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DualGSL: Prior-Guided Graph Structure Learning with Node-Adaptive Prediction Fusion

Yuxia Sun, Yutszyuk Wong, Huihong Chen, Longhao Lv, Chang-Dong Wang, Li Zeng

arXiv:2610.32462v1cs.LG

TL;DR

Feature-derived priors and task-learned relations may contribute differently to classification across nodes, motivating a node-adaptive way to combine them. DualGSL keeps separate propagation paths and fuses their predictions with node-specific weights. Across AMG18, 20News, and USPS, it achieves the highest cross-dataset average accuracy and Macro-F1 among evaluated methods.

  • Problem

    Prior and learned propagation can differ in predictive value across nodes, but a shared output coefficient applies the same balance to each node.

    Source: §I · p. 1

  • Method

    DualGSL retains separate prior and task-adaptive propagation paths and learns node-specific weights to fuse their predictions.

    Source: §I · pp. 1–2

  • Results

    85.49% accuracy and 84.62% Macro-F1 are DualGSL’s highest cross-dataset averages among the evaluated methods.

    Source: §I · p. 2

  • Takeaways & Limitations

    AMG18 analyses show that retaining both propagation paths and fusing their logits improves Macro-F1 over either branch head at a fixed checkpoint.

    Source: §VI · p. 11

Abstract

from arXiv · show

Graph structure learning (GSL) adapts propagation graphs to prediction tasks, but the relative predictive value of feature-derived priors and learned relations can vary across nodes. We propose DualGSL, a prior-guided framework for transductive node classification that learns node-specific weights for combining predictions from separate prior and task-adaptive propagation paths. The prior branch augments a feature graph with virtual class nodes to incorporate training-label information, while the structural branch combines learned affinity graphs with the feature-graph prior. The two branches share encoder parameters while preserving distinct representations and classification logits. A node-adaptive gate fuses the branch logits based on their projected representations, element-wise absolute difference, and prediction confidence. A joint objective integrates fused and branch-specific classification losses with prior-branch class-anchor alignment, coordinating graph construction, representation learning, and prediction fusion. Experiments against seven baselines on the AMG18 malware attribution dataset and the widely used 20News text classification and USPS handwritten-digit recognition benchmarks show that DualGSL achieves the highest cross-dataset average accuracy and Macro-F1 among the evaluated methods. Ablation studies on AMG18 further demonstrate the benefit of combining prior and learned propagation through logit fusion.

I. INTRODUCTION

Feature-derived graphs may not capture the relations most useful for classification, and the predictive value of prior and learned propagation can vary across nodes. DualGSL keeps separate paths and learns node-specific prediction weights; it achieves the highest cross-dataset average accuracy and Macro-F1 among evaluated methods.

I. INTRODUCTION

  • Prior and learned propagation can have different predictive value across nodes, while a shared output coefficient applies the same balance to each node.This motivates node-specific fusion of the two predictions.Source: §I · p. 1
  • DualGSL retains separate prior and task-adaptive propagation paths and learns node-specific weights to combine their predictions.The prior branch adds virtual class nodes to a feature graph; the structural branch combines learned affinity graphs with the feature-graph prior.Source: §I · pp. 1–2
  • DualGSL achieves the highest cross-dataset averages among evaluated methods, with 85.49% accuracy and 84.62% Macro-F1; branch-prediction analysis supports combining its two propagation paths through logit fusion.On AMG18, DualGSL outperforms variants without the structural and prior branches by 1.35 and 2.40 percentage points in mean Macro-F1, respectively.Source: §I · p. 2

A. Graph Construction and Graph Structure Learning

  • Graph structure learning learns or refines propagation relations when feature-similarity graphs may not provide task-useful neighborhoods.IDGL incorporates an initial adjacency into learned graph construction, whereas GSR refines edges through self-supervised pretraining before predictor fine-tuning.Source: A. Graph Construction and Graph… · p. 2

B. Multi-View Graph Learning and Prediction Fusion

  • DualGSL learns a node-specific logit gate conditioned on branch representations, their disagreement, and prediction confidence.This contrasts with CoGSL’s confidence-based adjacency fusion and ELU-GCN’s shared scalar for output mixing.Source: B. Multi-View Graph Learning and… · p. 3

C. Label-Aware Graph Learning

  • DualGSL builds on label-node augmentation and training-node selection by coordinating a class-aware prior branch with task-adaptive propagation through node-specific logit fusion.The cited training-node selection separates labels used to construct class connections from labels used for prediction supervision.Source: C. Label-Aware Graph Learning · p. 3

D. APT Malware Attribution

The paper frames malware attribution as transductive node classification over feature-derived graphs, with partially observed labels and no supplied relational graph. Its graph-construction method uses a fixed feature-based prior alongside task-adaptive affinities learned from shared hidden features.

D. APT Malware Attribution

  • DualGSL formulates APT malware attribution as node classification over feature-derived graphs, jointly learning inter-sample relations and node-adaptive prediction fusion.AMG18 is presented as a public dataset for evaluating APT group classification.Source: D. APT Malware Attribution · p. 3

III. PROBLEM FORMULATION

  • The task is transductive classification from node attributes and partially observed labels, without assuming a supplied relational graph.All node features are available for graph construction and prediction, but only training labels are used for optimization and label-aware graph construction.Source: §III · p. 3

IV. METHOD

  • DualGSL uses separate prior and task-adaptive propagation paths, with distinct representations and logits, and fuses their predictions using a node-adaptive gate.Fused and branch-specific classification losses jointly train the graph construction, representations, and prediction fusion; class-anchor alignment guides prior-branch embeddings.Source: §IV · p. 3

A. Dual-View Graph Construction

  • A shared hidden feature matrix supports both branches: the prior graph is built from input features, while task-adaptive affinities are learned from the hidden features.The hidden features are produced by a learnable projection of the input matrix.Source: A. Dual-View Graph Construction · p. 3

1) Feature-Based Prior Graph:

  • The feature-based prior graph encodes cosine k-nearest-neighbor relations and remains fixed throughout training.The affinities are symmetrized before row normalization to form the prior adjacency.Source: 1) Feature-Based Prior Graph · p. 4

2) Label-Augmented Prior Graph:

DualGSL separates prior and learned structural propagation: training-label information enters the prior graph through virtual class nodes, while learned affinities are combined with the feature-derived prior for structural propagation.

2) Label-Augmented Prior Graph:

  • Training nodes are split by class into source and prediction sets, so source labels connect to virtual class nodes while prediction nodes’ own labels do not determine those connections.The augmented adjacency changes with the resampled source set; validation and testing use all training nodes as sources.Source: 2) Label-Augmented Prior Graph · p. 4

3) Learned Structural Graph:

  • Four parameterized affinity functions learn real-node relations from shared hidden features, producing sparse adjacencies by retaining each row’s top-k scores.The learned adjacencies are not explicitly symmetrized, and diagonal entries may be selected.Source: 3) Learned Structural Graph · p. 4
  • The structural adjacency mixes the four learned graphs with the feature-derived prior using global coefficients shared across nodes.Including the prior preserves prior connectivity while learned affinities add task-adaptive relations.Source: 3) Learned Structural Graph · p. 4

B. Shared Graph Encoding

The prior and structural branches use a shared two-layer graph encoder but retain branch-specific normalization, representations, and classification logits.

B. Shared Graph Encoding

  • A shared two-layer graph encoder processes each branch’s input features and adjacency using shared learnable weights and biases.The encoder produces intermediate node representations before the branch transformations.Source: B. Shared Graph Encoding · p. 4
  • The branches apply shared fully connected transformations with branch-specific batch normalization, yielding distinct representations for real nodes and virtual class nodes.The prior branch includes virtual class representations; the structural branch produces real-node representations.Source: B. Shared Graph Encoding · pp. 4–5
  • Separate classification heads map the branch representations to logits, while projected real-node representations feed fusion and projected virtual class representations serve as class anchors.Source: B. Shared Graph Encoding · p. 5

C. Node-Adaptive Logit Fusion

DualGSL combines prior-branch and structural-branch logits using a node-adaptive mixing coefficient informed by branch representations, disagreement, and prediction confidence.

C. Node-Adaptive Logit Fusion

  • The node-specific mixing coefficient adjusts the prior-branch logits using the difference between the structural and prior logits to form fused predictions.Source: C. Node-Adaptive Logit Fusion · p. 5
  • The gate input combines projected branch representations, their element-wise absolute difference, and each branch’s maximum-softmax prediction confidence.The representation difference characterizes branch disagreement, while confidence summarizes each prediction.Source: C. Node-Adaptive Logit Fusion · p. 5
  • A learned gating network produces a node-wise gate, scaled by a learned global factor that sets an upper bound on structural mixing.The global factor and gate are learned jointly with graph construction and branch predictors.Source: C. Node-Adaptive Logit Fusion · p. 5

D. Joint Objective and Training

DualGSL trains fused and branch-specific predictions alongside prior-branch class-anchor alignment, using resampled source and prediction sets and validation Macro-F1 to select a model state.

1) Classification Supervision:

  • Fused predictions and both branch predictions receive classification supervision on the prediction set, giving the combined predictor and each propagation path direct classification signals.Source: 1) Classification Supervision · p. 5

2) Class-Anchor Alignment:

  • Class-anchor alignment minimizes the squared error between each supervised node’s projected prior representation and the propagated virtual anchor for its class.The objective encourages same-class prediction nodes to align with their shared virtual class anchor.Source: 2) Class-Anchor Alignment · p. 5
  • Each training epoch partitions training nodes within each class into source and prediction sets, constructs the label-augmented prior graph, and computes the dual-branch loss.Source: 2) Class-Anchor Alignment · p. 6
  • The training procedure evaluates validation Macro-F1, saves the best model state when the score improves, and then recomputes predictions for test nodes using all training nodes as sources.Source: 2) Class-Anchor Alignment · p. 6

3) Joint Learning Objective:

The dual-view objective jointly trains fused and branch-specific classification with class-anchor alignment; a separate prior-only configuration retains label-augmented propagation and alignment.

3) Joint Learning Objective:

  • The dual-view objective combines fused classification, branch-specific classification, and class-anchor alignment losses.These objectives jointly optimize graph construction, branch representations, and node-adaptive prediction fusion.Source: 3) Joint Learning Objective · p. 6
  • The nonnegative λview and λcenter terms control the contributions of branch-specific supervision and class-anchor alignment, respectively.Source: 3) Joint Learning Objective · p. 6
  • The prior-only configuration is trained independently and predicts directly from prior-branch logits while retaining virtual class nodes and class-anchor alignment.Source: 3) Joint Learning Objective · p. 6

4) Training Procedure:

Training alternates class-wise source and prediction nodes, selects checkpoints by validation Macro-F1, and evaluates transductive node classification across three datasets using shared protocols and seven baselines.

4) Training Procedure:

  • At each epoch, training nodes are partitioned within each class into source and prediction sets; source labels create virtual-class connections and prediction nodes receive the losses.Source: 4) Training Procedure · p. 6, 1) Datasets and Evaluation Protocol · p. 7
  • Validation Macro-F1 controls checkpoint updates and stopping, after which the saved state predicts test labels using all training nodes as sources.The procedure stops after p consecutive epochs without the required improvement or at T epochs.Source: 4) Training Procedure · p. 6

1) Datasets and Evaluation Protocol:

  • The evaluation covers AMG18 malware attribution, 20News text classification, and USPS handwritten-digit recognition under a transductive setting.All-partition node features are available for graph construction, while training labels alone support label-aware graph construction and optimization.Source: §V · p. 6, 1) Datasets and Evaluation Protocol · pp. 6–7

2) Baselines and Metrics:

  • Seven baselines span feature-only classification, fixed-graph propagation, graph structure learning, and label-enhanced learning, with accuracy and Macro-F1 reported as five-seed means.Macro-F1 equally weights class-wise F1 scores, and cross-dataset averages are unweighted means of the three dataset means.Source: 2) Baselines and Metrics · p. 7
  • Methods use the same node features and data partitions, validation-selected hyperparameters and checkpoints, and test labels only for final evaluation.Source: 2) Baselines and Metrics · p. 7

3) Implementation Details:

DualGSL leads the evaluated methods in cross-dataset averages, with dataset-level results and AMG18 ablations assessing its configurations and components.

3) Implementation Details:

  • The models use Adam at learning rate 0.005 and weight decay 5×10^-4, with a two-layer shared graph encoder and dropout 0.2; USPS uses the prior-only configuration.Runs use validation Macro-F1 for checkpoint selection and early stopping.Source: 3) Implementation Details · p. 7

B. Classification Performance

1) Malware Attribution on AMG18:

2) Text Classification on 20News:

  • 72.35% mean accuracy and 71.58% mean Macro-F1 are DualGSL’s 20News results; its Macro-F1 ranks second behind GCN’s 72.30%.Its Macro-F1 is higher than that of the evaluated graph structure learning baselines.Source: 2) Text Classification on 20News · p. 7

3) Handwritten-Digit Recognition on USPS:

  • 95.36% mean accuracy and 95.00% mean Macro-F1 are the highest USPS scores, achieved by the independently trained prior-only configuration.These exceed LEGNN by 0.19 and 0.21 percentage points, respectively.Source: 3) Handwritten-Digit Recognition on USPS · p. 8

C. Ablation Study

  • On AMG18, removing the structural or prior branch lowers Macro-F1 by 1.35 or 2.40 points; removing graph learners, virtual class nodes, or alignment lowers it by 1.24, 0.40, or 0.30 points.The full model achieves the highest mean accuracy and Macro-F1 among the evaluated variants.Source: C. Ablation Study · p. 8, Table IV · p. 8

D. Prediction and Structural Analysis

At a fixed AMG18 checkpoint, fused predictions outperform either branch alone, while the learned structural graph retains prior edges and adds new propagation links.

1) Prediction Fusion Analysis:

  • 1.64 and 2.21 percentage-point Macro-F1 gains over the prior and structural heads, respectively, accompany 13 net additional correct predictions from fusion.The comparison uses predictions from the same trained dual-view checkpoint.Source: 1) Prediction Fusion Analysis · pp. 8–9, Table V · p. 9
  • 19.28% is the mean structural mixing coefficient across test nodes, so fusion improves predictions while assigning greater average weight to the prior branch.Source: 1) Prediction Fusion Analysis · p. 9

2) Learned Graph Structure Analysis:

3) Representation and Fusion Visualization:

The section visualizes class-related organization in DualGSL’s branch representations and node-wise fusion, reports AMG18 hyperparameter sensitivity, and summarizes cross-dataset results and future directions.

3) Representation and Fusion Visualization:

  • The AMG18 projections show more visually distinct clusters for several APT groups in both learned branch representations than in the input-feature projection.Structural mixing coefficients vary across nodes, including within visible clusters.Source: 3) Representation and Fusion… · pp. 9–10, Figure 2 · p. 10

E. Hyperparameter Sensitivity

  • At k = 5, the neighborhood-size sweep reaches 89.22% mean accuracy and 87.63% mean Macro-F1; performance does not improve monotonically as k increases.Mean Macro-F1 ranges from 86.79% to 87.63% across evaluated values.Source: E. Hyperparameter Sensitivity · p. 10
  • At λview = 0.40, mean Macro-F1 rises from 86.32% to 87.28% versus λview = 0; λview = 0.10 gives the sweep’s highest accuracy and Macro-F1.The maxima at λview = 0.10 are 89.25% mean accuracy and 87.49% mean Macro-F1.Source: E. Hyperparameter Sensitivity · p. 10
  • Across source-node ratios 0.3–0.7, mean Macro-F1 ranges from 86.92% to 87.28%; λcenter = 0.05 exceeds no alignment by 0.30 percentage points in Macro-F1.The default source-node ratio of 0.5 gives the highest mean Macro-F1, while 0.7 gives the highest mean accuracy; λcenter = 0.05 gives the highest mean accuracy and Macro-F1 in its sweep.Source: E. Hyperparameter Sensitivity · p. 10

VI. CONCLUSION AND FUTURE WORK

  • DualGSL preserves separate propagation paths and learns a node-specific balance between their predictions within a jointly trained framework.Future work will examine prior-graph quality, label availability, branch confidence, inductive settings, and more efficient affinity learning for larger graphs.Source: §VI · pp. 10–11
  • DualGSL achieves the highest cross-dataset average accuracy and Macro-F1 among the compared methods.The conclusion also reports that AMG18 branch ablations and fixed-checkpoint comparisons support retaining both paths and fusing their logits.Source: §VI · p. 11

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