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Self-Explainable Multi-Label Graph Neural Network for Correlated Evidence Attribution

Yingqi Feng, Yufei Tang, Min Shi, Xingquan Zhu

arXiv:2608.27574v1cs.LGcs.AI

TL;DR

Multi-label graph learners need explanations that distinguish label-specific evidence while adapting sharing to label correlations, a capability missing from existing training and post-hoc approaches. SEMGNN jointly learns prediction and sparse edge attribution with correlation-aware components, achieving competitive predictive performance and faithful, compact explanations on synthetic and real-world graphs. Its main consequence is label-conditioned explanations that share support for related labels while preserving distinct rationales for weakly or negatively associated labels.

  • Problem

    Existing multi-label graph learning methods lack training-time interpretation, while post-hoc explainers do not explicitly model label-dependent evidence sharing for weakly or negatively associated labels.

  • Method

    SEMGNN jointly learns multi-label node prediction and sparse edge attribution under a unified objective, incorporating label correlations into both prediction and explanation.

  • Results

    Experiments on synthetic and real-world multi-label graphs show competitive predictive performance with faithful and compact label-conditioned explanations.

  • Takeaways & Limitations

    Label-conditioned explanations can share support for positively related labels while preserving distinct rationales for weakly or negatively associated labels.

Abstract

from arXiv · show

Multi-label graph learning intends to capture the intrinsic complexity of real-world applications, where one sample is often related to multiple groups or consists of multiple objects. To date, a handful of multi-label graph learning methods exist, but none of them integrate training-time interpretation capability. While post-hoc graph explainers have been developed, they do not explicitly model label-dependent evidence sharing in multi-label graph learners, especially when label pairs are weakly or negatively associated. As a result, post-hoc approaches may miss how evidence should be shared or separated across different labels. This paper advances a new end-to-end self-explainable multi-label graph neural network (SEMGNN), which aims to simultaneously classify multi-labeled nodes and identify edges significantly contributing to each target node w.r.t. predicted labels. Different from post-hoc methods, SEMGNN jointly learns a predictor and a sparse edge-mask explainer within a unified framework and training objective. Label-label correlations are used to improve multi-label node classification and enhance individual label explanations, so that different labels of a node can be supported by distinct yet coherent structural and/or correlated evidence. Experiments and comparisons on synthetic and real-world multi-label networks, in social networking, entertainment, and life sciences, show that SEMGNN achieves competitive or improved predictive performance while providing more faithful and compact label-conditioned explanations.

I. INTRODUCTION

Multi-label graph learning must explain label-specific evidence while accounting for correlations among labels. SEMGNN addresses this gap by jointly learning prediction and sparse, correlation-aware explanations.

  • Multi-label node classification is challenging because labels may be imbalanced and correlated, with overlapping or distinct structural evidence.
  • Existing explainers largely target single-label prediction or operate post hoc, weakening alignment between predictions and explanations.
  • Explaining labels independently can miss shared evidence, whereas one explanation for all labels can obscure label-specific rationales.
  • SEMGNN jointly learns multi-label prediction and attribution using a shared backbone, intrinsic edge scoring, and sparse explanatory subgraphs.
  • Label-correlation-aware attribution lets positively related labels share evidence while preserving distinct rationales for weakly or negatively associated labels.
  • A unified sufficiency–necessity–sparsity objective supports faithful, compact, label-conditioned explanations alongside competitive or improved prediction performance.

C. Self-Explainable GNNs

SEMGNN integrates prediction and explanation during training for multi-label graph learning. Its architecture learns intrinsic edge masks and refines label-conditioned attribution into compact explanatory subgraphs.

  • A. Problem Formulation: The predicted label set contains labels whose probabilities exceed τpred, while the highest-scoring label is retained when none passes the threshold.
  • A. Problem Formulation: For each predicted label, SEMGNN extracts a compact explanatory edge set from the target node’s K-hop computation subgraph.
  • C. Self-Explainable GNNs: SEMGNN jointly learns node prediction and attribution, promoting alignment between predicted labels and label-conditioned explanations.
  • B. SEMGNN: Architecture Overview: The shared prediction backbone supports full, masked, and removed forward passes, combining balanced message passing with a label-graph residual branch.
  • B. SEMGNN: Architecture Overview: Intrinsic edge masking learns soft masks that are sparse, near-binary, and non-degenerate, making the model self-explainable by construction.
  • B. SEMGNN: Architecture Overview: During inference, label-aware edge scores are refined with gradient-based necessity scores before compact explanatory subgraphs are extracted.

C. Shared Prediction Backbone

SEMGNN ties attribution to the same prediction backbone used for full, masked, and removed passes. Its balanced encoder and label-correlation residual produce representations and decision signals for multi-label prediction.

  • C. Shared Prediction Backbone: The full, masked, and removed passes share one prediction backbone, tying attribution learning to the decision function rather than a surrogate.
  • C. Shared Prediction Backbone: Mean aggregation combines each node’s representation with its neighbors while reducing high-degree neighbor dominance.
  • C. Shared Prediction Backbone: The encoder output H is the final node representation used by both the predictor and edge scorer.
  • C. Shared Prediction Backbone: A two-layer MLP maps H to base multi-label logits, which are augmented by a label-correlation residual branch.
  • C. Shared Prediction Backbone: The label-correlation graph is constructed only from training labels to avoid validation and test leakage.
  • C. Shared Prediction Backbone: A learnable gate combines base predictions with correlation-aware residual signals, preserving base-predictor stability while sharing predictive information across correlated labels.

D. Edge Scoring Strategy

SEMGNN learns label-conditioned edge masks during training and refines them at inference. Label-aware scoring and correlation propagation let labels share some evidence while retaining distinct structural rationales.

  • D. Edge Scoring Strategy: Training jointly uses label-agnostic and label-aware edge scorers to capture shared and label-specific structural evidence.
  • D. Edge Scoring Strategy: A sampled subset of labels is aggregated into one training mask to reduce the cost of modeling every label at each training step.
  • D. Edge Scoring Strategy: The soft mask supports masked and removed forward passes, whose combination with the full pass encourages sufficiency and necessity.
  • D. Edge Scoring Strategy: At inference, SEMGNN answers a node-label query with a label-specific soft mask over the node’s K-hop computation subgraph.
  • D. Edge Scoring Strategy: Propagating label representations over the correlation graph allows related labels to share attribution signals while preserving label-specific explanations.
  • D. Edge Scoring Strategy: Gradient-based necessity scores are fused with the queried-label mask, and adaptive Top-M selection produces the final edge scores.

E. Explanation Extraction

SEMGNN extracts label-specific explanations from local computation subgraphs for predicted positive labels. Adaptive edge-group selection keeps each explanation compact and aligned with local graph complexity.

  • E. Explanation Extraction: Explanations are generated only for predicted positive labels of a target node.
  • E. Explanation Extraction: For each target node and label, SEMGNN extracts explanations from the node’s K-hop computation subgraph.
  • E. Explanation Extraction: Directed edge pairs representing one connection are merged into undirected edge groups before explanation extraction.
  • E. Explanation Extraction: Final queried-label scores are assigned to undirected edge groups from the fused edge scores.
  • E. Explanation Extraction: An adaptive number of edge groups is selected using the explanation budget.
  • E. Explanation Extraction: Adaptive extraction keeps explanations compact while matching the complexity of the local computation subgraph.
  • E. Explanation Extraction: End-to-end training combines prediction, three explanation losses, and mask regularization in one objective.

1) Prediction Loss:

The objective uses focal BCE for imbalanced multi-label prediction and trains explanations through sufficiency, necessity, and auxiliary supervision. Degree-adaptive regularization encourages compact, non-degenerate masks.

  • 1) Prediction Loss:: Focal BCE with label-wise positive weights estimated from training-label frequencies provides the prediction loss.
  • 1) Prediction Loss:: Confidence weighting emphasizes explanation supervision for labels with more confident full-graph predictions.
  • 1) Prediction Loss:: Sufficiency supervision encourages masked predictions to preserve the full-graph prediction.
  • 1) Prediction Loss:: Necessity supervision penalizes confident predictions that remain after important edges are removed.
  • 1) Prediction Loss:: Auxiliary masked-target supervision stabilizes early training by supervising the masked forward pass with observed labels.
  • 1) Prediction Loss:: Degree-adaptive mask regularization targets compact but non-degenerate masks without overpenalizing high-degree neighborhoods.

3) Regularization:

The section describes regularization and the evaluation setting for correlated evidence attribution across synthetic and real-world multi-label graphs. Training uses staged coefficient scheduling, while datasets differ in graph type, label structure, and available rationales.

  • 3) Regularization:: The objective uses mask regularization to encourage near-binary explanations and prevent trivial collapse.
  • 3) Regularization:: A three-stage coefficient schedule stabilizes end-to-end training by adjusting auxiliary, necessity, and regularization losses over time.Bootstrap establishes an auxiliary signal, alignment focuses on sufficiency, and necessity training is introduced after the teacher signal stabilizes.
  • A. Datasets: Evaluation covers five datasets spanning synthetic reachability and motif evidence, social networks, and biological protein-localization graphs.SynAnchor provides shortest-path rationales, while SynMotif provides injected motif-edge rationales for positive node-label pairs.

B. Baselines

The evaluation compares prediction-only, self-explainable, and multi-label graph baselines, including methods that model label correlations, label importance, or independent label decisions.

  • Baseline groups: The baselines comprise prediction-only models, a self-explainable model, and approaches that explain frozen predictors.The comparison is organized into three groups: prediction baselines without explanations, a training-time self-explainable baseline, and post-hoc explanation baselines.
  • Prediction baselines: Predict-Only removes the explanation module from the shared prediction backbone.
  • Prediction baselines: GAT, ML-GCN, and LIP provide graph baselines with attention, coupled node-label propagation, or label-importance reweighting.ML-GCN explicitly models label correlations through coupled propagation, while LIP weights per-label losses by label influence.
  • Prediction baselines: Binary Relevance GNN trains one independent classifier per label, providing a label-separate comparison.
  • Self-explainable baseline: GSAT adapts stochastic attention to multi-label outputs but uses one task-level mask for all predicted labels of a node.Its multi-label adaptation replaces the output layer with sigmoid outputs and uses binary cross-entropy loss.

3) Explanation baselines:

Explanation evaluation uses frozen-predictor post-hoc baselines and a shared protocol for label-wise explanations, prediction metrics, and local edge selection.

  • Explanation baselines: All post-hoc explainers operate on the same frozen Predict-Only predictor and explain each predicted positive label independently.
  • Explanation baselines: The post-hoc comparison includes Ours-PH, GNNExplainer, and PGExplainer.GNNExplainer learns a soft edge mask independently for each target label, whereas PGExplainer predicts instance-wise edge selection probabilities.
  • Experimental protocol: Models share transductive splits, Adam optimization, early stopping, validation-based selection, training-split label weights, and a global validation threshold for test F1.The F1 threshold is selected over [0.1, 0.9] in increments of 0.01 and applied unchanged to the test set.
  • Explanation protocol: Explanations are extracted from shared 2-hop computation subgraphs, with opposite directed edges merged and identical adaptive Top-M budgets used across methods.
  • Metrics: Synthetic evaluation reports F1 and IoU against ground-truth masks, while all datasets report Fidelity+ and Fidelity-.Higher Fidelity+ and Fidelity- indicate better sufficiency and necessity, respectively.
  • Evaluation aims: The experiments test prediction quality, faithful compact label-conditioned explanations, and consistency between explanation sharing and label relatedness.

2) Faithfulness of Label-Conditioned Evidence Attribution:

SEMGNN’s label-conditioned explanations align strongly with synthetic ground-truth rationales and show fidelity across real-world graphs. Its correlation-aware design organizes sharing according to label relatedness rather than enforcing one common explanation.

  • Faithfulness results: SEMGNN achieves the best ground-truth F1 and IoU on both SynAnchor and SynMotif.These metrics evaluate whether selected edges recover the label-conditioned structural rationales used to generate synthetic labels.
  • Faithfulness results: On SynAnchor, SEMGNN achieves the best Fidelity+ and Fidelity-, combining prediction preservation with decision-critical evidence removal.
  • Faithfulness results: On SynMotif, GSAT has the highest Fidelity+, but SEMGNN has the highest Fidelity- and substantially better ground-truth alignment.The comparison indicates that sufficiency alone does not establish structurally correct label-specific attribution.
  • Faithfulness results: On real-world datasets, SEMGNN is strongest or competitive in fidelity, achieving both best fidelities on YouTube and best Fidelity+ on HumLoc.It also attains the second-best Fidelity- on HumLoc and balanced second-best performance on BlogCatalog.
  • Correlation-aware attribution: Post-hoc explainers do not explicitly model whether evidence should be shared or separated according to label relationships.
  • Correlation-aware attribution: SEMGNN conditions training-time edge attribution on correlation-aware label representations, supporting distinct but partially shared evidence for different labels.
  • Case studies: In a SynAnchor case, SEMGNN recovers the complete label set and all visible ground-truth explanatory edges, unlike GSAT’s shared mask and post-hoc label miss.
  • Case studies: For SynAnchor labels 17 and 25, enabling label correlation raises shared edge groups from 2 to 5 and explanation overlap from 0.333 to 0.778.

4) Ablation Study:

The ablation study finds that prediction-side and explanation-side label modeling play complementary roles in SEMGNN. Correlation–overlap analyses further show that label modeling can organize evidence sharing according to label relatedness, with dataset-dependent behavior.

  • Prediction ablations: Removing the prediction-side label-correlation residual generally lowers prediction performance, especially on SynAnchor, SynMotif, and BlogCatalog.The effect is less uniform on YouTube and HumLoc, where some AUPRC scores are comparable or slightly higher for ablated variants.
  • Explanation ablations: The full model often provides the strongest sufficiency–necessity balance, particularly on SynAnchor, SynMotif, BlogCatalog, and HumLoc.On synthetic datasets, some ablations achieve slightly higher GT F1/IoU in isolated cases, because GT recovery measures agreement with externally defined ground truth.
  • Correlation–overlap alignment: ρ increases from 0.165 to 0.410 on SynAnchor when label-correlation modeling is enabled, indicating stronger alignment between label relatedness and explanation overlap.BlogCatalog and YouTube also show positive alignment gains, while SynMotif and HumLoc show decreases consistent with dataset-specific evidence structures.
  • Complementary roles: Prediction-side correlation helps learn label-dependent decision signals, while explanation-side scoring converts them into label-conditioned edge attribution.The two label-aware components therefore contribute complementary functions within SEMGNN.
  • Evidence sharing: SEMGNN uses label correlations as a structured prior for sharing evidence across related labels while preserving distinct support for weakly or negatively associated labels.The label-correlation graph is constructed only from the training split to avoid validation or test label leakage.
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