Diagnosing Spectral Ceilings in Equivariant Neural Force Fields

• URL: http://arxiv.org/abs/2605.08286v1
• Date: Fri, 08 May 2026 08:02:51 GMT
• Title: Diagnosing Spectral Ceilings in Equivariant Neural Force Fields
• Abstract summary: We introduce a spectral-injection diagnostic for measuring which angular frequencies a trained equivariant force-field backbone.<n>A finite-degree span theorem calibrates the diagnostic: for a single marked direction, degree-ds of degree-L spherical-harmonic features span exactly H less than or equal to dL with multiplicity-one saturation at the boundary.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a spectral-injection diagnostic for measuring which angular frequencies a trained equivariant force-field backbone preserves: inject a controlled angular-frequency perturbation into a molecular force field, attach a lightweight Spectral Prediction Network (SPN) to the frozen backbone, and read off which frequencies are recoverable. On aspirin, a quadratic SPN attached to an L = 2 NequIP backbone recovers the boundary signal at l = 4 but collapses at l = 5: a 11.7x cliff at the predicted drL boundary, with p dropping from 0.913 to 0.078. The same boundary-vs-above contrast persists across n = 4 independently trained backbones (raw-gain delta contrast, hierarchical cluster bootstrap) and is corroborated by a denominator-free injected-residual metric (R2_inj(4) = 0.374 versus R2_inj(5) = 0.006). A finite-degree span theorem calibrates the diagnostic: for a single marked direction, degree-d polynomials of degree-L spherical-harmonic features span exactly H less than or equal to dL with multiplicity-one saturation at the boundary (scoped to single-direction degree-bounded probes, not a function-class upper bound on multi-atom MPNNs). A synthetic C5 calibration plus capacity, activation, and cross-architecture controls rule out parameter count alone as the explanation.

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