Atomistic models route geometric information by task and symmetry type

Steier introduces Compositional Probe Decomposition: linearly project out compositional (atom-count/formula-level) signal via QR/ridge residualization, then measure remaining geometric information accessible to a linear ridge probe [steier-2026-information-routing-in-atomistic-foundation-models] Validated on a structural-isomer benchmark (94.6% on geometric residuals versus chance for compositional projections), CPD across ten atomistic models finds a 6.6x linear-accessibility gradient driven mainly by task alignment [steier-2026-information-routing-in-atomistic-foundation-models] Task alignment matters: PaiNN's geometric R-squared drops 0.53->0.31 when retrained on energy instead of HOMO-LUMO gap; MACE drops 0.44->0.08 [steier-2026-information-routing-in-atomistic-foundation-models] Inside MACE, information routes by symmetry type across distinct linear subspaces (L=1 channels favor dipole, L=0 channels favor HOMO-LUMO gap), a pattern absent in ViSNet [steier-2026-information-routing-in-atomistic-foundation-models] Nonlinear probes give misleadingly inflated results on residualized representations, motivating exclusively linear probes here [steier-2026-information-routing-in-atomistic-foundation-models]