No Prize for Per-Atom Angular Bandwidth: Bounding Adaptive Angular Bandwidth in Equivariant Neural Force Fields
Hyunmog Kim
Abstract
$SE(3)$-equivariant interatomic potentials use a fixed global angular cutoff ($l_{max}$), prompting a natural hypothesis: allocate high angular resolution only to atoms where local geometry requires it. At matched parameter counts, we confirm the premise: increasing angular resolution from $l_{max}=0$ to 2 reduces force error by 25\% on rMD17 aspirin. However, dynamic per-atom allocation yields no empirical advantage. Using a cross-fitted oracle to isolate training noise, we demonstrate that an optimal per-atom routing policy gains exactly 0.0\% over the best fixed $l_{max}$. We further expose critical measurement traps in the literature, showing that apparent benefits of adaptive routing or varying $l_{max}$ are often artifacts of single-seed variance or gauge-degenerate budget penalties. We conclude that $l_{max}$ should be selected per-system, and marginal compute is better spent on dataset scaling.
Chat is not available.
Successful Page Load