HSG-12M

Classify each Hamiltonian spectral graph into one of 1,401 characteristic- polynomial classes. This is graph-level classification scored by top-1 accuracy.

Poly2Graph converts complex energy-band spectra of one-dimensional non-Hermitian crystal Hamiltonians into 11,601,681 static spatial multigraphs. Parallel curved trajectories between the same endpoints are retained as distinct edges.

The provided featurization includes multi-edge geometry such as curve length, endpoint distance, midpoint, average spectral potential, and density of states. The raw release also supports custom featurization.

The official stratified random split is 80/10/10 and preserves class proportions. Results are averaged over three seeds; the paper reports top-1 and top-10 accuracy.

Collapsing parallel edges destroys information by design. Coefficients within a class can generate deformed but related spectra, so a random split tests recognition within the generated class distribution rather than transfer to unseen polynomials.