WOMBAT: Whitebox Oracle for Molecular Benchmarking and Attribution Testing

Dominik Matuszek; Bartosz Zieliński; Tomasz Danel; Dawid Rymarczyk

cs.LGSep 30, 2026

WOMBAT: Whitebox Oracle for Molecular Benchmarking and Attribution Testing

Authors: Dominik Matuszek, Bartosz Zieliński, Tomasz Danel, Dawid Rymarczyk

Organizations: Jagiellonian University, Faculty of Mathematics and Computer Science · Jagiellonian University, Doctoral School of Exact and Natural Sciences · Jagiellonian University, Jagiellonian Center for Artificial Intelligence · Jagiellonian University, Faculty of Chemistry · Ardigen SA

Abstract

When a graph neural network (GNN) explainer produces an unexpected attribution on a molecule, the attribution alone cannot reveal whether the explainer has failed or the model has learned a shortcut. We introduce WOMBAT, a benchmark of 14 whitebox GNNs, each with message-passing weights set by hand to detect a specific SMARTS motif. Each model's decision rule is known by construction, providing attribution ground truth against which explainer errors can be identified and studied. We validate the models on millions of PubChem molecules and evaluate post-hoc explainers including GNNExplainer, PGExplainer, and Integrated Gradients. Guided by our qualitative analysis, we construct a model that causes Integrated Gradients to spread attribution across the graph, even though the model reliably detects the intended motif. We release the dataset, models, and evaluation code to help researchers in the development of newer XAI tools for GNNs.

Figures & tables

Figure 1: Overview of WOMBAT. For each motif $m$ , we handcraft a whitebox GNN $f$ that detects this motif in the input graph $G$ with $f(G)\!=\!1\iff m\subseteq G$ . This yields a ground truth explanation against which post-hoc explainers can be benchmarked.

Feature	MUTAG	Benzene	Flu.-Carb.	Alk.-Carb.	BA-2Mot.	ShapeG	B-XAIC	Tttm	WOMBAT
Real molecules	✔	✔	✔	✔	✗	✗	✔	✗	✔
Neg. Expl. eval.	✗	✗	✗	✗	✗	✗	✔	✗	✔
Whitebox Models	✗	✗	✗	✗	✗	✗	✗	✔	✔
No. of Tasks	1	1	1	1	1	1	7	3	14

Table 1: Comparison of graph datasets and benchmarks. WOMBAT is the only one that combines designed-to-be-correct MPNNs (to eliminate confusion in explanation evaluations) with real molecular structures. Abbreviations of features and benchmarks are explained in the Related Work section.

Figure 2: WOMBAT introduces 14 whitebox GNN models for detection of 14 distinct, chemically meaningful motifs. The biggest model, detecting Pattern 3, uses 7 MPNN layers before readout.

Figure 3: Schematic of the whitebox MPNN architecture and molecular computation flow. The process begins by defining the message-passing weights $W_{\text{from}}$ , $W_{\text{to}}$ , and $W_{e}$ ; notably, weights corresponding to wildcard tokens in the target motif are initialized to 1. Input graphs are represented via one-hot encoding. Message propagation from node $v_{i}$ to $v_{j}$ is computed according to Eq. 1 , followed by the update of node representations $z_{i}$ via Eq. 2 (here, the bias term $b=[0,0]$ ). The final prediction, in this case, a value of 1, is obtained through the readout operation defined in Eq. 3 . Note that, we only present one type of readout, and the colorcoding denotes the destination of incoming messages: cyan, gray, and red correspond to nodes $v_{1}$ , $v_{2}$ , and $v_{3}$ , respectively.

Panel of Figure 4 — Figure 4: Attributions generated by different explainers when evaluated on the whitebox task of recognizing Pattern 4. Other explainers (i.e., PGExplainer, GNNExplainer, Saliency, and Input $\times$ Gradient) produced null explanations. Integrated Gradients and Shapley Value Sampling attribute all motif nodes higher than non-motif nodes, whereas SubgraphX attributes importance to multiple non-motif nodes.

Pattern	GNN Expl.		Input $\times$ Grad.		IG		PG Expl.		SHAP Sampl.		Saliency		SubgraphX
Pattern	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$
1	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗
2	✗	✗	✗	✗	✗	✔	✗	✗	✗	✗	✗	✗	✗	✗
3	✗	✗	✔	✗	✔	✔	✗	✗	✗	✗	✔	✗	✗	✗
4	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗
5	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗

Table 2: Explainer performance across different motifs. We observe that IG is the most successful in this scenario. Moreover, we can see that a change of a readout function directly impacts the performance of IG. A checkmark indicates the explainer achieved a perfect score (

\mathrm{AUROC}=1

) for all positive instances of the given pattern. The sub-columns

r_{1}

and

r_{2}

denote the readout functions utilized by the whitebox models, corresponding to Eq. 3 and Eq. 4 , respectively.

Panel of Figure 5 — Figure 5: Comparison of attribution generated by Integrated Gradients and the ground truth. Integrated Gradients is unfaithful to the model by assigning higher attribution to the non-motif carbon in the cyclohexane ring than to the $\mathrm{NH}_{2}$ functional group.

Panel of Figure 6 — Figure 6: Analysis of causes of spurious attribution of the non-motif atom in Pattern 5. Figure 6(a) shows gradients that are accumulated by this atom near the decision boundary. Figure 6(b) demonstrates that under readout $r_{2}$ the atom does not impact the network’s final prediction, regardless of its interpolation state. However, it increased the network’s output under readout $r_{1}$ , as it increases internal activations. Figure 6(c) shows the effect of interpolating the non-motif atom on activation of a neighbouring node and final network’s prediction under readout $r_{2}$ , providing a justification for curve observed in the Figure 6(a) .

Panel of Figure 7 — Figure 7: IG attributions for two Pattern 12 implementations with identical $r_{2}$ predictions on one-hot molecular inputs. Here, the regular implementation yields perfect AUROC, while redundant computations involving neighbours cause attribution spillover.

Appendix figures & tables19 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 10 — Figure S1: Ground truth attribution for one of molecules containing Pattern 4 vs. IG’s attributions. IG is unfaithful to the model by attributing the $\mathrm{CH}_{3}$ carbon neighbouring the nitrogen ion, even though it does not belong to the ground truth attribution.

Panel of Figure 11 — Figure S2: Atom indexes (Figure 2(a) ) and impact of interpolation of atom 3’s representation (Figure 2(b) ).

Panel of Figure 12 — Figure S4: Case study of IG’s failure in Pattern 5. Figure 4(a) represents node indices and their respective attributions, while Figure 4(b) shows some of activations impacted by interpolation of the Atom 7 when all elements are interpolated at $\alpha=0.98$ .

Panel of Figure 13 — Figure S5: Figure 5(a) demonstrates that while presence of B1 activation in one of edges terminals increases logit values, A1 activation is sufficient and necessary for PGExplainer to attribute the edge connecting 2 nodes. As such, carbons belonging to formyl anions, despite only being $\mathrm{A1}$ -activated (Figure 5(b) ) still get attributed by PGExplainer.

Panel of Figure 14 — Figure S6: In case of both negative (Figure 6(a) ) and positive samples (Figure 6(b) ), PGExplainer fails by misattributing formyl anions. In the former, this causes IQR criterion failure (as null explanation was expected); in the latter, formyl anions are attributed alongside legitimate occurrences of Pattern 12 in molecule, causing AUROC to drop.

Panel of Figure 15 — Figure S7: Shapley Value Sampling’s ideal attribution rate is dependent on the size of the motif (Figure 7(a) ). Increasing of the sample size helps it achieve better performance (Figure 7(b) ). Here, we define the “Pattern Size” as number of heavy atoms in a molecule after substituting all wildcards as carbons.

Pattern No.	Shapley Value Sampling			Integrated Gradients
Pattern No.	Perfect	Total	Perfection Rate	Perfect	Total	Perfection Rate
1	85	100	0.85	7621	7660	0.99
2	57	94	0.61	236	236	1.00
3	3	22	0.14	22	22	1.00
4	60	100	0.60	964	1137	0.85
5	20	31	0.65	29	31	0.94

Appendix

Table S1: Comparison of amount of perfect (i.e. equal to 1.0) AUROCs for Shapley Value Sampling and Integrated Gradients.

Panel of Figure 17 — Figure S8: PGExplainer’s design choice of attributing edges based on their terminal nodes’ activations greatly limits its performance in WOMBAT. Figure 8(a) shows that, on average, total number of nodes with non-zero activations is very limited, limiting PGExplainer’s ability to discriminate between important and unimportant edges. To formalise this intuition, we present a loose upper bound to AUROC it could achieve in WOMBAT for every Pattern (Figure 8(b) ).

Explainer	Mean AUROC $\uparrow$	Perfect explanations	Perfect rate	Mean Success Rate (IQR criterion)
PGExplainer	0.5000	0 / 9,999	0.00%	1.0000
Integrated Gradients	0.7077	0 / 9,999	0.00%	0.1478
Saliency	0.7884	3 / 9,999	0.03%	0.0590
SHAP Sampling	0.6494	0 / 100	0.00%	0.3600
Input $\times$ Gradient	0.7077	0 / 9999	0.00%	0.2274
GNN Explainer	0.7075	0 / 9999	0.00%	0.1516

Appendix

Table S2: Explainer performance on the GINEConv whitebox detecting the simultaneous presence of fluorine and a carbonyl group. Mean AUROC and perfect explanations (AUROC = 1) are evaluated on positive molecules; IQR success rates are evaluated on negative molecules. Only Saliency produces any perfect explanations, in 3 of 9,999 cases. PGExplainer’s perfect IQR success rate reflects collapsed, uniformly zero attributions. Conversely, non-uniform attributions on negative molecules may faithfully reflect the contribution of one of the two required substructures.

Panel of Figure 19 — Figure S10: Layer-by-layer activations of the anti-IG Pattern 12 on an example molecule.

	mean AUROC $\uparrow$
No.	GNN Expl .	Input x Grad.	IG	PG Expl.	SHAP Sampl.	Saliency	SubgraphX
Pattern 1	$0.500\pm 0.000$	$0.994\pm 0.000$	$0.994\pm 0.000$	$0.500\pm 0.000$	$0.989\pm 0.002$	$0.994\pm 0.000$	$0.935\pm 0.011$
Pattern 2	$0.500\pm 0.000$	$0.997\pm 0.002$	$0.997\pm 0.002$	$0.500\pm 0.000$	$0.975\pm 0.003$	$0.997\pm 0.002$	$0.960\pm 0.012$
Pattern 3	$0.500\pm 0.000$	$1.000\pm 0.000$	$1.000\pm 0.000$	$0.500\pm 0.000$	$0.966\pm 0.006$	$1.000\pm 0.000$	$0.916\pm 0.026$
Pattern 4	$0.500\pm 0.000$	$0.982\pm 0.002$	$0.982\pm 0.002$	$0.500\pm 0.000$	$0.980\pm 0.003$	$0.986\pm 0.002$	$0.798\pm 0.019$
Pattern 5	$0.500\pm 0.000$	$0.987\pm 0.006$	$0.989\pm 0.005$	$0.500\pm 0.000$	$0.939\pm 0.030$	$0.991\pm 0.004$	$0.857\pm 0.032$

Appendix

Table S3: Mean AUROCs of all explainers across different whiteboxes (using readout function from Equation 3 ) when evaluated on positive examples.

	mean AUROC $\uparrow$
No.	GNN Expl .	Input x Grad.	IG	PG Expl.	SHAP Sampl.	Saliency	SubgraphX
1	$0.500\pm 0.000$	$0.500\pm 0.000$	$1.000\pm 0.000$	$0.500\pm 0.000$	$0.992\pm 0.002$	$0.500\pm 0.000$	$0.929\pm 0.011$
2	$0.500\pm 0.000$	$0.500\pm 0.000$	$1.000\pm 0.000$	$0.500\pm 0.000$	$0.980\pm 0.003$	$0.500\pm 0.000$	$0.957\pm 0.012$
3	$0.500\pm 0.000$	$0.500\pm 0.000$	$1.000\pm 0.000$	$0.500\pm 0.000$	$0.964\pm 0.004$	$0.500\pm 0.000$	$0.895\pm 0.027$
4	$0.500\pm 0.000$	$0.500\pm 0.000$	$0.992\pm 0.001$	$0.500\pm 0.000$	$0.975\pm 0.004$	$0.500\pm 0.000$	$0.793\pm 0.019$
5	$0.500\pm 0.000$	$0.500\pm 0.000$	$0.995\pm 0.003$	$0.500\pm 0.000$	$0.976\pm 0.007$	$0.500\pm 0.000$	$0.854\pm 0.031$

Appendix

Table S4: Mean AUROCs of all explainers across different whiteboxes (using readout function from Equation 4 ) when evaluated on positive examples.

	mean AP $\uparrow$
No.	Baseline	GNN Expl .	Input x Grad.	IG	PG Expl.	SHAP Sampl.	Saliency	SubgraphX
1	$0.406\pm 0.001$	$0.406\pm 0.001$	$0.995\pm 0.000$	$0.995\pm 0.000$	$0.406\pm 0.001$	$0.987\pm 0.003$	$0.995\pm 0.000$	$0.886\pm 0.018$
2	$0.581\pm 0.012$	$0.581\pm 0.012$	$0.998\pm 0.001$	$0.998\pm 0.001$	$0.581\pm 0.012$	$0.979\pm 0.003$	$0.998\pm 0.001$	$0.935\pm 0.018$
3	$0.678\pm 0.020$	$0.678\pm 0.020$	$1.000\pm 0.000$	$1.000\pm 0.000$	$0.678\pm 0.020$	$0.980\pm 0.003$	$1.000\pm 0.000$	$0.929\pm 0.022$
4	$0.462\pm 0.005$	$0.462\pm 0.005$	$0.980\pm 0.002$	$0.980\pm 0.002$	$0.462\pm 0.005$	$0.978\pm 0.004$	$0.984\pm 0.002$	$0.687\pm 0.031$
5	$0.587\pm 0.041$	$0.587\pm 0.041$	$0.995\pm 0.003$	$0.995\pm 0.002$	$0.587\pm 0.041$	$0.972\pm 0.008$	$0.995\pm 0.002$	$0.786\pm 0.048$

Appendix

Table S5: Mean APs of all explainers across different whiteboxes (using readout function from Equation 3 ) when evaluated on positive examples.

	mean AP $\uparrow$
No.	Baseline	GNN Expl .	Input x Grad.	IG	PG Expl.	SHAP Sampl.	Saliency	SubgraphX
1	$0.406\pm 0.001$	$0.406\pm 0.001$	$0.406\pm 0.001$	$1.000\pm 0.000$	$0.406\pm 0.001$	$0.991\pm 0.002$	$0.406\pm 0.001$	$0.872\pm 0.018$
2	$0.581\pm 0.012$	$0.581\pm 0.012$	$0.581\pm 0.012$	$1.000\pm 0.000$	$0.581\pm 0.012$	$0.983\pm 0.003$	$0.581\pm 0.012$	$0.933\pm 0.018$
3	$0.678\pm 0.020$	$0.678\pm 0.020$	$0.678\pm 0.020$	$1.000\pm 0.000$	$0.678\pm 0.020$	$0.978\pm 0.003$	$0.678\pm 0.020$	$0.911\pm 0.022$
4	$0.462\pm 0.005$	$0.462\pm 0.005$	$0.462\pm 0.005$	$0.991\pm 0.001$	$0.462\pm 0.005$	$0.967\pm 0.006$	$0.462\pm 0.005$	$0.682\pm 0.031$
5	$0.587\pm 0.041$	$0.587\pm 0.041$	$0.587\pm 0.041$	$1.000\pm 0.000$	$0.587\pm 0.041$	$0.984\pm 0.005$	$0.587\pm 0.041$	$0.783\pm 0.047$

Appendix

Table S6: Mean APs of all explainers across different whiteboxes (using readout function from Equation 4 ).

No.	GNN Expl.		Input $\times$ Grad.		IG		PG Expl.		SHAP Sampl.		Saliency		SubgraphX
No.	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$
1	0.500	0.500	0.994	0.500	0.994	1.000	0.500	0.500	0.989	0.992	0.994	0.500	0.935	0.929
2	0.500	0.500	0.997	0.500	0.997	1.000	0.500	0.500	0.975	0.980	0.997	0.500	0.960	0.957
3	0.500	0.500	1.000	0.500	1.000	1.000	0.500	0.500	0.966	0.964	1.000	0.500	0.916	0.895
4	0.500	0.500	0.982	0.500	0.982	0.992	0.500	0.500	0.980	0.975	0.986	0.500	0.798	0.793
5	0.500	0.500	0.987	0.500	0.989	0.995	0.500	0.500	0.939	0.976	0.991	0.500	0.857	0.854

Appendix

Table S7: Mean AUROCs of explainers across different whiteboxes evaluated on positive examples. Sub-columns

r_{1}

and

r_{2}

denote the readout functions utilized by the whitebox models (Equation 3 and Equation 4 , respectively).

No.	Baseline	GNN Expl.		Input $\times$ Grad.		IG		PG Expl.		SHAP Sampl.		Saliency		SubgraphX
No.	Baseline	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$	$r_{1}$	$r_{2}$
1	0.406	0.406	0.406	0.995	0.406	0.995	1.000	0.406	0.406	0.987	0.991	0.995	0.406	0.886	0.872
2	0.581	0.581	0.581	0.998	0.581	0.998	1.000	0.581	0.581	0.979	0.983	0.998	0.581	0.935	0.933
3	0.678	0.678	0.678	1.000	0.678	1.000	1.000	0.678	0.678	0.980	0.978	1.000	0.678	0.929	0.911
4	0.462	0.462	0.462	0.980	0.462	0.980	0.991	0.462	0.462	0.978	0.967	0.984	0.462	0.687	0.682
5	0.587	0.587	0.587	0.995	0.587	0.995	1.000	0.587	0.587	0.972	0.984	0.995	0.587	0.786	0.783

Appendix

Table S8: Mean Average Precision (AP) of explainers across different whiteboxes evaluated on positive examples. Sub-columns

r_{1}

and

r_{2}

denote the readout functions utilized by the whitebox models (Equation 3 and Equation 4 , respectively). Standard errors are omitted for brevity. Cell colors represent a piecewise continuous gradient based on landmark colors: Red (

\leq 0.50

), Pale Red (

\approx 0.65

), Light Green (

\approx 0.85

), and Green (

1.00

Pattern No.	Disagreements	Total	%
1	1	7,674	0.01
2	184	248	74.19
3	0	24	0.00
4	2	1,146	0.17
5	10	34	29.41
6	591	10,000	5.91

Appendix

Table S9: Fractions of molecules for which the original KRFP SMARTS and our relaxed SMARTS disagree either in motif detection or in the identified atom set.

Figure S11: Structural similarity distributions relative to ECFP4 motif fingerprints. Similarity scores (Tversky and Tanimoto) for molecules used to all of our patterns.

Pattern No.	All molecules			Valid molecules
Pattern No.	Positives	Tversky	Negatives	Positives	Tversky	Negatives
1	7,674	491,447	4,976,465	7,674	491,447	4,976,452
2	248	118,672	4,994,354	248	118,672	4,994,352
3	24	1,568,016	4,925,632	24	1,568,016	4,925,626
4	1,146	569,455	4,972,881	1,146	569,455	4,972,877
5	34	70,609	4,996,581	34	70,609	4,996,571

Appendix

Table S10: In this table, we showcase the sizes of the validation sets for each of our patterns. Molecule counts under the ”All molecules” field show the factual size of our validation dataset that was prepared by us by filtering PubChem. Unfortunately, a small subset of SMILES strings was corrupted during preprocessing; as such, the ”Valid molecules” field shows on how many molecules each of the whiteboxes was actually tested. Note that there is very little difference between the two subsets; however, we’ve chosen to compare these numbers for transparency.

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