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Interpretable Hypergraph Learning via Neural Additive Models

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

arXiv:2610.07458v1cs.LGcs.SI

TL;DR

Hypergraph neural networks can entangle node attributes with higher-order structure, complicating interpretation of what drives predictions. HGNAN combines feature-wise additive functions with hypergraph-aware structural aggregation for node- and hyperedge-level tasks. Its node-level results are competitive with HGNN baselines, and the method provides intrinsic decompositions.

  • Problem

    Existing HGNNs jointly transform features and aggregate structure, making their respective contributions difficult to identify in predictions.

    Source: §I · p. 1

  • Method

    HGNAN expresses predictions as sums of feature-wise nonlinear responses and explicit hypergraph structural influences, with node- and hyperedge-level variants.

    Source: §I · p. 2, §III · p. 3

  • Results

    HGNAN-node achieves the best average rank, 3.2, among compared methods and the best mean accuracy on NTU2012 and Mushroom, while some HGNN baselines lead on individual homophilic benchmarks.

    Source: 2) Results · p. 5

  • Takeaways & Limitations

    HGNAN provides direct feature-, neighbor-, and distance-level decompositions alongside predictive performance competitive with leading HGNN baselines.

    Source: §I · p. 2, §V · p. 10

Abstract

from arXiv · show

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.

I. INTRODUCTION

Hypergraph neural networks model higher-order interactions, but their joint feature transformations and structural aggregation can obscure what drives predictions. HGNAN addresses this gap with decomposable feature and structural contributions, while hypergraph-specific distances characterize connectivity at multiple scales.

A. Hypergraphs

  • A hypergraph represents group interactions by allowing each hyperedge to connect an arbitrary number of nodes.The paper defines an incidence matrix for this structure and associates feature vectors with nodes and optionally with hyperedges.Source: §I · p. 1, A. Hypergraphs · p. 2

I. INTRODUCTION

  • HGNNs jointly transform features and aggregate structure, entangling their contributions; post-hoc explanations do not constrain the model and are not guaranteed to reflect its reasoning.This motivates separating attribute effects from higher-order structural effects in scientific predictions.Source: §I · pp. 1–2
  • HGNAN extends neural additive models to hypergraphs, summing feature-wise nonlinear responses and explicit structural influences for node- and hyperedge-level predictions.Its variants provide feature-, neighbor-, or distance-level decompositions, with reported competitive predictive performance and faithful attributions.Source: §I · pp. 1–2

B. Distance on Hypergraphs

  • In the s-intersection graph, hyperedges are adjacent when they share at least s nodes, and shortest-path distance measures their separation in that graph.Changing s alters connectivity: smaller thresholds create broader connectivity, while larger thresholds require stronger overlap; distance shells are normalized to avoid domination by large shells.Source: B. Distance on Hypergraphs · p. 2

III. METHODS

HGNAN combines NAM-style feature-wise shape functions with structural functions that encode higher-order relations. Its node-level variant aggregates feature contributions across hypergraph neighborhoods and exposes feature, neighbor, and adjacency-scale contributions.

III. METHODS

  • HGNAN separates individual feature effects from structural influence, using local neighborhood aggregation for node prediction and distance-based modeling for hyperedge prediction.Each feature-related function operates on a single feature, preserving feature-level decomposability.Source: §III · pp. 2–3, Figure 1 · p. 3

A. Node-Level Prediction

  • HGNAN-node applies a separate nonlinear shape function to each node feature, then aggregates its feature-channel contributions over hypergraph-induced neighborhoods.Learned neighbor weights are shared across feature channels, so they represent structural contributions rather than feature-specific effects.Source: A. Node-Level Prediction · p. 3
  • Sparse learned neighbor weights make node predictions attributable to the neighbors contributing under each s-adjacency order.Larger weights indicate stronger neighbor contributions, and cached attention weights are reused at inference.Source: A. Node-Level Prediction · p. 3
  • HGNAN-node combines feature contributions with normalized feature weights and learns scale weights β to aggregate scores across adjacency orders.For multiclass tasks it uses vector-valued shape functions; the resulting scores pass to a linear prediction head.Source: A. Node-Level Prediction · p. 3

B. Hyperedge-Level Prediction

HGNAN-edge targets hyperedge prediction by combining explicit hyperedge features with global, distance-aware influence over s-intersection graphs. This makes predictions traceable to both candidate attributes and relations among hyperedges.

B. Hyperedge-Level Prediction

  • HGNAN-edge addresses the limits of pooled node embeddings by modeling explicit hyperedge features and potentially nonlocal, distance-dependent structural evidence.It performs global, distance-aware aggregation over s-intersection graphs.Source: B. Hyperedge-Level Prediction · p. 4
  • A domain-specific function Γ constructs hyperedge features from raw node features, allowing feature meanings to reflect the application.For metabolic reactions, these features can encode changes in functional-group counts before and after a reaction.Source: B. Hyperedge-Level Prediction · p. 4
  • HGNAN-edge aggregates feature-wise responses from reachable hyperedges using learned distance modulation, with shell normalization preventing large distance shells from dominating solely by size.Learnable feature and adjacency-order weights combine the contributions.Source: B. Hyperedge-Level Prediction · p. 4
  • The resulting decomposition provides feature-level and distance-level interpretations, tracing predictions to candidate hyperedge attributes and higher-order relations.For multiclass prediction, the decomposition is applied component-wise with vector-valued shape functions.Source: B. Hyperedge-Level Prediction · p. 4

C. Comparison Between HGNAN-node and HGNAN-edge

HGNAN-node and HGNAN-edge share additive feature modeling but aggregate structure in different domains. The paper presents these choices as modular, guided by the structural characteristics of the application.

C. Comparison Between HGNAN-node and HGNAN-edge

  • Both variants decompose predictions into feature-wise shape functions and hypergraph structural influence.Their shared additive principle preserves feature-wise interpretation across prediction levels.Source: C. Comparison Between HGNAN-node and… · p. 4
  • HGNAN-node aggregates over local node neighborhoods, while HGNAN-edge models hyperedge influence across structural distances in s-intersection graphs.The former targets node prediction; the latter targets hyperedge prediction, including settings where evidence may extend beyond immediate neighborhoods.Source: C. Comparison Between HGNAN-node and… · p. 4
  • Local and global structural mechanisms are modular choices that can in principle be paired with either prediction level according to application structure.Source: C. Comparison Between HGNAN-node and… · p. 4

D. Training Pipeline

HGNAN trains node- and hyperedge-level predictors through feature-wise additive representations combined with hypergraph structure. On node-classification benchmarks, it achieves the best average rank while exposing feature- and neighbor-level decompositions.

D. Training Pipeline

  • For node prediction, HGNAN applies feature-wise shape functions and neighborhood aggregation to node features and the incidence matrix, then uses a linear prediction layer.For hyperedge prediction, it constructs hyperedge features and applies the additive mechanism over the s-intersection graph before a prediction head; structural distances come from the original hypergraph.Source: D. Training Pipeline · p. 5

IV. EXPERIMENTS

  • The evaluation spans node benchmarks, metabolic reaction recovery, ablations, controlled mechanism recovery, cross-dataset transfer, and interpretability case studies.The study evaluates HGNAN from six complementary perspectives.Source: §IV · p. 5

A. Node-Level Prediction on Hypergraph Benchmarks

  • Node-level evaluation uses six classification datasets and compares HGNAN-node with an MLP and nine representative hypergraph neural network baselines.The datasets include Zoo, Mushroom, NTU2012, Cora, Pokec, and Actor; methods use the same data splits and evaluation protocol.Source: 1) Datasets and Baselines · p. 5

2) Results:

  • HGNAN-node achieves the best average rank (3.2) across compared methods, with the best mean accuracy on NTU2012 and Mushroom.The table reports test accuracy averaged over ten random splits; several baselines lead on individual homophilic datasets.Source: 2) Results · p. 5
  • On Pokec and Actor, a structure-agnostic MLP outperforms every hypergraph model, and adding neighbor features lowers its accuracy on both datasets.HGNAN-node trails the MLP by 1.0 and 1.4 accuracy points on Pokec and Actor, respectively.Source: 2) Results · p. 5

B. Hyperedge-Level Prediction on Metabolic Networks

For missing-reaction recovery in metabolic networks, HGNAN-edge combines interpretable reaction features with distance-aware structural modeling. It achieves the highest mean AUROC on all four evaluated GEM datasets, while ablations show that features and aggregation contribute differently across tasks.

B. Hyperedge-Level Prediction on Metabolic Networks

1) Datasets and Baselines:

  • HGNAN-edge uses binary MACCS fingerprints for metabolites and reaction features encoding net changes in functional-group counts.Positive values indicate groups generated by a reaction, while negative values indicate groups consumed.Source: 1) Datasets and Baselines · pp. 5–6

2) Results:

  • HGNAN achieves the highest mean AUROC on all four BiGG GEM datasets, with particularly large improvements on iAF1260b and iJR904.The comparison is against baselines using incidence structure in their original implementations.Source: 2) Results · p. 6, Table II · p. 6

C. Ablation Study

  • Removing node features brings node-classification AUROC close to random, while removing aggregation substantially reduces performance on hyperedge-prediction datasets.Aggregation has dataset-dependent effects on node tasks, including a Cora drop of 2.22 AUROC and 7.56 AUPRC; the non-additive variant underperforms the full model on most datasets.Source: C. Ablation Study · p. 7, Table III · p. 7

D. Feature–Structure Recovery

The experiments test whether HGNAN-edge recovers known mechanisms and transfers learned functions across metabolic hypergraphs, alongside interpretability case studies. Results show accurate recovery in a controlled setting and effective zero-shot transfer across related GEMs.

D. Feature–Structure Recovery

  • Aligned recovered feature and distance functions achieve MSE values between 5 × 10^-4 and 1.4 × 10^-3, with R2 and Pearson correlations close to 0.99.The synthetic task uses known feature functions and a distance-based structural mechanism; Fig. 2 visualizes the ground-truth and recovered functions.Source: D. Feature–Structure Recovery · p. 7, Figure 2 · p. 7

E. Cross-Network Transfer Across Metabolic Hypergraphs

  • In zero-shot transfer across 12 source-target GEM pairs, HGNAN-edge achieves the best result on 8 pairs, including AUROC 0.899 from iAF1260b to iJR904.Models are trained on a source GEM, frozen, and evaluated on the target; the results suggest the learned functions capture transferable biochemical regularities.Source: E. Cross-Network Transfer Across… · p. 7

F. Quantitative and Qualitative Interpretability Evaluation

  • For Mammal classification, the learned feature response assigns a positive contribution to milk and a negative one to feathers.The feature-response plots show learned responses for binary feature presence and absence.Source: Figure 3 · p. 8
  • For the illustrated target node, HGNAN-node assigns non-zero weight to only 7 of 52 nodes in its neighborhood, concentrating aggregation on structurally and semantically consistent neighbors.Source: E. Cross-Network Transfer Across… · p. 8

1) Node-Level Interpretability:

The examples show that HGNAN exposes node feature and neighbor contributions, while hyperedge decompositions separate chemical responses from distance effects. Faithfulness tests find that selected node and hyperedge components track changes in predictions.

1) Node-Level Interpretability:

  • For the Mammal prediction, milk has the largest positive response when present, while feathers have a negative response.The paper relates these patterns to biological knowledge about mammalian milk production and birds’ feathers.Source: 1) Node-Level Interpretability · p. 8
  • On NTU2012, removing the highest-weight neighbor causes a 12.2 times larger probability decrease than random removal, falling to 3.0 times for the top ten neighbors.Across ten runs, the selected-neighbor count has a median of 7, and all seven selected neighbors share the target’s class.Source: 1) Node-Level Interpretability · p. 8

2) Hyperedge-Level Interpretability.:

  • On iAF1260b, the learned distance response is positive at distance 0, negative at one hop, and weakens with distance before becoming mildly positive.The paper relates the negative one-hop response to possible contrast among adjacent reactions and the long-range response to label consistency and broader metabolic organization.Source: 2) Hyperedge-Level Interpretability · pp. 8–9, Figure 6 · p. 9
  • The Carbonyl response is larger for positive feature increases, and the same chemical input can contribute differently at different structural distances.The heatmap combines net Carbonyl-group change with hyperedge distance; experts can inspect the chemical response, distance response, and their combined contribution.Source: 2) Hyperedge-Level Interpretability · p. 9, Figure 5 · p. 9

3) Quantitative Faithfulness Evaluation:

  • On NTU2012, HGNAN feature attribution COMP is 0.502 versus 0.361 for G×I and 0.074 for random attribution; SUFF is 0.232 versus 0.391 and 0.766, respectively.Source: 3) Quantitative Faithfulness Evaluation · p. 9
  • Across four networks, HGNAN-edge feature attributions outperform random attribution and compare favorably with G×I on sufficiency, although G×I has higher comprehensiveness on iJR904 and iYO844.Source: 3) Quantitative Faithfulness Evaluation · p. 9
  • On iAF1260b and iSB619, top-ten structural removals reduce AUROC by 4.70 and 5.04 points (66% and 81% of full contextual effect), versus 0.00 and 0.02 for random removals.The reported percentages correspond, respectively, to iAF1260b and iSB619.Source: 3) Quantitative Faithfulness Evaluation · pp. 9–10

G. Computation Complexity Analysis

HGNAN’s dominant parameter cost is linear in the input feature dimension, and an experiment finds approximately linear growth in epoch time and peak GPU memory as features increase. The conclusion also notes that one network per feature can be costly on very high-dimensional datasets.

1) Theoretical Analysis of Computational Cost:

  • HGNAN’s dominant parameter cost is Θ(p #θf), linear in input feature dimension p; node aggregation costs Θ(SEdHa), while edge aggregation evaluates distances across N² pairs per interaction scale.The paper notes that Nyström approximation of the N × N distance matrix can reduce the quadratic dependence on N in practice.Source: 1) Theoretical Analysis of… · p. 10

2) Practical Analysis of Computational Cost:

V. CONCLUSION

  • HGNAN-node remains competitive with leading HGNN baselines, while HGNAN-edge achieves strong missing-reaction recovery performance; one network per feature can be costly on very high-dimensional datasets.The conclusion also reports reusable feature and distance responses across related metabolic systems and biologically meaningful case-study evidence.Source: §V · p. 10

APPENDIX A ADDITIONAL DETAILS FOR DATASETS

The appendix describes node-classification datasets and BiGG metabolic datasets, including their feature sources and training protocol. It also reports distance-dependent label patterns and notes that isolated units have no structural evidence to aggregate.

APPENDIX A ADDITIONAL DETAILS FOR DATASETS

  • The node-classification datasets span binary and multiclass tasks with varied entities, relations, and features, while the BiGG data comprise genome-scale metabolic models of organisms and their reactions and metabolites.Source: Appendix A · p. 12, Table IV · p. 12, Table V · p. 12
  • BiGG metabolite features use 167-dimensional binary MACCS vectors encoding predefined substructures or functional groups; missing valid features are zero-padded.The appendix reports the missing-feature rate in Table V.Source: Appendix A · p. 12
  • Mushroom, NTU2012, and Cora have SLR(1) between 0.75 and 0.82, while Pokec stays near 0.5 and Actor’s same-label ratio increases with distance; hyperedge datasets rise to 0.67–0.79 beyond six hops.The figure presents SLR and coverage by distance, with isolated units reported separately.Source: Appendix A · pp. 12–13, Figure 8 · p. 13
  • SLR and coverage averages exclude units without neighbors at a given distance; 47.0% of Cora nodes and 78.7% of Pokec nodes have no neighbor at any finite distance.For such units, the appendix says prediction necessarily falls back on unit attributes.Source: Appendix A · p. 13

APPENDIX B DETAILS FOR MODEL TRAINING

  • Experiments use random 2:1:1 train-validation-test splits and ten seeds; hyperedge-prediction distances are constructed only from positive training hyperedges.The appendix describes separate tuning ranges for node- and hyperedge-prediction methods.Source: Appendix B · p. 13

APPENDIX C HYPEREDGE PREDICTION WITH NODE-LEVEL MOLECULAR FEATURES

The appendix compares hyperedge prediction after giving baselines molecular features and evaluates feature- and structure-level faithfulness. Results show that comparative performance depends on the feature representation and that selected components can track prediction changes.

APPENDIX C HYPEREDGE PREDICTION WITH NODE-LEVEL MOLECULAR FEATURES

  • With shared node-level MACCS fingerprints, the 504-dimensional variant is best or statistically indistinguishable from the best method on every dataset and metric, while CHESHIRE beats 167-dimensional HGNAN-edge in AUROC on three networks.The 504 features combine reaction-level semantics with fingerprint means and standard deviations, Tanimoto-similarity statistics, and hyperedge size.Source: Appendix C · pp. 13–14, Table VI · p. 14

A. Node-Level Feature Faithfulness

  • At a 20% perturbation budget, HGNAN feature explanations outperform random attribution on all three datasets and G×I on NTU2012 and Zoo; the margin over G×I is smaller on Pokec.On NTU2012, HGNAN also has higher comprehensiveness and lower sufficiency than G×I across nearly the entire perturbation range.Source: A. Node-Level Feature Faithfulness · p. 14

B. Node-Level Structural Faithfulness

  • On NTU2012, removing the highest-weight neighbor causes a 12.2× larger probability decrease than random removal, declining to 3.0× for the top ten neighbors; the effect is weaker but significant on Pokec.Source: B. Node-Level Structural Faithfulness · p. 14

C. Hyperedge-Level Feature Faithfulness

  • Across four metabolic networks and two smax values, HGNAN has equal or lower SUFF than G×I in all eight settings, while COMP is higher on iAF1260b and iSB619 but lower on iJR904 and iYO844.Both attribution methods substantially outperform random attribution.Source: C. Hyperedge-Level Feature Faithfulness · p. 14

APPENDIX E HYPEREDGE-LEVEL STRUCTURAL FAITHFULNESS

HGNAN-edge’s structural attributions reflect meaningful source-hyperedge contributions, and zero-shot transfer varies by target network. Transfer to iSB619 is bounded by a shift in MACCS-derived reaction-feature distributions.

APPENDIX E HYPEREDGE-LEVEL STRUCTURAL FAITHFULNESS

  • HGNAN outperforms G×I and random attribution on all three node-level datasets; on NTU2012 it does so across nearly the full perturbation range, and highest-weight-neighbor removal lowers class probability more than random removal.Source: Table VII · p. 15, Table VIII · p. 15, Table IX · p. 15
  • Removing all structural context reduces AUROC by 7.17 points on iAF1260b and 6.26 points on iSB619; removing the target hyperedge’s self term causes the largest degradation, while non-self context also contributes.Source: Appendix E · pp. 14–15
  • Removing the top ten source hyperedges lowers AUROC by 4.70 points on iAF1260b and 5.04 on iSB619, while random removal changes it by at most 0.02 points.Those ten sources account for approximately 66% and 81% of the full contextual effects, respectively.Source: Appendix E · p. 15, Table XII · p. 16

APPENDIX F ADDITIONAL RESULTS FOR CROSS-DATASET TRANSFER

  • Excluding iSB619, HGNAN-edge averages AUROC 0.825 versus HyperSAGNN 0.781, NHP 0.639, and CHESHIRE 0.621, and leads in 8 of 9 transfer directions.Across all targets, it leads in 8 of 12 directions, but none of the three transfers to iSB619.Source: Table XIII · p. 16, Appendix F · p. 16
  • iSB619 has more extreme MACCS-key values than the other GEMs, producing covariate shift that bounds zero-shot transfer without adaptation.Its weaker transfer therefore reflects feature-distribution alignment as well as transfer of the learned structural mechanism.Source: Appendix F · p. 16
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