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GraphCroc: Cross-Correlation Autoencoder for Graph Structural Reconstruction
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Proposes GraphCroc, a U-Net-style graph autoencoder whose decoder uses cross-correlation (sigmoid(PQ^T)) with loss balancing, aiming to reconstruct multi-graph adjacency structures better than self-correlation GAEs.
Problem
Self-correlation decoders in graph autoencoders cannot represent islands (no self-loops), symmetric structures, or directed edges, and are harder to optimize, especially on multi-graph datasets; sparse adjacency also biases training toward zeros.
Approach
Replace the self-correlation decoder sigmoid(ZZ^T) with a cross-correlation decoder sigmoid(PQ^T) from two parallel mirrored GNN decoders, paired with a Graph U-Net-style encoder and a class-balanced BCE loss.
Key results
- On directed Cora_ML (N=77), GraphCroc reaches AUC 0.9996 versus 0.8296 for DiGAE; on CiteSeer, 0.9999 vs 0.9083.
- GraphCroc reports AUC over 0.98 on PPI reconstruction, and outperforms self-correlation GAEs across the tested multi-graph tasks.
- On graph classification with 100-epoch finetuning, GraphCroc gets 79.09 on PROTEINS, 78.75 on IMDB-B and 82.40 on COLLAB, the best among compared methods.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GraphCroc encoder instead of the strongest listed baseline, S2GAE | Graph classification · PROTEINS | accuracy: 76.37 -> 79.09$^{\pm1.63}$ | Helped |
| Use GraphCroc encoder instead of the strongest listed baseline, S2GAE | Graph classification · IMDB-B | accuracy: 75.76 -> 78.75$^{\pm1.35}$ | Helped |
| Use GraphCroc encoder instead of the strongest listed baseline, S2GAE | Graph classification · COLLAB | accuracy: 81.02 -> 82.40$^{\pm0.20}$ | Helped |
| Use GraphCroc instead of DiGAE | Directed graph reconstruction · Cora_ML (N̄=41) | AUC: 0.6879 -> 0.9946 | Helped |
| Use GraphCroc instead of DiGAE | Directed graph reconstruction · Cora_ML (N̄=77) | AUC: 0.8296 -> 0.9996 | Helped |
| Use GraphCroc instead of DiGAE | Directed graph reconstruction · CiteSeer (N̄=16) | AUC: 0.9083 -> 0.9999 | Helped |
| Train GraphCroc for 100 epochs rather than 10 epochs (ablation) | GraphCroc graph-classification encoder · PROTEINS | accuracy: 73.99$^{\pm1.32}$ -> 79.09$^{\pm1.63}$ | Helped |
| Train GraphCroc for 100 epochs rather than 10 epochs (ablation) | GraphCroc graph-classification encoder · IMDB-B | accuracy: 76.69$^{\pm1.02}$ -> 78.75$^{\pm1.35}$ | Helped |
| Train GraphCroc for 100 epochs rather than 10 epochs (ablation) | GraphCroc graph-classification encoder · COLLAB | accuracy: 81.70$^{\pm0.54}$ -> 82.40$^{\pm0.20}$ | Helped |
| Replace standard inner-product decoding with variational decoding (ablation) | Cross-correlation GAE on PROTEINS · PROTEINS | AUC | Mixed |
| Replace standard inner-product decoding with edge masking (ablation) | Cross-correlation GAE on graph tasks · Graph tasks | AUC | Mixed |
| Replace standard inner-product decoding with L2-norm representation (ablation) | Cross-correlation GAE on graph tasks · Graph tasks | AUC | Mixed |
Surprising findings
- L2-norm decoding achieves high AUC yet reconstructs few whole graphs exactly under the WL-test, indicating some patterns are hard for it to capture.
- Contrastive learning methods underperform generative GAE methods on multi-graph classification, with negative sampling offering little benefit there.
Limitations
- Self-correlation baselines were not averaged over multiple runs due to heavy compute, so reconstruction results are single-run.
- Large graphs such as PPI exceed GPU memory for some baselines (e.g., L2-norm EGNN), and fine-tuning of alternative architectures was limited.
- Attacks change edge sets in discrete ways that are hard to control at low distortion.
Experimental setup
Datasets: PROTEINS IMDB-B COLLAB PPI QM9 Cora_ML CiteSeer
Benchmarks: PROTEINS IMDB-B COLLAB PPI QM9 Cora_ML directed subgraphs CiteSeer directed subgraphs
Metrics: ROC-AUC WL-test pass rate graph classification accuracy attack accuracy modified edge percentage
Baselines: GAE VGAE EGNN DiGAE GraphMAE S2GAE StructMAE InfoGraph GraphCL InfoGCL PGD C&W
Builds on: graph autoencoder Graph U-Net DiGAE GraphMAE EGNN
Closest papers by meaning
- HC-GAE: The Hierarchical Cluster-based Graph Auto-Encoder for Graph Representation Learning (NeurIPS 2024 · similarity 0.91)
- The quest for the GRAph Level autoEncoder (GRALE) (NeurIPS 2025 · similarity 0.88)
- Self-supervised Masked Graph Autoencoder via Structure-aware Curriculum (ICML 2025 · similarity 0.86)
- Teacher-guided Edge Discriminator for Personalized Graph Masked Autoencoder (AAAI 2025 · similarity 0.86)
- Transitivity-Preserving Graph Representation Learning for Bridging Local Connectivity and Role-Based Similarity (AAAI 2024 · similarity 0.86)
- Rethinking Graph Masked Autoencoders through Alignment and Uniformity (AAAI 2024 · similarity 0.86)
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