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REVIEW 4 major objections 6 minor 41 references

Ignoring Directionality Leads to Compromised Graph Neural Network Explanations

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Symmetrizing directed graphs strips edge direction and lowers the ceiling on faithful GNN explanations.

desk verdict A real but under-controlled claim about directionality in GNN explanations; the empirical comparison is confounded by swapping GCN for DiGCN. read the letter →

arxiv 2506.04608 v1 pith:UFP6WHAU submitted 2025-06-05 cs.LG

Changsheng Sun , Xinke Li , Jin Song Dong This is my paper
classification cs.LG
keywords graphneuralnetworkspost-hocexplanationssymmetrizationdirectedgraphsGNNExplainerPGExplainerLaplaciannormalizationmutualinformation
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

The paper argues that the standard preprocessing step of symmetrizing a directed graph—adding reverse edges so spectral graph neural networks can run—destroys directional information that post-hoc explanations need. It proves a mutual-information inequality stating that the best subgraph explanation available in the original directed graph can never be worse than the best explanation available in the symmetrized version, and it adds a von Neumann entropy argument that symmetrization removes structural complexity. Empirically, on the new DiLink synthetic graphs, GNNExplainer's explanation AUC rises from 0.793 under bidirectional symmetrization to 0.914 under Laplacian normalization, while undirected benchmarks stay roughly unchanged. The authors conclude that direction-aware preprocessing should be part of graph neural network explanation pipelines in applications where edge direction carries causal or temporal meaning, such as financial transaction graphs.

What carries the argument

The load-bearing object is Theorem 3.3, the Directional Semantic Gain inequality. It compares the best mutual information a size-$k$ explanation subgraph can carry about the model output in the original directed graph, $\max_{G_s \subseteq G} MI(Y, G_s)$, with the same quantity in the symmetrized graph, $\max_{G_s^u \subseteq G_u} MI(Y, G_s^u)$, and proves the first is at least the second. The proof chain uses the fact that symmetrization is a deterministic transformation, so $H(G_s^u \mid G_s) = 0$, and then conditional entropy to conclude $H(Y \mid G_s) \le H(Y \mid G_s^u)$. The paper also uses the von Neumann entropy inequality $H_v(G) \ge H_v(G_u)$ to argue that symmetrization discards structural complexity. On the empirical side, the direction-preserving pipeline is Laplacian normalization from the DiGCN directed graph convolutional architecture, which replaces the symmetrized adjacency matrix used by the GCN baseline.

What would settle it

Train a single direction-capable base GNN twice on DiLink-Motif—once on the directed adjacency matrix and once on its symmetrized version—with matched node-classification accuracy, then run GNNExplainer on both frozen models. If explanation AUC does not fall under symmetrization once accuracy is matched, the observed gain cannot be attributed to directionality.

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Extended reading notes

Core claim

The central claim is that replacing a directed graph with its symmetrized undirected form does not merely lose a modeling nicety: it lowers the best possible quality of a post-hoc explanation. The formal statement is Theorem 3.3, the Directional Semantic Gain inequality, which says the maximum mutual information between a size-$k$ explanation subgraph and the model prediction in the directed graph is at least as large as the corresponding maximum in the symmetrized graph. The experiments show the loss is visible in practice: on DiLink-Motif, GNNExplainer's explanation AUC rises from 0.793 with bidirectional symmetrization to 0.914 with Laplacian normalization, and PGExplainer rises from 0.778 to 0.905, while undirected benchmarks remain essentially flat. The authors read these results as evidence that preserving directional semantics improves explanation fidelity and should be standard when explaining predictions on directed graphs.

Load-bearing premise

The causal conclusion assumes the only meaningful difference between the symmetrized and direction-preserving pipelines is how edge direction is handled; in the experiments the two pipelines also use different base graph neural network architectures, and the paper does not report whether their accuracies were matched.

Editorial extensions

If this is right

  • On the paper's DiLink synthetic graphs, both tested explainers show higher explanation AUC with Laplacian normalization than with symmetrization, with GNNExplainer rising from 0.793 to 0.914 on DiLink-Motif.
  • On undirected benchmarks such as BA-Shapes and Tree-Cycles, direction-preserving preprocessing performs comparably to symmetrization, so adopting it does not appear to hurt cases where edge direction is irrelevant.
  • Real-world citation and product graphs show the same directionality trend in Fidelity and Characterization Score, suggesting the phenomenon is not confined to synthetic data.
  • If the theorem is correct, no post-hoc explainer working on a symmetrized graph can recover the directional explanations available from the original graph, because the deficit is introduced in the graph representation itself.

Reading between the lines

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

  • Beyond the paper's pipeline, the mutual-information inequality suggests that mask-based explainers could be extended to select directed subgraphs—choosing not just which edges matter but which orientation of each edge—rather than inheriting an undirected mask space.
  • A direct test of the directionality mechanism would randomly shuffle edge directions while keeping the topology fixed; if explanation quality does not fall when directions are randomized, the observed gain is not specifically about directionality.
  • The entropy inequality implies the explanation gap should widen as graphs become more asymmetric, so datasets dominated by one-way edges should show larger gains from Laplacian normalization than nearly symmetric graphs.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper argues that the standard practice of symmetrizing directed graphs before GNN training discards directional information and thereby reduces the fidelity of post-hoc explanations. It offers a theoretical inequality (Theorem 3.3) about mutual information between a model's output and an optimal explaining subgraph, and reports experiments on synthetic (BA-Shapes, BA-Community, Tree-Cycles, Tree-Grid, and new DiLink variants) and real-world datasets comparing 'Bidirectional Symmetrical Relaxation' with 'Laplacian Normalization' pipelines. The empirical results show higher explanation AUC and Char scores for the direction-preserving pipeline.

Significance. If the causal claim is established, the work would fill a genuine gap in the GNN explainability literature, with practical implications for security-critical applications. The paper is honest about the importance of directionality, and the synthetic DiLink dataset is a reasonable construct for controlled study. However, the current evidence does not yet support the strong causal conclusion because the two compared pipelines differ in both the directionality handling and the base GNN architecture, and the theoretical proof contains an error. The paper does include a formal theorem and reproducible configuration details, which are strengths, but the empirical confound is load-bearing.

major comments (4)
  1. [Section 4, Tables 1 and 2] The comparison confounds directionality with base GNN architecture. The bidirectional symmetrization pipeline uses GCN [18], while the Laplacian normalization pipeline uses DiGCN [14]. Since no model accuracy, parameter counts, or error bars are reported, the observed explanation improvements (e.g., GNNExplainer AUC 0.793→0.914 on DiLink-Motif) could reflect the higher capacity or accuracy of DiGCN rather than the preservation of direction. A fixed-architecture comparison (e.g., DiGCN trained on directed vs. symmetrized adjacency, or GCN with a direction-aware Laplacian) is required to support the abstract's causal claim.
  2. [Section 3.2, Theorem 3.3] The proof contains a sign error. From the premise that G_u_s is a deterministic function of G_s, the correct inequality is H(Y|G_s) ≤ H(Y|G_u_s) (equivalently MI(Y,G_s) ≥ MI(Y,G_u_s)), not "H(Y|G_s) − H(Y|G_u_s) ≥ 0" as written. The step from H(G_u_s | Y, G_s) ≤ H(G_u_s | G_s) to the claimed entropy difference is not derived and contradicts the standard data-processing inequality. The theorem statement also needs to specify that G_u_s is the symmetrization of a subgraph of G; if G_u_s ranges over all subgraphs of G_u, the inequality is false.
  3. [Section 3.2 vs. Section 4] The theorem assumes a fixed output Y and an optimal explainer, but in the experiments Y is the output of two different base models (GCN vs. DiGCN). Thus the empirical results in Tables 1 and 2 are not a direct instantiation of the theorem, and the "Directional Semantic Gain" label may overstate what the inequality shows.
  4. [Section 2, Eq. (3)] The Char score weights w+ and w− are never specified in the paper. The reported Char values in Table 2 are therefore unreproducible without additional information on how these weights were chosen.
minor comments (6)
  1. [Abstract] The phrase "Our analysis demonstrates" is too strong given the empirical confound; suggest softening to "Our analysis suggests" or "Our theoretical and empirical results indicate."
  2. [Section 4] "Our proposed Laplacian normalization" cites [14] (DiGCN); please clarify whether Lap-Norm is a novel contribution of this paper or a re-use of DiGCN's preprocessing.
  3. [Table 2 caption] "PGExplaienr" is a typo for "PGExplainer."
  4. [Section 3.1] The inequality H_v(G) ≥ H_v(G_u) is asserted without proof or citation; either provide a reference or a brief justification.
  5. [References] Reference [11] is cited as GCN, but GCN is reference [18]; please check citation accuracy.
  6. [Appendix] The paper refers to "Appendix C" for real-world experiments, but the appendix structure is not clear in the manuscript; ensure appendices are properly included and labeled.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the paper's theory is an information-theoretic inequality and its empirical claims are new measurements, not reductions to fitted inputs.

full rationale

The paper's derivation chain is not circular. Theorem 3.3 (Eq. 7) states a mutual-information inequality between directed and symmetrized subgraphs; it is intended as a data-processing-style consequence of the deterministic symmetrization map and is not obtained by fitting any parameter to the reported explanation scores. The empirical comparison in Section 4/Table 1 measures GNNExplainer/PGExplainer AUC and fidelity on frozen base models; no fitted parameter is renamed as a prediction. The direction-preserving arm uses DiGCN, a prior work co-authored by two of the present authors (ref [14]), and this is a genuine self-citation. However, it is used as a tool/architecture, not as the evidence that directionality helps; the improvement is measured in this paper, not imported from [14]. The more serious weakness is an experimental confound: the direction-preserving pipeline (DiGCN) differs from the symmetrized baseline (GCN) in base architecture and normalization, so the reported gains cannot be cleanly attributed to directionality without a matched-architecture control. That is a validity/correctness concern, not a circularity. No equation reduces to its own inputs, and no known result is merely renamed as the central claim. Hence no significant circularity; score 0.

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

The central claim does not depend on fitted numerical parameters, but on a comparison of two preprocessing/model pipelines. The listed free parameters are evaluation choices (Char weights) and dataset construction choices (DiLink) that are unspecified and could shift the reported numbers. The axioms are mostly standard background from information theory and the GNN explainability literature; the last axiom, that DiGCN is a fair direction-preserving surrogate for GCN, is load-bearing and unargued.

free parameters (2)
  • Char score weights w+ and w- = not reported (w+ + w- = 1)
    Equation 3 defines the Characterization Score with weights w+ and w-; the paper never states the values used, so the reported Char numbers depend on an undeclared choice.
  • DiLink graph generation parameters = not reported
    The new synthetic dataset DiLink is described only as connecting two base graphs via unidirectional/bidirectional edges; the node counts, motif sizes, edge densities, and noise levels are not given, so the benchmark cannot be reconstructed or compared.
assumptions (4)
  • domain assumption The GNN explanation objective is approximately the mutual information between a subgraph and the prediction (Definition 2.1, Eq. 1).
    This definition is borrowed from GNNExplainer [8] and the survey [13]; it is an accepted modeling choice for explanation search but not a theorem.
  • standard math Symmetrization is a deterministic function of the directed graph, so H(G_u_s | G_s) = 0 (used in Theorem 3.3).
    Conditional entropy of a deterministic function is zero; this is a standard information-theoretic fact.
  • domain assumption The von Neumann entropy inequality H_v(G) >= H_v(G_u) for a directed graph and its symmetrization, stated as Eq. (5), holds under the directed entropy definition of Ye et al. [16].
    The paper states the inequality without proof and relies on the definition and results in [16].
  • ad hoc to paper Laplacian normalization (Lap-Norm) as implemented by DiGCN [14] is an appropriate direction-preserving preprocessing for training GCN-based models and yields a fair comparison with symmetrized GCN.
    This assumption is implicit throughout Section 4; it is what makes the empirical attribution of improvement to directionality valid, but it is not argued and is confounded by architecture differences.

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Cite this review

Pith. "Pith review of Ignoring Directionality Leads to Compromised Graph Neural Network Explanations." pith.science (2026). https://pith.science/paper/UFP6WHAU

@misc{pith2026250604608,
  author       = {Pith},
  title        = {Pith review of: Ignoring Directionality Leads to Compromised Graph Neural Network Explanations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UFP6WHAU}},
  note         = {Machine review of arXiv:2506.04608}
}
read the original abstract

Graph Neural Networks (GNNs) are increasingly used in critical domains, where reliable explanations are vital for supporting human decision-making. However, the common practice of graph symmetrization discards directional information, leading to significant information loss and misleading explanations. Our analysis demonstrates how this practice compromises explanation fidelity. Through theoretical and empirical studies, we show that preserving directional semantics significantly improves explanation quality, ensuring more faithful insights for human decision-makers. These findings highlight the need for direction-aware GNN explainability in security-critical applications.

Figures

Figures reproduced from arXiv: 2506.04608 by the authors.

Figure 1
Figure 1. Comparison of explanation tasks in image classification vs. graph [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Overview of the explainable graph explanation pipeline. It consists of four key components: (1) Graph data and processing, (2) GNN model [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Motivating example: Tracing illicit money flows. Directional [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Comparison of adjacency matrices before and after symmetric [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

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