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Topological-materials ML: match the symmetry, exactly

Classifying topological phases of the Haldane model: the physically matched C3 prior wins everywhere data is scarce — and the too-large C6 group, broken by the physics, underperforms it everywhere. The law cuts both ways.

What was measured

The Haldane model's sublattice mass breaks the honeycomb's 6-fold symmetry down to 3-fold — so a C3-equivariant classifier is the physically matched prior, while C6 is a built-in mismatch control. Classifying Chern number from band structure on a hex k-mesh, at matched parameters (~15k), with the dataset verified exactly C3-symmetric and all architectures verified exactly equivariant (error 0).

Headline numbers

C3 − plain: +0.06 / +0.11 / +0.15 / +0.08 at 5/10/20/40 samples per class; converged by 80 (the sample-efficiency signature)
C3 beats C6 at every size (+0.03–0.06): too much symmetry is a wrong prior, measurably
6 seeds; labels from the analytic Haldane phase diagram

Method & discipline

The point of the design is the two-sided test: the matched group must win and the over-large group must lose, on the same data, at the same budget. Both halves landed. Crystallographic point-group equivariance for topological-phase classification is a comparatively quiet corner of materials ML — most work uses continuous SO(3)/E(3) machinery.

Honest limits: synthetic (model-generated) band structures with analytic labels; modest network scale; the advantage is confined to the scarce-data regime, as the law predicts.

Part of a ~30-experiment program run under one hard rule: no result is recorded before its run completes. Methods and logs: github.com/dwatces.