spectral-graph-diffusion-n30

Spectral Graph Diffusion (n=30)

Conditional discrete-diffusion denoiser for graphs targeting the algebraic connectivity (Fiedler value, λ₂) of the graph Laplacian. Trained on 100K stratified synthetic graphs at n=30 from six random-graph families.

• Architecture: graph transformer, ~25M parameters, three-FiLM conditioning (timestep, global features, λ* target).
• Training: best loss 0.3601 nats at step 52,000 (vs marginal baseline 0.5669; 36% below). 7 hours on a single GCP T4 ($4.50 USD).
• Sampling: discrete absorbing diffusion with classifier-free guidance.

Code · Paper (arXiv: TBD) · Companion search-based project

Intended use

Research and educational use. Generates undirected graphs at n=30 conditioned on a target algebraic connectivity λ₂*. Not intended for production decisions or applications relying on graph robustness in real-world deployments.

Headline empirical findings

• Sample format validity: 100% (architecturally enforced by upper-triangle sampling, mirror-to-lower, diagonal forced to zero; not learned).
• Regime-flip critical value: λ*_c ≈ 9.5. Classifier-free guidance with w > 0 helps tracking at λ* ∈ [10, 14], collapses samples at λ* ≤ 9, and over-amplifies toward K_30 at λ* ≥ 16.
• Bidirectional Pareto sweet-spot: w=2 at λ*=10. Both fidelity and diversity improve with guidance — contrary to the standard CFG framing.
• Family attribution at high targets: 32/32 samples classified as ER-like at λ*=20, w=4.

See the paper for full empirical tables, sweep details, and mechanism analysis.

Limitations

• Single graph size (n=30); does not generalize to other sizes.
• Single trained model, single seed, single hub layout — no variance estimates.
• The CFG-collapse regime at λ* < λ*_c is a measured limitation of the conditioning-corpus interaction, not a model bug.
• Hamming diversity is density-sensitive; reported with this caveat.

Quick start (Python, JAX)

from huggingface_hub import snapshot_download

# Download checkpoint
checkpoint_dir = snapshot_download(
    repo_id="cpennetier/spectral-graph-diffusion-n30",
    repo_type="model",
)

# Use with the spectral-graph-diffusion repo's sampler:
# https://github.com/cpennetier/spectral-graph-diffusion
# python -m model.sample --ckpt {checkpoint_dir} --target_lambda 12 --w 2.0

Citation

@misc{pennetier2026diffusion,
  author = {Pennetier, Christophe},
  title = {Regime-Dependent Guidance in Spectral Graph Diffusion},
  year = {2026},
  url = {https://arxiv.org/abs/XXXX.XXXXX},
  note = {Code: https://github.com/cpennetier/spectral-graph-diffusion}
}

License

MIT. See the code repository for full license text.