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MPGE: A Multi-Perspective Graph Explainer for Molecular Classification Explanation

Mahtab Sarvmaili

arXiv:2610.12039v1cs.LGcs.AI

TL;DR

Molecular GNN predictions do not show which graph information supports a decision, what edits reverse it, or what edits it tolerates. MPGE operationalizes these views for a frozen classifier and evaluates them across five datasets, finding bounded counterfactual coverage from 4.8% to 67.6% and exemplar preservation coverage from 98.9% to 100.0%.

  • Problem

    Predictive performance alone does not reveal which graph information supports an individual molecular model decision or which changes reverse or preserve it.

    Source: §I · p. 1

  • Method

    MPGE unifies factual, bounded counterfactual, and non-trivial exemplar explanations for a frozen classifier through separate objectives and hard checks of discrete candidates.

    Source: §I · p. 1

  • Results

    Across datasets, bounded counterfactual flip coverage was 4.8–67.6% and exemplar preservation coverage was 98.9–100.0%, with conditional ranges interpreted alongside coverage denominators.

    Source: B. Semantic coverage and conditional… · p. 7

  • Takeaways & Limitations

    Semantic coverage and conditional quality should be reported separately, and high preservation coverage does not imply stable masks.

    Source: C. Complementarity and repeatability… · p. 7, §VIII · p. 13

    MPGE explains a trained classifier rather than a causal chemical mechanism, and RDKit sanitation establishes representability, not synthesizability, safety, or experimentally changed activity.

    Source: §VII · p. 13

Abstract

from arXiv · show

Graph neural networks (GNNs) predict molecular properties from chemical graph data, but predictive accuracy does not explain how graph information supports an individual decision. A compact prediction-preserving rationale does not necessarily reveal which changes reverse the decision or which modifications the model tolerates. We propose the Multi-Perspective Graph Explainer (MPGE), unifying factual support, counterfactual sensitivity, and exemplar tolerance for a frozen classifier. The factual view, originally termed prototype (PT), seeks a compact retained edge set with the same label and required confidence. Counterfactual (CF) explanations seek bounded prediction-changing deletions; exemplar (EXE) explanations seek non-trivial bounded deletions that preserve the label and confidence. A shared constrained formulation connects prediction behavior, compactness, and edit cost, while separate objectives generate the three views. Our graph-classification extension of CF-GNNExplainer learns symmetric edge rankings and verifies discrete candidates, recording unsuccessful searches. A separate BBBP fragment backend returns RDKit-sanitized molecules. We evaluate the primary GCN implementation on MUTAG, Mutagenicity, AIDS, COX2_MD, and BBBP using semantic coverage, conditional quality, stability, and runtime. Successful factual masks retained 8.6%--15.5% of input edges on average across datasets; bounded counterfactual coverage was 4.8%--67.6%, and exemplar preservation coverage was 98.9%--100.0%. Exploratory controls reveal the influence of hard projection and retained node information. Quantitative comparisons and molecular visualizations characterize model support, sensitivity, and tolerance without treating them as validated chemical mechanisms.

I. Introduction

Molecular predictions need explanations that distinguish what supports a decision, what changes it, and what changes can preserve it. MPGE combines these views for a frozen classifier and evaluates them with constrained graph and molecular-fragment procedures.

I. Introduction

  • Factual support, counterfactual sensitivity, and exemplar tolerance answer distinct questions about one molecular prediction.A compact rationale may support a prediction without revealing what reverses it or what changes the model tolerates.Source: §I · p. 1
  • MPGE links the three views through a constrained formulation, while its graph-classification extension uses view-specific objectives and hard checks of discrete candidates.The search records failures when no ranked candidate meets the requested constraints; a separate BBBP backend returns RDKit-sanitized fragments.Source: §I · pp. 1–2

A. Factual graph explanations

  • Factual graph explainers such as GNNExplainer and PGExplainer motivate differentiable edge ranking, but MPGE evaluates the final hard subgraph rather than its continuous surrogate.Prior work couples factual and counterfactual reasoning; MPGE additionally specifies a bounded, non-trivially edited query that preserves the prediction.Source: A. Factual graph explanations · p. 2, B. Counterfactual and coupled reasoning · p. 2

B. Counterfactual and coupled reasoning

  • Distribution-aware molecular explainers address a different question from whether a discrete graph changes a prediction; MPGE’s fragment backend adds sanitation, not a learned molecular-manifold constraint.Its deletion-only fragment search therefore explores a restricted candidate family.Source: B. Counterfactual and coupled reasoning · p. 2

C. Molecular and distribution-aware explanations

Molecular explanation methods differ in their candidate spaces and explanatory objects, while MPGE makes prediction, edit, and validity constraints explicit. Its factual structural candidates retain all query nodes and features, so compactness is measured by retained edges.

C. Molecular and distribution-aware explanations

  • Molecular counterfactual methods use varied candidate-generation strategies, while MPGE’s deletion-only fragment search instantiates all three views without claiming broader generation capabilities.Other approaches use valid molecular actions, SELFIES mutations, or generatively completed fragments.Source: C. Molecular and distribution-aware… · p. 2

D. Exemplars and evaluation

  • A class-level generated motif or latent prototype differs from MPGE’s compact query-specific factual mask, because prediction preservation alone does not identify a unique structure.The same-outcome-under-change perspective also motivates EXE’s positive edit requirement, which prevents returning the original graph as its own exemplar.Source: C. Molecular and distribution-aware… · p. 2, D. Exemplars and evaluation · p. 2

III. Problem Formulation

  • The formulation fixes the query’s original class and restricts structural candidates to valid edge deletions with unchanged nodes and features; neither structural nor molecular validity establishes physical properties.Structural edit cost counts deleted edges, while the fragment backend uses deletion steps and an additional removed-heavy-atom fraction limit.Source: §III · p. 3

A factual explanation

  • Structural factual candidates retain every query node and feature while selecting a non-empty edge subset, making their compactness an edge measure rather than a compact molecular fragment.The feasible set includes the full query, so feasibility is expected for valid non-empty structural queries; compactness, not coverage alone, distinguishes outputs.Source: A factual explanation · p. 3

B. Counterfactual explanation

Counterfactuals seek valid, minimum-cost interventions that change the decision, whereas exemplars seek bounded, non-trivial edits that preserve the decision and minimum confidence. Structural difference is measured explicitly, but a positive edit cost and budget do not ensure domain-expert meaningfulness.

B. Counterfactual explanation

C. Exemplar explanation

  • An exemplar is a bounded, non-trivial edit that preserves the query label and minimum confidence.Positive structural cost excludes a no-op, but neither cost nor budget guarantees domain-expert meaningfulness.Source: C. Exemplar explanation · p. 3
  • The implementation searches restricted candidate families and does not certify global optima.Source: C. Exemplar explanation · p. 3

IV. MPGE Framework and MPGX-CF Architecture

MPGX-CF freezes the graph classifier and learns symmetric gates over existing undirected edges, then searches discrete ranked candidates for feasible factual, counterfactual, or exemplar outputs. The views use separate masks and differ in their prediction constraints and edit objectives.

A. Frozen predictor and perturbation generator

  • The perturbation generator reuses the frozen classifier’s weights and learns only structural gates, with dropout disabled and BatchNorm statistics fixed.Source: A. Frozen predictor and perturbation… · p. 3
  • One logit per unique undirected edge is mirrored across directions, producing symmetric masks that cannot add non-edges or gate GCN self-messages.The graph normalization is recomputed during each forward pass, and each requested view learns a separate mask.Source: A. Frozen predictor and perturbation… · p. 3

B. Perspective-specific objectives

  • The three perspective-specific relaxations distinguish retained mass for factuals, removed mass for counterfactuals, and confidence-preserving non-trivial deletion for exemplars.Source: B. Perspective-specific objectives · p. 3
  • After optimization, ranked hard masks are scanned for the smallest sufficient factual, first label-changing counterfactual, or largest feasible confidence-preserving exemplar.If no candidate satisfies its hard constraints, the method records failure rather than accepting a soft mask as the explanation.Source: B. Perspective-specific objectives · p. 4
  • Hard-scan selections are extremal only within the ranked candidate sequence, not globally optimal over the full edit space.Source: B. Perspective-specific objectives · p. 4
  • The structural backend retains all nodes and self-messages, so edge sufficiency is not equivalent to a two-node induced subgraph or chemically complete fragment.Source: B. Perspective-specific objectives · p. 4

C. Chemistry-aware fragment search

The chemistry-aware backend searches sanitized molecular fragments, while the primary predictive model is a three-layer GCN operating on node features and topology. Sanitization checks molecular representability, not synthetic or property-change validity.

C. Chemistry-aware fragment search

  • The fragment search cuts non-ring single bonds, retains connected components, restores implicit hydrogens, and accepts only RDKit-sanitized candidates.It searches at most three deletion steps and retains at most 100 candidates per depth, with at least two atoms and no unchanged query.Source: C. Chemistry-aware fragment search · p. 4
  • Factual selection minimizes retained heavy atoms, counterfactual selection minimizes deletion steps, and exemplar selection maximizes Morgan-fingerprint distance.Only counterfactual and exemplar candidates have a 35% heavy-atom removal limit; the search does not establish synthetic accessibility or likely occurrence.Source: C. Chemistry-aware fragment search · p. 4
  • Sanitization checks representability and valence consistency, not synthetic accessibility, likely occurrence, or a physically changed property.Source: C. Chemistry-aware fragment search · p. 4

D. Predictive model

  • The primary classifier is a three-layer GCN that sum-pools node representations and uses node features and topology, not edge labels or distance attributes.Each convolution is followed by BatchNorm, ReLU, and training-only dropout; GINE additionally encodes edge features in validation sensitivity checks, not as a completed held-out robustness study.Source: D. Predictive model · pp. 4–5

V. Experimental Protocol

The protocol evaluates hard-output validity, conditional quality, structural differences, repeatability, and projection sensitivity across molecular datasets using a frozen GCN. Explanations are assessed for model-faithfulness regardless of predictor correctness, with incomplete AIDS explanation folds excluded from reporting.

A. Research questions and evaluation scope

  • Five research questions assess hard-output semantics, quality conditional on success, differences between views, repeatability, and sensitivity to representation, edit budget, and projection.The projection replay does not isolate every difference in optimization or training budget.Source: A. Research questions and evaluation… · p. 5

B. Datasets, features, and splits

  • The evaluation covers MUTAG, Mutagenicity, AIDS, COX2 MD, and scaffold-held-out BBBP, with no documented edge-level explanation masks for these datasets.COX2 MD edges encode interatomic distances and need not correspond to chemical bonds; AIDS explanation reporting uses folds 0–7 while predictor reporting uses all ten.Source: B. Datasets, features, and splits · p. 5, Table I · p. 6
  • BBBP uses a scaffold-group split with approximately 80/10/10 train, validation, and test proportions and zero scaffold overlap.Explanations are reported for complete dataset–fold–predictor cells, excluding the unstarted AIDS fold 9 and incomplete fold 8 as whole cells.Source: B. Datasets, features, and splits · p. 5

C. Predictors and eligibility

  • All frozen-model predictions are eligible for faithfulness analysis, while a dagger flags dataset means below 0.55 balanced accuracy or 0.60 AUROC.The dagger cautions against application-utility interpretation; explanation eligibility is not conditioned on predictive correctness.Source: C. Predictors and eligibility · p. 5

D. Hyperparameter selection and budgets

  • One global configuration per perspective is selected using validation success, view-specific edit criteria, confidence, and runtime, with dataset means macro-averaged.The default hard budget is min(|E|, 8, max(1, floor(0.35|E|))) and the confidence fraction is 0.8; the minimum-one clamp can relax the fractional limit on small graphs.Source: D. Hyperparameter selection and budgets · p. 5

E. Comparison methods

The evaluation compares compatible explanation methods under shared model and feasibility conditions, then defines how success, quality, stability, and runtime are measured. Qualitative examples and reproducibility artifacts are selected and recorded through explicit procedures.

E. Comparison methods

  • Factual, counterfactual, and exemplar comparisons use view-appropriate methods; the BBBP fragment search is separate, and RDKit validity does not establish synthesizability.Methods share predictor checkpoints, graph identifiers, splits, and output-feasibility criteria, but native discretization rules differ.Source: E. Comparison methods · p. 6

F. Outcomes and statistical analysis

  • Success is a hard label/confidence predicate, while quality, stability, and runtime use distinct measures and retain failed searches in the coverage denominator.Statistical summaries use graph–model analysis units; paired tests compare shared examples, and timing is specific to the implementation and hardware.Source: F. Outcomes and statistical analysis · p. 6

G. Qualitative selection and reproducibility

  • Qualitative examples follow a deterministic selection rule, while artifacts record run configurations, provenance, outputs, and failures; the raw experiment directory lacks a public accession.The illustration rule is not prospective preregistration, and panels are regenerated from graph IDs and hard masks.Source: G. Qualitative selection and… · pp. 6–7

VI. Results and Discussion

Across five datasets, the proposed views show different coverage and conditional-quality profiles, while predictor performance and the interpretation of sparse masks constrain what the results establish. Complementarity, repeatability, and exploratory controls further show that outputs depend on the view, projection, budget, and retained node information.

A. Predictor performance and calibration

  • Held-out GCN AUROC ranged from 0.561 ± 0.133 on COX2 MD to 0.985 ± 0.015 on AIDS; COX2 MD explanations characterize a weak frozen predictor, not application utility.The prespecified weak-predictor rule flagged COX2 MD.Source: A. Predictor performance and calibration · p. 7

B. Semantic coverage and conditional quality (RQ1–RQ2)

  • Complete factual coverage is expected because the full-graph prefix reproduces the query prediction; sparse masks alone do not establish a small connected mechanism.The projection accepts the first retained-edge prefix preserving the label and at least 0.8p_y(G), with node features and self-loops potentially dominating.Source: B. Semantic coverage and conditional… · p. 7
  • A greedy deletion ranking matches or exceeds the proposed exemplar method on preservation coverage and edited fraction, so the three-view contribution is a common semantic and audit protocol.Native-output comparisons are descriptive because counterfactual discretizers differ, not an attribution of coverage differences to learned losses.Source: B. Semantic coverage and conditional… · p. 7

C. Complementarity and repeatability (RQ3–RQ4)

  • Mean factual–counterfactual overlap exceeds factual–exemplar overlap in every dataset, but differing edit sizes and successful-triplet selection affect Jaccard values.The comparison does not establish independent explanations or distinct biochemical mechanisms.Source: C. Complementarity and repeatability… · p. 7
  • Seed-level Jaccard stability ranges from 0.06–0.42 for factuals, 0.31–0.94 for counterfactuals, and 0.02–0.24 for exemplars, conditional on repeated successes.Low factual and exemplar repeatability means multiple edge sets can satisfy similar prediction constraints; outputs are not uniquely recovered structural truth.Source: C. Complementarity and repeatability… · p. 7

B. Semantic coverage and conditional quality (RQ1–RQ2)

  • 100.0% hard factual coverage and 98.9–100.0% exemplar preservation coverage contrasted with 4.8–67.6% counterfactual flip coverage; factuals retained 0.09–0.16 of input edges.These are coverage and conditional retained-edge ranges across datasets; conditional outcomes should be read with their coverage denominators.Source: B. Semantic coverage and conditional… · p. 7, Table IV · p. 8

D. Exploratory projection and representation controls (RQ4– RQ5)

  • Under a common hard-prefix replay, BBBP CF2 coverage changed from 2.8% to 63.9%, while AIDS CF2 and the proposed ranking both reached 6.9%; native-output gaps cannot be assigned solely to learned objectives.On COX2 MD, raising the absolute cap from 8 to 32 changed coverage from 9.7% to 23.6%, while AIDS remained at 6.9%.Source: D. Exploratory projection and… · pp. 7–8
  • The zero-edge input retained factual sufficiency for 48.6%–91.7% of selected units, versus 37.5%–61.1% with only nodes incident to selected factual edges.The induced-node intervention changes the model input and does not itself produce a validated molecular fragment.Source: D. Exploratory projection and… · p. 8

E. Qualitative successes and failures

The section presents factual, counterfactual, and exemplar outputs across five datasets, alongside native-output comparisons. It distinguishes explanation coverage from quality conditional on success and separates the chemistry-aware BBBP case from edge-mask explanations.

E. Qualitative successes and failures

  • Factual native-output comparisons report success with failures included, but quality only conditional on success.The supplied table caption identifies graph–model means ± standard deviation after averaging explainer repetitions.Source: Table V · p. 9
  • Counterfactual comparisons use the locked budget, but native discretization and optimization differ across methods.Exemplar coverage requires a non-trivial prediction-preserving edit, and its conditional quality follows Table IV’s aggregation.Source: Table VI · p. 10, Table VII · p. 10
  • The overview shows input and three explanation views across five datasets, with unavailable rows retained rather than silently omitted.Panels report class-1 probability, label, and deleted unique-edge count; TU graphs are categorical renderings, while the primary chemistry-aware BBBP example appears separately.Source: Figure 2 · p. 11
  • The BBBP fragment case uses RDKit-sanitized outputs: factual and exemplar fragments preserve the query decision, while the counterfactual reverses it.The factual criterion minimizes retained heavy atoms, unlike the structural comparison’s retained-edge criterion; this case is not experimental evidence about synthesized compounds.Source: E. Qualitative successes and failures · pp. 8–9, Figure 3 · p. 12
  • Hard-constraint coverage is shown before conditional quality, so unsuccessful cases remain visible in the coverage denominator.The quality figure combines structural size and prediction behavior; neither alone establishes semantic validity.Source: Figure 1 · p. 9, Figure 4 · p. 12

VII. Limitations and Responsible Use

The paper limits MPGE’s interpretation to explanations of a trained classifier under specific representations, search procedures, and study samples. Its conclusion frames the results as model auditing and hypothesis generation, not validation of broader architectural or chemical utility.

VII. Limitations and Responsible Use

  • MPGE explains a trained classifier, not a causal chemical mechanism, and complete distance-graph edges in COX2 MD are not consumed by the primary GCN.Factual masks may preserve predictions through node features and self-messages rather than identify a compact molecular fragment; weak predictive performance, calibration errors, and altered input distributions further constrain interpretation.Source: §VII · p. 13
  • Ranked prefixes and fragment beams explore restricted deletion families, so success verifies a returned candidate while failure does not establish global infeasibility.Masks can vary by seed, preservation does not certify robust attribution, quality comparisons condition on success, and methods differ in discretizers and optimization budgets.Source: §VII · p. 13
  • The study’s scope includes three GCN seeds, eight completed AIDS explanation folds, and one BBBP scaffold split; selected controls and GINE validation do not establish broader robustness.GINE validation does not establish held-out architectural robustness or performance on new training samples.Source: §VII · p. 13
  • RDKit sanitation establishes representability, not synthesizability, stability, safety, or experimentally changed activity.The fragment backend cannot search atom or bond additions or enforce a learned molecular distribution; expert evaluation and experimental validation remain necessary before medicinal-chemistry utility is claimed.Source: §VII · p. 13
  • The uploaded artifacts lack a public row-level record and checkpoint accession, limiting independent reruns.The paper cautions that local completeness should not be equated with a public reproducibility release.Source: §VII · p. 13

VIII. Conclusion

  • The framework supports transparent multi-perspective model auditing, while broader architectural, chemical, and human utility remains a separate validation task.The conclusion reports bounded counterfactual coverage of 4.8–67.6% and exemplar coverage of 98.9–100.0% across five datasets, and cautions that preservation coverage does not imply stable masks.Source: §VIII · p. 13

Appendix A Chemistry-Aware BBBP Fragment Analysis

The appendices describe a separate sanitized-fragment search for BBBP, validation-only configuration selection, exploratory held-out controls, and statistical aggregation procedures. These analyses use distinct intervention spaces and conditional summaries, with failures retained in coverage accounting.

Appendix A Chemistry-Aware BBBP Fragment Analysis

  • The BBBP fragment backend cuts non-ring single bonds, sanitizes retained components, and reports results separately from edge-mask explanations.Its search space and edit unit differ; factual size is measured by retained heavy atoms, and conditional rows summarize only returned sanitized molecules.Source: Appendix A · p. 14, Table VIII · p. 14

Appendix B Validation-Only Selection

  • The primary GCN test configuration is selected using a complete 3 × 3 regularization grid on deterministic class-balanced validation subsets; test graphs are excluded.GINE results are a validation sensitivity check, not a held-out GINE explanation comparison.Source: Appendix B · p. 14

Appendix C Exploratory Held-Out Controls

  • In exploratory controls, ranked-prefix search flips more often than a fixed 0.5 threshold, and increasing the absolute edge cap raises COX2 MD coverage while AIDS remains unchanged.The controls use selected held-out units and a common hard projection; the cap comparison holds rankings and the 35% relative budget fixed, and is not a redefinition of the primary outcome.Source: Appendix C · pp. 16–17

Appendix D Statistical Tables

  • Statistical summaries average explainer repetitions within graph–model pairs, then use graphs as the resampling and test unit for paired effects.Conditional quality effects require both methods to return valid explanations, so they are not population-wide quality comparisons.Source: Appendix D · pp. 17–18

Appendix E Expanded Per-Dataset Explanations

The expanded appendix enlarges the five-dataset explanation overview and clarifies how to read its edge-mask panels. It also describes provenance and failure-record practices for reproducibility.

Appendix E Expanded Per-Dataset Explanations

  • The expanded strips show factual, counterfactual, and exemplar outputs with all query nodes visible; grey nodes may have no retained incident edge while their features still reach the predictor.Red dashed edges are removed and green edges retained; TU node labels are dataset categories, not inferred chemical elements.Source: Appendix E · p. 19
  • The BBBP strip uses RDKit coordinates but remains an edge-mask explanation, distinct from the sanitized fragment search shown in Fig. 3.COX2 MD is a dense distance graph, so its retained context is faint and removed edges are shown in red dashed styling.Source: Appendix E · p. 19

Appendix F Reproducibility and Failure Records

  • Failed explanations remain recorded with their violated constraint and runtime, and records retain keys for dataset, fold, model, graph, method, perspective, budget, and protocol.A claim-to-artifact map links generated artifacts to sources; a separate submission map lists referenced artifacts and hashes.Source: Appendix F · p. 21, Table XIX · p. 21

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