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Graph Learning Tasks

This guide provides an overview of the graph learning experiments conducted with spikeDE. These experiments demonstrate the effectiveness of our fractional-order Spiking Neural Networks (f-SNNs) in capturing long-range dependencies on graph-structured data, outperforming traditional integer-order SNNs.

All source code for these experiments is open-source and reproducible. You can access the specific implementation scripts and configurations in our GitHub repository.

Overview

Traditional Spiking Neural Networks (SNNs) typically model neuron dynamics using first-order Ordinary Differential Equations (ODEs), which assume a Markovian property where the current state depends only on the immediate past. This limits their ability to capture complex temporal correlations often present in graph data sequences.

Our f-SNN framework integrates Fractional Differential Equations (FDEs) into Spiking Graph Neural Networks (SGNNs). By replacing standard integer-order neurons with fractional-order neurons, our models introduce a power-law memory kernel. This allows the network to retain information from distant past time steps, leading to:

  • Higher Node Classification Accuracy: Consistently outperforming baselines like SpikingJelly and snnTorch across multiple datasets.
  • Enhanced Robustness: Superior stability against feature masking and structural perturbations (edge dropping).
  • Energy Efficiency: Comparable or lower energy consumption due to optimized firing rates, despite the added expressivity of fractional dynamics.

Datasets

We evaluated our framework on six mainstream graph learning benchmarks, covering citation networks, co-purchase graphs, and large-scale academic graphs:

Dataset Description Task # Nodes # Classes
Cora Citation network of machine learning papers. Node Classification 2,708 7
Citeseer Citation network of scientific publications. Node Classification 3,327 6
Pubmed Citation network of biomedical articles. Node Classification 19,717 3
Photo Amazon co-purchase graph (cameras). Node Classification 7,650 8
Computers Amazon co-purchase graph (computers). Node Classification 13,752 10
ogbn-arxiv Large-scale citation network of arXiv papers. Node Classification 169,343 40

Experimental Setup

Architecture & Baselines

To ensure fair comparison, we integrated our f-LIF neurons into two established Spiking Graph Neural Network architectures:

  • SGCN (Spiking Graph Convolutional Network)
  • DRSGNN (Dynamic Reactive Spiking Graph Neural Network)

Baselines: We compared our results against the original implementations of these models using standard LIF neurons from popular frameworks including SpikingJelly and snnTorch.

Key Hyperparameters

  • Encoding: Poisson spike encoding.
  • Time Steps (\(T\)): 100 steps for all graph tasks.
  • Batch Size: 32.
  • Data Split: Training/Validation/Test ratio of 0.7/0.2/0.1.
  • Fractional Order (\(\alpha\)): Tuned per dataset. Setting \(\alpha=1\) recovers the standard integer-order model.
  • Positional Encoding (for DRSGNN): Dimension 32, using Laplacian Eigenvectors (LSPE) or Random Walk (RWPE).

Key Results

Our fractional adaptations of SGCN and DRSGNN achieved superior accuracy across all datasets. For example, on the Cora dataset, SGCN (f-SNN) achieved 88.08% accuracy, significantly outperforming the SpikingJelly baseline (81.81%).

Method Cora Citeseer Pubmed Photo Computers ogbn-arxiv
SGCN (SpikingJelly) 81.81 71.83 86.79 87.72 70.86 50.26
SGCN (snnTorch) 83.12 71.68 59.82 83.34 74.88 21.55
SGCN (f-SNN) 88.08 73.80 87.17 92.49 89.12 51.10
DRSGNN (SpikingJelly) 83.30 72.72 87.13 88.31 76.55 50.13
DRSGNN (snnTorch) 80.98 68.00 59.56 82.28 76.78 28.46
DRSGNN (f-SNN) 88.51 75.11 87.29 91.93 88.77 53.13

Robustness Experiments

The f-SNN framework demonstrated exceptional robustness under feature masking and edge dropping scenarios, maintaining high accuracy even when significant portions of graph information were corrupted. Detailed robustness analysis can be found in our ICLR 2026 Paper.

Reproducing the Results

The experiments are organized in the examples/ICLR_Release/Graph directory of our repository.

Directory Structure

examples/ICLR_Release/Graph/
├── README.md
├── models.py             # SGCN and DRSGNN definitions with f-LIF support
├── run.py                # Main entry point for training and evaluation
├── utils.py              # Data loading and preprocessing utilities
└── scripts/
    ├── run_sgcn_cora.sh
    ├── run_drsgnn_citeseer.sh
    └── ...

Running the Experiments

You can reproduce the results using the provided shell scripts or by running the main python script directly.

Using Shell Scripts: 

# Run SGCN on Cora
bash scripts/run_sgcn_cora.sh

# Run DRSGNN on Citeseer
bash scripts/run_drsgnn_citeseer.sh

Using Command Line: 

python run.py \
  --backbone SGCN \
  --dataset Cora \
  --time_steps 100 \
  --alpha 0.3 \
  --epochs 100

For detailed dataset download links and specific configuration parameters, please refer to the README.md inside the examples/ICLR_Release/Graph folder.

Tip

For more theoretical details on why fractional calculus improves graph learning, please refer to our ICLR 2026 Paper or other tutorials in this documentation.