Diagnosing Spectral Ceilings in Equivariant Neural Force Fields

Researchers introduce a spectral-injection diagnostic method to measure which angular frequencies equivariant neural force fields can preserve, revealing sharp performance cliffs at theoretical capacity boundaries. Testing on aspirin with NequIP backbones shows a dramatic 11.7x performance drop at the predicted boundary, validated across multiple architectures and calibrated through polynomial span theorems.

This research addresses a fundamental challenge in machine learning for molecular systems: understanding the representational capacity limits of equivariant neural networks. The authors develop a diagnostic tool that probes which frequency components a trained force-field model can capture by injecting controlled perturbations and measuring recovery rates. Their findings on aspirin demonstrate a sharp performance cliff precisely at theoretical boundaries predicted by harmonic analysis, suggesting equivariant architectures have hard limits on feature expressivity rather than gradual degradation.

The work builds on growing interest in equivariant neural networks for physics simulations, where symmetry-preserving models like NequIP have shown promise for accurate molecular dynamics. However, understanding when and why these models fail remains poorly characterized. This diagnostic framework provides empirical validation of theoretical capacity bounds, showing that a quadratic spectral prediction network can recover signals up to l=4 angular frequencies but completely fails at l=5, with extensive validation ruling out simple explanations like parameter count.

For the broader AI and scientific computing communities, this represents progress toward interpretable, bounded machine learning systems. Practitioners designing force fields for molecular simulations can now identify architectural limitations explicitly rather than encountering mysterious performance drops. The finite-degree span theorem provides theoretical grounding, while cross-architecture validation suggests these capacity boundaries generalize. This work matters because reliable failure detection enables better system design and more trustworthy computational chemistry applications.

• →Spectral-injection diagnostics reveal sharp 11.7x performance cliffs at predicted equivariant network capacity boundaries
• →Angular frequency l=4 signals recover well while l=5 signals collapse completely on aspirin molecules
• →Finite-degree span theorem mathematically predicts capacity limits as H ≤ dL for degree-d polynomials of L-order features
• →Performance degradation persists across independently trained backbones and multiple evaluation metrics, ruling out random variation
• →Findings enable better understanding of when equivariant neural networks fail for molecular force field tasks