Interpretable Hypergraph Learning via Neural Additive Models

Shihan Feng; Xin Zheng; Shiyi Yang; Ren Wang; Chudi Zhong; Can Chen

cs.LGOct 5, 2026

Interpretable Hypergraph Learning via Neural Additive Models

Authors: Shihan Feng, Xin Zheng, Shiyi Yang, Ren Wang, Chudi Zhong, Can Chen

Organizations: School of Data and Information Sciences, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA · Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA · Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA · School of Data and Information Sciences and the Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA · School of Data and Information Sciences, the Department of Mathematics, and the Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA

Abstract

Hypergraphs offer a natural framework for modeling networked data, where dependencies among entities are governed by higher-order interactions. While hypergraph learning methods such as hypergraph neural networks have demonstrated remarkable predictive performance, most existing approaches rely on black-box message-passing architectures, making it difficult to disentangle the contributions of node attributes and higher-order structural information. To address this challenge, we introduce the hypergraph neural additive network (HGNAN), an inherently interpretable framework for learning on hypergraph-structured data. HGNAN extends classical neural additive models to higher-order relational data by integrating feature-wise nonlinear decomposition with hypergraph-aware structural aggregation, enabling transparent prediction for both node- and hyperedge-level tasks. Extensive experiments on benchmark datasets demonstrate that HGNAN achieves performance comparable with state-of-the-art hypergraph learning methods while providing intrinsic and meaningful interpretability.

Figures & tables

Fig. 1: Overview of HGNAN. HGNAN takes a hypergraph and a feature matrix as input and processes them through two interpretable components: feature-wise nonlinear transformations and structure-aware influence functions. For node prediction, HGNAN performs neighborhood aggregation over hypergraph-structured information using $s$ -adjacency. For hyperedge prediction, it builds $s$ -intersection graph and applies a distance-aware function to capture structural influence between hyperedges. As in NAMs, each feature-related function operates only on a single feature, which preserves feature-level decomposability.

Method	Zoo	Mushroom	NTU2012	Cora	Pokec	Actor	Avg. Rank
MLP	0.935 $\pm$ 0.035	1.000 $\pm$ 0.000	0.883 $\pm$ 0.012	0.744 $\pm$ 0.019	0.597 $\pm$ 0.007	0.868 $\pm$ 0.005	4.8
AllDeepSets	0.946 $\pm$ 0.031	0.999 $\pm$ 0.001	0.876 $\pm$ 0.011	0.767 $\pm$ 0.016	0.587 $\pm$ 0.006	0.847 $\pm$ 0.007	6.5
AllSetTransformer	0.969 $\pm$ 0.041	0.999 $\pm$ 0.001	0.884 $\pm$ 0.010	0.792 $\pm$ 0.020	0.587 $\pm$ 0.007	0.855 $\pm$ 0.005	3.4
HGNN	0.950 $\pm$ 0.042	0.998 $\pm$ 0.001	0.872 $\pm$ 0.017	0.784 $\pm$ 0.012	0.580 $\pm$ 0.006	0.768 $\pm$ 0.005	7.5
HyperGCN	0.423 $\pm$ 0.000	0.482 $\pm$ 0.000	0.765 $\pm$ 0.031	0.781 $\pm$ 0.022	0.581 $\pm$ 0.008	0.623 $\pm$ 0.000	9.7
UniGCNII	0.958 $\pm$ 0.047	0.999 $\pm$ 0.001	0.891 $\pm$ 0.011	0.787 $\pm$ 0.014	0.587 $\pm$ 0.008	0.829 $\pm$ 0.006	4.3

TABLE I: Comparison of test accuracy (mean

\pm

standard deviation) between HGNAN-node and baselines across node classification datasets. Bold indicates the highest test accuracy. HGNAN achieves best average rank among all compared methods.

Method	iAF1260b	iJR904	iSB619	iYO844
CHESHIRE	$0.814\pm 0.011$	$0.836\pm 0.017$	$0.845\pm 0.023$	$0.883\pm 0.013$
NHP	$0.723\pm 0.018$	$0.729\pm 0.022$	$0.720\pm 0.021$	$0.797\pm 0.015$
HyperSAGNN	$0.759\pm 0.029$	$0.784\pm 0.011$	$0.777\pm 0.020$	$0.830\pm 0.028$
HGNAN (ours)	$\mathbf{0.914\pm 0.010}$	$\mathbf{0.908\pm 0.021}$	$\mathbf{0.904\pm 0.010}$	$\mathbf{0.908\pm 0.012}$

TABLE II: Comparison of hyperedge prediction AUROC (mean

\pm

standard deviation) across four BiGG GEM datasets: iAF1260b, iJR904, iSB619, and iYO844. Bold highlights the best result for each dataset. HGNAN outperforms all baseline models across all datasets.

	Zoo		NTU2012		Cora		Pokec		iJR904		iSB619
Model	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC
HGNAN (full)	$\mathbf{98.40}_{\pm 1.90}$	$\mathbf{94.11}_{\pm 5.19}$	$\mathbf{99.56}_{\pm 0.29}$	$\mathbf{93.18}_{\pm 1.06}$	$\mathbf{96.06}_{\pm 0.71}$	$\mathbf{85.30}_{\pm 2.11}$	$64.38_{\pm 0.69}$	$66.86_{\pm 0.76}$	$\mathbf{90.81}_{\pm 2.07}$	$\mathbf{87.54}_{\pm 3.12}$	$\mathbf{90.44}_{\pm 1.03}$	$\mathbf{87.39}_{\pm 1.95}$
w/o Aggregation (NAM)	$97.95_{\pm 1.90}$	$93.56_{\pm 5.16}$	$98.51_{\pm 0.31}$	$92.23_{\pm 1.02}$	$93.84_{\pm 0.86}$	$77.74_{\pm 2.37}$	$63.84_{\pm 0.66}$	$66.63_{\pm 0.73}$	$88.72_{\pm 0.80}$	$86.48_{\pm 1.18}$	$87.16_{\pm 1.60}$	$84.21_{\pm 2.73}$
w/o Additive Structure	$98.32_{\pm 1.74}$	$93.17_{\pm 6.23}$	$99.33_{\pm 0.16}$	$87.96_{\pm 0.89}$	$95.19_{\pm 0.71}$	$83.27_{\pm 2.06}$	$\mathbf{64.64}_{\pm 0.68}$	$\mathbf{67.17}_{\pm 0.77}$	$89.55_{\pm 1.98}$	$85.24_{\pm 2.98}$	$82.16_{\pm 11.35}$	$79.83_{\pm 11.58}$
w/o Node Features	$52.21_{\pm 5.69}$	$17.54_{\pm 3.01}$	$54.94_{\pm 6.07}$	$4.15_{\pm 0.88}$	$51.71_{\pm 2.06}$	$16.70_{\pm 1.30}$	$51.17_{\pm 1.01}$	$51.45_{\pm 0.67}$	$61.20_{\pm 1.66}$	$60.12_{\pm 1.75}$	$62.24_{\pm 3.34}$	$60.72_{\pm 4.08}$

TABLE III: Ablation study across node classification and hyperedge prediction datasets. Results are AUROC/AUPRC (%) reported as mean

\pm

standard deviation over 10 runs. Bold indicates the best result in each column.

Fig. 2: Controlled recovery of ground-truth feature and structural mechanisms on the synthetic hyperedge prediction task. HGNAN-edge closely recovers the two feature-wise shape functions and the distance-based structural influence function. This demonstrates that the learned decompositions can recover the underlying data-generating mechanism in a controlled setting.

Fig. 3: Feature contribution scores for predicting the “Mammal” class in the Zoo dataset. Each bar plot shows the learned response

w_{k}f_{k}(x_{k})

for a binary feature, where

x=1

indicates feature presence and

x=0

indicates feature absence. The feature “milk” strongly supports mammal classification, whereas “feathers” suppresses it, consistent with biological knowledge of mammalian traits.

Fig. 4: Local structural decomposition for node 232 in the NTU2012 dataset. The red star denotes the target node, and squares with black outlines are the neighbors that receive a non-zero aggregation weight

\sum_{s}\beta_{s}a^{(s)}_{ij}

, with thicker outlines and thicker arcs indicating larger weights. The three largest weights are annotated. The blue circle are neighbours that share the same class as the target but not receiving weights. White circles are nodes belongs to other classes and not selected. Shaded regions are hyperedges. HGNAN-node assigns a non-zero weight to only

7

of the

52

nodes in the neighborhood of the target. It shows that HGNAN-node can suppress misleading local evidence and concentrate aggregation on structurally and semantically consistent neighbors.

Fig. 5: Heatmap for Carbonyl group. The horizontal axis denotes the hyperedge feature value $[\mathbf{y}_{j}]_{\mathrm{C=O}}$ , corresponding to the net change in Carbonyl-group count. The vertical axis denotes hyperedge distance $d^{(1)}(e_{i},e_{j})$ . Each cell shows the contribution induced by a specific chemical input value and structural-distance combination.

Fig. 6: Hyperedge-level contribution decomposition on iAF1260b. Left: learned structural contribution

\rho_{1}(1/(1+d))

as a function of hyperedge distance

d

. Right: feature-wise contribution

w_{k}f_{k}(\cdot)

for the Carbonyl group

(\mathrm{C{=}O})

. Linear interpolation is used only for visualization.

Fig. 7: Empirical scaling of computational cost with feature dimension. We expand Zoo node features to dimension

P

by concatenating repeated copies of the original features, and measure the training time per epoch and peak CUDA memory for one training epoch. Both metrics grow approximately linearly with

P

, supporting the theoretical linear-in-

P

efficiency in practice.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

	NTU2012	Mushroom	Zoo	Cora	Pokec	Actor
$\|V\|$	2012	8124	101	2708	14998	16255
$\|E\|$	2012	298	43	1579	2406	10164
# feature	100	22	16	1433	65	50
# class	67	2	7	7	2	3
$\max\|E\|$	5	5	93	5	7	28
$\min\|E\|$	5	1	2	2	2	1

Appendix

TABLE IV: Summary of node classification datasets.

|E|

stands for the number of nodes on a hyperedge

E

, and

d_{v}

stands for the number of hyperedges containing a node

v

Fig. 8: Distance-dependent label structure of the ten networks. (a)–(b) Same-label ratio

SLR(d)

and (c)–(d) coverage

\mathrm{Cov}(d)

as a function of hop distance, shown separately for the node-classification datasets and the hyperedge (GEM) datasets. (e) Fraction of units that have no neighbor at any finite distance. Both

SLR(d)

and

\mathrm{Cov}(d)

are averages over the units that do have a neighbor at distance

d

, so isolated units leave no trace in (a)–(d); panel (e) reports them explicitly. For the GEM datasets the distances are those used by the model, i.e. computed from the

1

-intersection graph built from training positive hyperedges only.

	iAF1260b	iJR904	iSB619	iYO844
$\|V\|$	2388	1075	743	1250
$\|E\|$	1668	761	655	990
Missing Rate	0.236	0.088	0.171	0.160
$\max\|E\|$	67	56	61	63
$\min\|E\|$	1	1	1	1
$\text{avg }\|E\|$	3.88	4.18	5.14	4.19

Appendix

TABLE V: Summary of four datasets from the BiGG dataset.

Metric	Method	iAF1260b	iJR904	iSB619	iYO844
AUROC	CHESHIRE	$\mathbf{95.76\pm 0.53}^{\dagger}$	$94.53\pm 1.05$	$90.71\pm 1.16$	$95.16\pm 0.91$
	NHP	$89.34\pm 0.63$	$84.26\pm 1.43$	$81.18\pm 2.24$	$87.98\pm 1.14$
	HyperSAGNN	$94.36\pm 0.48$	$92.19\pm 1.22$	$86.51\pm 1.07$	$93.43\pm 0.93$
	HGNAN-edge (167-d)	$91.42\pm 0.97$	$90.81\pm 2.07$	$90.42\pm 1.15$	$90.80\pm 1.25$
	HGNAN-edge (504-d)	$95.34\pm 0.77$	$\mathbf{95.51\pm 0.51}$	$\mathbf{94.45\pm 0.88}$	$\mathbf{96.67\pm 0.52}$
Accuracy	CHESHIRE	$\mathbf{89.31\pm 1.13}^{\dagger}$	$86.32\pm 1.68$	$81.79\pm 2.77$	$87.52\pm 2.56$

Appendix

TABLE VI: Hyperedge prediction when all baselines additionally receive node-level MACCS fingerprints. Entries are mean

\pm

standard deviation (%) over 10 runs with identical splits for all methods. Bold marks the best entry in each column;

\dagger

marks baseline entries whose difference from HGNAN-edge (504-d) is not statistically significant (paired Wilcoxon,

p\geq 0.05

), and all unmarked baseline entries are significantly worse.

	HGNAN		Gradient $\times$ Input		Random
Dataset	COMP@20% $\uparrow$	SUFF@20% $\downarrow$	COMP@20% $\uparrow$	SUFF@20% $\downarrow$	COMP@20% $\uparrow$	SUFF@20% $\downarrow$
NTU2012	$\mathbf{0.5019\pm 0.0190}$	$\mathbf{0.2324\pm 0.0196}$	$0.3610\pm 0.0123$	$0.3912\pm 0.0178$	$0.0741\pm 0.0082$	$0.7656\pm 0.0058$
Zoo	$\mathbf{0.2700\pm 0.0724}$	$\mathbf{0.2589\pm 0.0576}$	$0.2367\pm 0.0659$	$0.2980\pm 0.0425$	$0.0538\pm 0.0226$	$0.4970\pm 0.0352$
Pokec	$\mathbf{0.0997\pm 0.0063}$	$\mathbf{0.0069\pm 0.0018}$	$0.0916\pm 0.0066$	$0.0141\pm 0.0049$	$0.0202\pm 0.0012$	$0.0841\pm 0.0046$

Appendix

TABLE VII: Node-level feature attribution faithfulness at a 20% perturbation budget. Higher COMP and lower SUFF indicate more faithful attribution. Results are averaged over 10 runs. HGNAN outperforms G

\times

I and random attribution on all three datasets.

Metric	$q$	HGNAN	Gradient $\times$ Input	Random
COMP $\uparrow$	0.10	$\mathbf{0.2572\pm 0.0175}$	$0.2090\pm 0.0108$	$0.0301\pm 0.0045$
	0.20	$\mathbf{0.5019\pm 0.0190}$	$0.3610\pm 0.0123$	$0.0741\pm 0.0082$
	0.30	$\mathbf{0.6850\pm 0.0136}$	$0.4715\pm 0.0159$	$0.1352\pm 0.0142$
	0.40	$\mathbf{0.7857\pm 0.0094}$	$0.5554\pm 0.0135$	$0.2246\pm 0.0180$
	0.50	$\mathbf{0.8318\pm 0.0092}$	$0.6358\pm 0.0135$	$0.3483\pm 0.0189$
	0.60	$\mathbf{0.8522\pm 0.0094}$	$0.7167\pm 0.0091$	$0.5003\pm 0.0159$

Appendix

TABLE VIII: Full feature-attribution faithfulness curve on NTU2012. COMP removes the top-

q

fraction of attributed features, whereas SUFF retains only the top-

q

fraction. Results are mean

\pm

standard deviation over 10 runs. HGNAN achieves higher comprehensiveness and lower sufficiency than G

\times

I over nearly the entire range of perturbation budgets

Dataset	$k$	Importance $\Delta$ Prob	Random $\Delta$ Prob	Ratio
NTU2012	1	$0.0048\pm 0.0021$	$0.0004\pm 0.0002$	$\mathbf{12.2\times}$
	3	$0.0160\pm 0.0027$	$0.0017\pm 0.0006$	$\mathbf{9.7\times}$
	10	$0.0387\pm 0.0034$	$0.0128\pm 0.0020$	$\mathbf{3.0\times}$
	20	$0.0419\pm 0.0038$	$0.0248\pm 0.0027$	$1.7\times$
Pokec	1	$0.0014\pm 0.0003$	$0.0008\pm 0.0001$	$1.8\times$
	3	$0.0015\pm 0.0003$	$0.0011\pm 0.0002$	$1.4\times$

Appendix

TABLE IX: Node-level structural faithfulness under neighbor removal.

\Delta

Prob denotes the decrease in the probability of the original predicted class. Ratio denotes the degradation under importance-based removal divided by random removal. Results are mean

\pm

standard deviation over 10 runs. Removing the highest-weight neighbor causes a significantly larger probability decrease than random removal.

Dataset	HGNAN	Gradient $\times$ Input	Random
iAF1260b	30.4	25.3	3.0
iJR904	29.5	36.4	2.4
iSB619	16.9	5.4	1.0
iYO844	26.8	35.5	1.7

Appendix

TABLE X: Hyperedge-level feature comprehensiveness at a 20% perturbation budget. Entries report the decrease in AUROC after removing the top 20% attributed features. Higher values indicate greater comprehensiveness.

Dataset	Remove self	Remove all context	Context/self
iAF1260b	$26.98\pm 1.86$	$7.17\pm 0.59$	26.6%
iJR904	$30.85\pm 3.89$	$2.92\pm 1.39$	9.5%
iSB619	$29.60\pm 2.63$	$6.26\pm 1.34$	21.1%
iYO844	$30.29\pm 2.97$	$3.38\pm 1.08$	11.2%

Appendix

TABLE XI: Decomposition of HGNAN-edge predictions into target-hyperedge self contribution and non-self structural context. Entries report

\Delta

AUROC after removing the corresponding additive terms. Context/self is the ratio of the full contextual effect to the self effect. Results are mean

\pm

standard deviation over 10 runs.

Dataset	Removal	$k=1$	$k=3$	$k=5$	$k=10$	$k=25$	$k=50$
iAF1260b	HGNAN	0.97	2.78	3.76	4.70	4.86	4.89
iAF1260b	Random	0.00	-0.00	-0.00	0.00	0.00	0.01
iJR904	HGNAN	0.20	0.38	0.46	0.51	0.62	0.73
iJR904	Random	0.00	0.00	0.01	0.00	0.01	0.01
iSB619	HGNAN	0.22	1.22	2.63	5.04	4.57	4.94
iSB619	Random	-0.00	0.00	0.01	0.02	0.04	0.03

Appendix

TABLE XII: Structural faithfulness of HGNAN-edge under source-hyperedge removal. Non-self source hyperedges are ranked by

|\kappa^{(s)}(e_{i},e_{j})\phi(e_{j})|

. Entries report

\Delta

AUROC after removing the top-

k

ranked sources or

k

randomly selected sources.

Training Data	Testing Data	NHP	HyperSAGNN	CHESHIRE	HGNAN-edge
iAF1260b	iJR904	$0.6213\pm 0.0468$	$0.7769\pm 0.0204$	$0.6785\pm 0.0440$	$\mathbf{0.8992\pm 0.0183}$
iAF1260b	iSB619	$0.6460\pm 0.0273$	$\mathbf{0.7445\pm 0.0391}$	$0.5455\pm 0.0593$	$0.5497\pm 0.0140$
iAF1260b	iYO844	$0.6284\pm 0.0397$	$\mathbf{0.7479\pm 0.0250}$	$0.5059\pm 0.0390$	$0.7068\pm 0.0590$
iJR904	iAF1260b	$0.6476\pm 0.0119$	$0.7657\pm 0.0031$	$0.6717\pm 0.0257$	$\mathbf{0.8555\pm 0.0154}$
iJR904	iSB619	$0.6291\pm 0.0295$	$\mathbf{0.7137\pm 0.0430}$	$0.5017\pm 0.0316$	$0.5477\pm 0.0726$
iJR904	iYO844	$0.6667\pm 0.0377$	$0.7306\pm 0.0674$	$0.6406\pm 0.0158$	$\mathbf{0.7641\pm 0.0331}$

Appendix

TABLE XIII: Zero-shot cross-dataset transfer results across the four BiGG GEM datasets. AUROC is used as the evaluation metric. For each source-target pair, all model parameters are trained on the source GEM and frozen during evaluation on the target GEM, with no target-domain fine-tuning. Bold values indicate the best result for each transfer direction. Results are mean

\pm

standard deviation over 10 runs.

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Existing interpretable graph additive models still face limitations in either computational scalability or modeling flexibility. In terms of structural modeling, previous approaches either face quadratic scaling costs or sacrifice explicit source-to-target contribution decomposition. In terms of feature components, they rely either on per-feature neural networks or on single shared bases with limited feature specialization. We address both problems by introducing HARMONIA: Interpretable Graph Learning through Mixtures of Neural Bases, an interpretable-by-design framework. For feature modeling, HARMONIA introduces a Mixture of Neural Bases (MoNB), which routes features to specialized basis experts, enabling parameter sharing without sacrificing feature-specific specialization. For structural modeling, HARMONIA uses Relative Random Walk Probabilities (RRWP) to capture multi-hop and multi-path relationships, and proposes Sparse RRWP Aggregation (SRA) to compute these interactions through sparse graph propagation without quadratic pairwise complexity. HARMONIA retains a simple additive form in which predictions decompose into feature responses modulated by structural influence. Empirically, HARMONIA achieves stronger explanation recovery than existing interpretable graph baselines while maintaining competitive predictive performance and scaling to graphs with millions of nodes. These results show that interpretable graph learning can remain both faithful and scalable without sacrificing predictive effectiveness.

Abstract

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