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arxiv: 2505.12437 · v2 · submitted 2025-05-18 · 💻 cs.LG · cs.AI

A method for the systematic generation of graph XAI benchmarks via Weisfeiler-Leman coloring

Michele Fontanesi , Alessio Micheli , Marco Podda , Domenico Tortorella This is my paper

Pith reviewed 2026-05-22 13:45 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords graph neural networksexplainable AIWeisfeiler-Lemanbenchmark generationsubgraph matchingmolecular classificationgraph classificationXAI evaluation
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The pith

Weisfeiler-Leman color refinement mines class-discriminating motifs from any graph classification dataset to serve as proxy ground-truth explanations for GNNs.

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

The paper presents a method that automates the creation of benchmarks for testing graph explainers. It applies the Weisfeiler-Leman algorithm to identify motifs that distinguish between classes in existing datasets and treats these motifs as reliable stand-ins for the explanations a GNN should produce. Because the motifs are chosen to match the distinguishing power of WL procedures, they remain within the capabilities of standard GNNs. The approach yields fifteen ready-to-use molecular datasets plus open code that can produce thousands more benchmarks from generic inputs.

Core claim

The central claim is that Weisfeiler-Leman color refinement performs efficient approximate subgraph matching to extract class-discriminating motifs, which then function as proxy ground-truth class explanations; these motifs are learnable by GNNs precisely because their discriminating power is aligned with the expressiveness limit of the WL algorithm.

What carries the argument

The Weisfeiler-Leman color refinement algorithm applied to approximate subgraph matching for extraction of class-discriminating motifs.

If this is right

  • Any existing graph classification dataset can be turned into a ready XAI benchmark without requiring domain-expert curation of explanations.
  • The resulting collection supplies a large, reproducible testbed for measuring how well graph explainers recover the motifs that actually drive predictions.
  • Because the motifs respect WL expressiveness, the benchmarks remain appropriate for evaluating standard message-passing GNNs rather than more powerful architectures.
  • The public release of fifteen molecular datasets and code for over two thousand additional ones removes the previous scarcity of systematic evaluation resources.
  • Experimental comparisons of explainers gain statistical power when performed across many independently generated benchmarks instead of a handful of hand-crafted tasks.

Where Pith is reading between the lines

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

  • The same motif-mining procedure could be adapted to regression or link-prediction tasks by replacing class labels with continuous targets or edge properties.
  • Benchmarks produced this way may expose weaknesses in current explainers that remain hidden on the small synthetic sets used today.
  • Developers of new GNN architectures could use the WL alignment test as a quick filter to decide whether a proposed model can even represent the explanations in these benchmarks.
  • Extending the method to heterogeneous or temporal graphs would require only a suitable generalization of the color-refinement step.

Load-bearing premise

The motifs identified by Weisfeiler-Leman color refinement accurately reflect the actual decision rules that GNNs learn when solving the same classification task.

What would settle it

Train a GNN to high accuracy on one of the generated benchmarks and then show that the highest-ranked explanations returned by multiple popular graph explainers consistently fail to recover the WL-mined motif.

read the original abstract

Graph neural networks have become the de facto model for learning from structured data. However, the decision-making process of GNNs remains opaque to the end user, which undermines their use in safety-critical applications. Several explainable AI techniques for graphs have been developed to address this major issue. Focusing on graph classification, these explainers identify subgraph motifs that explain predictions. Therefore, a robust benchmarking of graph explainers is required to ensure that the produced explanations are of high quality, i.e., aligned with the GNN's decision process. However, current graph-XAI benchmarks are limited to simplistic synthetic datasets or a few real-world tasks curated by domain experts, hindering rigorous and reproducible evaluation, and consequently stalling progress in the field. To overcome these limitations, we propose a method to automate the construction of graph XAI benchmarks from generic graph classification datasets. Our approach leverages the Weisfeiler-Leman color refinement algorithm to efficiently perform approximate subgraph matching and mine class-discriminating motifs, which serve as proxy ground-truth class explanations. At the same time, we ensure that these motifs can be learned by GNNs because their discriminating power aligns with WL expressiveness. This work also introduces the OpenGraphXAI benchmark suite, which consists of 15 ready-made graph-XAI datasets derived by applying our method to real-world molecular classification datasets. The suite is available to the public along with a codebase to generate over 2,000 additional graph-XAI benchmarks. Finally, we present a use case that illustrates how the suite can be used to assess the effectiveness of a selection of popular graph explainers, demonstrating the critical role of a sufficiently large benchmark collection for improving the significance of experimental results.

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.

Referee Report

2 major / 2 minor

Summary. The paper proposes a method to systematically generate graph XAI benchmarks from generic graph classification datasets by leveraging the Weisfeiler-Leman color refinement algorithm for approximate subgraph matching and mining class-discriminating motifs. These motifs are positioned as proxy ground-truth explanations for GNN predictions, with the claim that their alignment to WL expressiveness ensures they are learnable by GNNs. The method is used to construct the OpenGraphXAI suite of 15 datasets derived from real-world molecular classification tasks, accompanied by public code for generating over 2000 additional benchmarks, and illustrated via a use case evaluating several popular graph explainers.

Significance. If the proxy motifs reliably reflect GNN decision processes, the work would provide a scalable, automated alternative to simplistic synthetic or expert-curated benchmarks, enabling more rigorous, reproducible, and statistically powered evaluations of graph XAI methods. The public release of the benchmark suite and generation codebase is a clear strength for community adoption and reproducibility.

major comments (2)
  1. [Method and Use Case sections] The central claim that WL-derived motifs serve as valid proxy ground-truth explanations because 'their discriminating power aligns with WL expressiveness' (abstract and method overview) does not address whether a trained GNN (e.g., GIN or GCN) on the resulting dataset actually bases its predictions on the mined motifs rather than other label-correlated substructures that are also WL-expressible. This assumption is load-bearing for the proxy validity but receives only illustrative treatment in the use case.
  2. [Use Case / Experiments] No quantitative verification is described (e.g., via motif ablation, feature importance alignment, or comparison against GNN attention/gradients) to confirm that the WL-mined motifs are the features actually used by the GNN rather than co-occurring alternatives. This weakens the claim that the benchmarks test explainer fidelity to the model's decision process.
minor comments (2)
  1. [Method] Clarify the exact WL iteration depth and subgraph matching threshold used in the mining procedure, as these choices directly affect motif size and fidelity.
  2. [Benchmark Suite] The abstract states the suite contains 15 datasets; provide a table listing the source molecular datasets, number of graphs, and motif statistics for each.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment point by point below, providing clarifications on the proxy validity of the WL-derived motifs and indicating where revisions have been made to strengthen the presentation.

read point-by-point responses

  1. Referee: [Method and Use Case sections] The central claim that WL-derived motifs serve as valid proxy ground-truth explanations because 'their discriminating power aligns with WL expressiveness' (abstract and method overview) does not address whether a trained GNN (e.g., GIN or GCN) on the resulting dataset actually bases its predictions on the mined motifs rather than other label-correlated substructures that are also WL-expressible. This assumption is load-bearing for the proxy validity but receives only illustrative treatment in the use case.

    Authors: We agree that the proxy validity rests on an assumption about GNN behavior. The method identifies class-discriminating motifs through WL color refinement, which guarantees both their discriminative power and their expressibility within the WL framework that bounds standard GNNs such as GIN. While a trained GNN could theoretically rely on other co-occurring WL-expressible features, the mined motifs are the systematically extracted primary patterns that distinguish classes in the original data. In the revised manuscript we have added an explicit discussion paragraph in the Method section clarifying this assumption, noting that the benchmarks evaluate explainer fidelity relative to these salient WL-discriminating motifs under the standard premise that high-accuracy GNNs learn such features. We have also expanded the use-case discussion to better connect the mined motifs to the observed explainer outputs. revision: yes

  2. Referee: [Use Case / Experiments] No quantitative verification is described (e.g., via motif ablation, feature importance alignment, or comparison against GNN attention/gradients) to confirm that the WL-mined motifs are the features actually used by the GNN rather than co-occurring alternatives. This weakens the claim that the benchmarks test explainer fidelity to the model's decision process.

    Authors: We acknowledge that the original use case was primarily illustrative. To address the request for quantitative verification, the revised manuscript now includes a new subsection in the Experiments section reporting motif-ablation results on three representative datasets from the suite. Removing the mined motifs leads to measurable drops in GNN accuracy, while ablation of randomly selected WL-expressible substructures does not, supporting that the motifs are among the features driving predictions. We have also added a comparison of explainer rankings against gradient-based feature importance scores on the same datasets. These additions provide the requested quantitative grounding without altering the core method. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the WL-based benchmark construction

full rationale

The paper presents an explicit construction method that applies the standard Weisfeiler-Leman color refinement algorithm to existing graph classification datasets in order to mine class-discriminating motifs. These motifs are positioned as proxy ground-truth explanations precisely because their discriminating power is defined by WL, and WL-expressiveness is an independently established property of certain GNN architectures. No step reduces a claimed prediction or uniqueness result to a fitted parameter, a self-referential definition, or a load-bearing self-citation chain; the derivation remains self-contained against external graph-theoretic benchmarks and does not rename or smuggle in prior author-specific ansatzes.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on standard properties of the Weisfeiler-Leman algorithm and the introduction of WL-derived motifs as proxy explanations without external validation of their fidelity to GNN decision processes.

axioms (1)
  • domain assumption Weisfeiler-Leman color refinement performs efficient approximate subgraph matching for class-discriminating motifs
    Invoked to mine proxy ground-truth explanations from graph classification datasets.
invented entities (1)
  • WL-derived class-discriminating motifs as proxy ground-truth explanations no independent evidence
    purpose: Serve as aligned, learnable explanations for evaluating graph explainers
    Postulated as faithful proxies because of alignment with WL expressiveness; no independent evidence provided in abstract.

pith-pipeline@v0.9.0 · 5851 in / 1378 out tokens · 61644 ms · 2026-05-22T13:45:50.093388+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean bare_distinguishability_of_absolute_floor echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    Our approach leverages the Weisfeiler-Leman color refinement algorithm to efficiently perform approximate subgraph matching and mine class-discriminating motifs, which serve as proxy ground-truth class explanations. At the same time, we ensure that these motifs can be learned by GNNs because their discriminating power aligns with WL expressiveness.

  • IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    the discriminating motifs are extracted from the set C = union over G in D of C(<=L)_G ... the explanation motif M_G is a subgraph whose nodes are those of the union graph comprising all rooted subgraphs in G corresponding to c-bar-colored nodes

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unclear
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Reference graph

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