Graph Neural Additive Networks (GNANs) have emerged as effective, interpretable-by-design architectures for graph learning. They achieve transparency by combining per-feature shape functions with simple distance-based reweighting. However, GNANs have three limitations. First, node-wise relevance scores aggregate information from all graph nodes, allowing irrelevant nodes to inherit spurious relevance from relevant ones. Second, topology is represented only through shortest-path distances, so structurally distinct graphs may share identical distance profiles. Third, feature and distance information are combined multiplicatively, entangling feature, distance, and interaction effects in a single rescalable term. We introduce AMIGA, which represents topology through a vocabulary of mined motifs and decomposes each node contribution into three additive channels: feature, structure, and feature-structure interaction. The channels are centered around a graph-balanced training baseline, making the decomposition well-defined and unique under the chosen reference distribution. Across ten graph classification and regression benchmarks, AMIGA outperforms GNAN on most datasets and narrows the gap with standard black-box GNNs. Because each channel is centered and assigned to a single node, AMIGA produces node-local explanations that reconstruct the model output exactly and support interpretation at multiple levels of granularity.
Figures & tables
Figure 1: Two limitations of GNAN : (a) node relevance mixes neighboring feature contributions; (b) shortest-path profiles cannot distinguish K3,3 from the triangular prism.
Figure 2: Overview of AMIGA . Left: motifs are selected when they occur significantly more often than in randomly rewired training graphs with unchanged node degrees. Each node is then described by its participation in the selected motifs. Center: each node contribution is decomposed into feature, structural, and feature–motif interaction channels, and then pooled into the graph score. Right: this decomposition represents the model-level explanation of AMIGA , and enables full model transparency by independently inspecting feature, structural, and interaction contributions, allowing the model’s computations to be exactly reconstructed.
Figure 3: AMIGA can recover known effects from only label supervision. (a) True and learned node-level channel contributions. (b) Graph-level channel totals for one test graph. (c) Node-level total contributions for the same graph. (d–g) Active and inactive main effects. (h–i) True and learned I22(0) , shown with common axes and color scale.
Model
BA-Reg 1
BA-Reg 2
GIN + GNNExpl.
0.94±0.11
0.72±0.19
GIN + IG
0.88±0.11
0.22±0.11
GNAN
0.71±0.12
0.45±0.16
G-NAMRFF
0.50±0.11
0.54±0.08
AMIGA (ours)
0.99±0.02
1.00±0.00
Table 1: Explanation AUROC on BA-Reg 1 and BA-Reg 2, averaged over 5 seeds.
Black-box models
Interpretable models
Dataset
GCN
GIN
GTrans
GNAN
G-NAMRFF
AMIGA (ours)
Graph classification: AUROC ↑
Mutagenicity
0.851±0.005
0.868±0.018
0.849±0.010
0.751±0.002
0.698±0.068
0.828±0.015
NCI1
0.840±0.017
0.868±0.013
0.807±0.007
0.651±0.045
0.734±0.042
0.768±0.020
PROTEINS
0.791±0.010
0.811±0.012
0.697±0.020
0.821±0.008
0.786±0.036
0.733±0.046
PTC-MR
0.524±0.037
0.518±0.044
0.593±0.056
0.501±0.029
0.555±0.056
0.574±0.026
Table 2: Predictive performance averaged over five seeds. Classification rows report test AUROC ( ↑ ); regression rows report test MAE ( ↓ ). Bold marks the best result within each model group.
Figure 4: Global response functions learned by AMIGA on Mutagenicity. Left: centered atom-type effects f(atom) . Center: structural effects sm(k) against the number k of motif occurrences containing a node. Right: interaction I3(atom,k) between atom identity and motif m3 . Positive and negative values raise and lower the positive-class logit relative to the graph-balanced reference.
Figure 5: Example of the exact AMIGA decomposition for one molecular graph . Rows correspond to atoms; columns report the feature contribution, motif contributions, atom–motif interaction contributions, and node total zv . The bottom row aggregates each component across nodes. Adding the bias β0 reconstructs s(G) exactly. Outlined cells mark the contributions discussed in the text.
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Dataset
Task
Train/Val/Test
Avg. nodes
Avg. edges
Features
Mutagenicity
B
3035/651/651
30.32
30.77
14→1
NCI1
B
2877/616/617
29.87
32.30
37→1
PROTEINS
B
779/167/167
39.06
72.82
4→2
PTC-MR
B
240/52/52
14.29
14.69
18→1
BA-Reg 1
R
700/150/150
25.00
25.00
10→10
BA-Reg 2
R
700/150/150
120.00
128.90
10→10
Appendix
Table 3: Dataset statistics. B and R denote binary classification and regression. Edges count undirected pairs; feature dimensions are shown before and after AMIGA encoding.
Dataset
Selected
Dataset
Selected
Mutagenicity
4
BA-Reg 1
7
NCI1
7
BA-Reg 2
5
PROTEINS
21
Crippen
4
PTC-MR
6
QM9 (all targets)
7
Appendix
Table 4: Selected motif-vocabulary sizes across the five seed-specific training splits. The three QM9 targets share the same seed-specific vocabulary because they use identical graph indices within each seed.
Dataset
Selected motifs
Enumeration time (s)
Mutagenicity
4
0.148
NCI1
7
0.128
PROTEINS
21
0.164
PTC-MR
6
0.005
BA-Reg 1
7
0.044
BA-Reg 2
5
0.580
Appendix
Table 5: Wall-clock time required to enumerate all 29 candidate graphlets, averaged over the five seed-specific training splits. The QM9 time is averaged over the three equivalent measurements.
Dataset
GCN
GIN
GTrans
GNAN
G-NAMRFF
AMIGA
Mutagenicity
108±25
60±22
51±8
193±61
838±443
19±9
NCI1
99±35
93±23
81±19
132±46
958±440
14±3
PROTEINS
21±9
16±7
19±7
60±9
125±41
7±1
PTC-MR
2±0
3±1
4±1
3±1
8±3
2±1
BA-Reg 1
43±2
38±8
28±9
100±29
119±30
25±8
BA-Reg 2
97±0
75±23
37±15
187±136
115±41
56±8
Appendix
Table 6: Wall-clock training time in seconds, averaged over the five final runs and rounded to the nearest second. Hyperparameter search and motif discovery are excluded. Lower is better; the best result is bold.
Dataset
F
F+S
F+I
F+S+I
Classification: test AUROC (%), ↑
Mutagenicity
75.48±0.06
80.00±0.37
80.09±0.26
82.81±1.50
NCI1
64.24±0.46
75.76±0.29
78.17±0.68
76.81±2.01
PROTEINS
64.90±0.95
70.36±0.84
65.44±1.08
73.32±4.63
PTC-MR
49.69±3.99
54.09±3.74
49.69±3.99
57.43±2.62
Regression: test MAE, ↓
Appendix
Table 7: Channel ablation across five independently generated test splits. Entries report the mean ± standard deviation over five seeds, each defining both the data split and model training. The F+S+I column reuses the full-model runs reported in the main results. Bold indicates the best mean in each row.
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.
Quan D. Bui, Nguyen Do, An Nguyen Dang +3
Center for AI Research, VinUniversity, Hanoi, Vietnam · University of Florida, Gainesville, USA · Posts and Telecommunications Institute of Technology, Hanoi, Vietnam +1
Graph Neural Networks (GNNs) achieve strong performance on node classification tasks but remain difficult to interpret, particularly with respect to which input features drive their predictions. Existing global GNN explainers operate at the structural level identifying recurring subgraph motifs, but none explain model behaviour globally at the level of input node attributes. We propose GRAFT, a posthoc global explanation framework that identifies class-level feature importance profiles for GNNs. The method combines diversity-guided exemplar selection, Integrated Gradients-based attribution, and aggregation to construct a global view of feature influence for each class, which can be further expressed as concise natural language rules using a large language model with self-refinement. We evaluate GRAFT across multiple datasets, architectures, and experimental settings, demonstrating its effectiveness in capturing model-relevant features, supporting bias analysis, and enabling feature-efficient transfer learning. In addition, we introduce a structured human evaluation protocol to assess the interpretability of generated rules along dimensions such as accuracy and usefulness. Our results suggest that GRAFT provides a practical and interpretable approach for analysing feature-level behaviour in GNNs, bridging quantitative attribution with human-understandable explanations.
Rishi Raj Sahoo, Subhankar Mishra
National Institute of Science Education and Research (NISER), Bhubaneswar, India · Homi Bhabha National Institute, Mumbai, India
Graph Neural Networks (GNNs) have proven effective for graph analytical tasks, yet their "black-box" nature complicates the understanding of their layer-wise behavior and hinders their application to large graphs. We demonstrate SliceGXQ, an end-to-end declarative and interactive system for querying and exploring layer-wise explanations for GNNs over large-scale graphs. In particular, SliceGXQ provides (1) an interactive graphical user interface for dataset, model, and explanation configuration; (2) a lightweight SPARQL-like parser that allows users to specify target nodes, layers, explanation modes, and constraints; and (3) an integrated execution and visualization workflow that invokes SliceGX as its underlying explanation engine. We demonstrate how users can diagnose a misclassified node, identify problematic layers and influential messages, and perform targeted model debugging, together with large-scale graph interpretation and fraud-detection analysis. Our demonstration video and source code are available at https://github.com/jinzhaoqet/SliceGXQ.
Cibo Yu, Haitong Tang, Yinghui Wu +4
Zhejiang University, Hangzhou, China · Case Western Reserve University, Cleveland, USA · Bowling Green State University, Bowling Green, USA