A Controlled Study of Physics-Informed Auxiliary Supervision and Scalar Triplet Attention in Equivariant Molecular...

Machine-learned molecular force fields require many-body geometry, but obtaining it through Clebsch-Gordan tensor products is computationally expensive. For a strong no-Clebsch-Gordan backbone such as GotenNet, we ask whether the limitation in handling three-body geometry is one of representational capacity or one of training supervision, and separate the two factors with three controlled probes on a single-seed, paper-aligned rMD17 aspirin split. (i) While frame projection of tensor features is comparable to scalar cos-angle triplet cross-attention (SCTA) at pilot scale, algebraically its diagonal scalar collapses to a frame-independent inner product and the remaining channel is parity-odd, making SCTA's cos-angle input the principled O(3) scalar choice. (ii) SCTA matches GotenNet's converged force accuracy within ∼0.4% without independent gain, indicating that three-body representational capacity is not the binding constraint. (iii) A graph-level auxiliary loss on bond-angle and dihedral statistics gives the best force mean absolute error (MAE; 0.1280 vs. 0.1303 kcal/mol/Å) and reduces epochs-to-validation-target by 26-55%. Cross-molecule probes do not extend this finding; a paired salicylic acid comparison shows a directional degradation that, under a configuration-level paired block bootstrap, is significant and opposite in sign to the aspirin effect. Across three random seeds, the auxiliary force-MAE gain is small and seed-dependent but consistently reduces seed-to-seed variance and accelerates convergence, indicating that low-cost three-body supervision can be a more effective lever than added three-body capacity.