mlsanityData to 7 Oct 2026

Diagnosing Spectral Ceilings in Equivariant Neural Force Fields

arXiv 2605.08286 ↗First posted 8 May 2026cs.LG cs.AIcited by 0

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 23 of its 40 references that are in the map. First posted on arXiv 8 May 2026.

Builds on

23 of 40 references.

References · 23

  1. 2018On the Spectral Bias of Neural Networkscited by 1,321
  2. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  3. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  4. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
  5. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
  6. 2018Spherical CNNscited by 452
  7. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  8. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  9. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  10. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 254
  11. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
  12. 2022e3nn: Euclidean Neural Networkscited by 171
11 more
  1. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 168
  2. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  3. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  4. 2022The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentialscited by 100
  5. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  6. 2020On the Universality of Rotation Equivariant Point Cloud Networkscited by 80
  7. 2023FAENet: Frame Averaging Equivariant GNN for Materials Modelingcited by 72
  8. 2023TensorNet: Cartesian Tensor Representations for Efficient Learning of Molecular Potentialscited by 53
  9. 2025The Price of Freedom: Exploring Expressivity and Runtime Tradeoffs in Equivariant Tensor Productscited by 14
  10. 2023Completeness of Atomic Structure Representationscited by 7
  11. 2023Wigner kernels: body-ordered equivariant machine learning without a basiscited by 7

Built on by

Not cited yet.