Spectral Graph Diffusion (n=30)

• 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.

Intended use

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.

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.

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