArXiv:2312.09016

    2023 arXiv

  36. [46]

    Kazius, J.; McGuire, R.; and Bursi, R. 2005. Derivation and Validation of Toxicophores for Mutagenicity Prediction. Journal of Medicinal Chemistry, 48(1): 312--320

    2005

  37. [47]

    N.; and Welling, M

    Kipf, T. N.; and Welling, M. 2017. Semi-Supervised Classification with Graph Convolutional Networks. In International Conference on Learning Representations

    2017

  38. [48]

    Kosan, M.; Verma, S.; Armgaan, B.; Pahwa, K.; Singh, A.; Medya, S.; and Ranu, S. 2024. GNNX-Bench : Unravelling the Utility of Perturbation-based GNN Explainers through In-depth Benchmarking. In International Conference on Learning Representations

    2024

  39. [49]

    Lawrence, H.; et al. 2025. Equivariance Everywhere All At Once: A Recipe for Graph Foundation Models. arXiv preprint arXiv:2503.21985

    2025 arXiv

  40. [50]

    Ling, H.; Yu, H.; Jiang, Z.; Zou, N.; and Ji, S. 2025. On Explaining Equivariant Graph Networks via Improved Relevance Propagation. In Proceedings of the 42nd International Conference on Machine Learning

    2025

  41. [51]

    Luo, D.; Cheng, W.; Xu, D.; Yu, W.; Zong, B.; Chen, H.; and Zhang, X. 2020. Parameterized Explainer for Graph Neural Network. In Advances in Neural Information Processing Systems, volume 33

    2020

  42. [52]

    Luong, K.-D.; Kosan, M.; Silva, A. L. d.; and Singh, A. 2024. Robust Ante-hoc Graph Explainer using Bilevel Optimization. arXiv preprint arXiv:2305.15745

    2024 arXiv

  43. [53]

    D.; and Piperno, A

    McKay, B. D.; and Piperno, A. 2014. Practical Graph Isomorphism, II . Journal of Symbolic Computation, 60: 94--112

    2014

  44. [54]

    M.; Bause, F.; Kersting, K.; Mutzel, P.; and Neumann, M

    Morris, C.; Kriege, N. M.; Bause, F.; Kersting, K.; Mutzel, P.; and Neumann, M. 2020. TUDataset : A Collection of Benchmark Datasets for Learning with Graphs. In ICML Workshop on Graph Representation Learning and Beyond

    2020

  45. [55]

    L.; Lenssen, J

    Morris, C.; Ritzert, M.; Fey, M.; Hamilton, W. L.; Lenssen, J. E.; Rattan, G.; and Grohe, M. 2019. Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks. In Proceedings of the AAAI Conference on Artificial Intelligence

    2019

  46. [56]

    E.; Geiger, M.; and Miller, B

    Smidt, T. E.; Geiger, M.; and Miller, B. K. 2021. Finding Symmetry Breaking Order Parameters with Euclidean Neural Networks. Physical Review Research, 3(1): L012002

    2021

  47. [57]

    Srinivasan, B.; and Ribeiro, B. 2020. On the Equivalence between Positional Node Embeddings and Structural Graph Representations. In International Conference on Learning Representations

    2020

  48. [58]

    Sundararajan, M.; Taly, A.; and Yan, Q. 2017. Axiomatic Attribution for Deep Networks. In Proceedings of the 34th International Conference on Machine Learning

    2017

  49. [59]

    N.; Gomes, J.; Geniesse, C.; Pappu, A

    Wu, Z.; Ramsundar, B.; Feinberg, E. N.; Gomes, J.; Geniesse, C.; Pappu, A. S.; Leswing, K.; and Pande, V. 2018. MoleculeNet : A Benchmark for Molecular Machine Learning. In Chemical Science, volume 9, 513--530

    2018

  50. [60]

    Xu, K.; Hu, W.; Leskovec, J.; and Jegelka, S. 2019. How Powerful are Graph Neural Networks? In International Conference on Learning Representations

    2019

  51. [61]

    Ying, Z.; Bourgeois, D.; You, J.; Zitnik, M.; and Leskovec, J. 2019. GNNExplainer : Generating Explanations for Graph Neural Networks. In Advances in Neural Information Processing Systems, volume 32

    2019

  52. [62]

    Yuan, H.; Yu, H.; Wang, J.; Li, K.; and Ji, S. 2021. On Explainability of Graph Neural Networks via Subgraph Explorations. In Proceedings of the 38th International Conference on Machine Learning

    2021

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.