Can end-to-end learning from raw electronic structure explain magnetic anisotropy?

Abstract

Machine-learning models trained directly on electronic spectra can predict spin--orbit-driven properties, yet models with comparable predictive accuracy may learn different electronic dependencies. We examine this problem using magnetic anisotropy in atomic-scale magnets and a validation strategy designed to assess the physical relevance of learned spectral relationships. We compare a bidirectional gated recurrent unit and a one-dimensional convolutional neural network, both trained to predict magnetic anisotropy energy (MAE) from spin- and orbital-resolved scalar-relativistic densities of states (SR-DOS). Despite comparable in-domain (ID) accuracy, the architectures learn only partly overlapping spectral dependencies. Shapley additive explanations identify spectral features shared between the two architectures that can be associated with plausible spin--orbit-coupling pathways consistent with second-order perturbation theory (PT2). Adding PT2-derived MAE contributions to the model inputs has little effect on ID performance but can improve transfer beyond the training domain, with gains differing between architectures. Controlled spectral perturbations further demonstrate that similar attribution patterns do not imply the same functional dependence of the predicted MAE on spectral weight. The contrasting responses provide a functional context for architecture-dependent out-of-domain transfer. End-to-end learning can identify candidate electronic signatures of magnetic anisotropy. Their credible microscopic interpretation, however, rests on convergent evidence from predictive performance, model comparison, physical theory, controlled spectral interventions, and evaluation under distribution shift.

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Cite

BibTeX RIS

BibTeX

@misc{topolnicki2026endtoend,
  title = {{Can end-to-end learning from raw electronic structure explain magnetic anisotropy?}},
  author = {Rafał Topolnicki and Jan Navrátil and Piotr Błoński},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11742},
  eprint = {2610.11742},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11742},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Can end-to-end learning from raw electronic structure explain magnetic anisotropy?
AU  - Rafał Topolnicki
AU  - Jan Navrátil
AU  - Piotr Błoński
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11742
UR  - https://arxiv.org/abs/2610.11742
AB  - Machine-learning models trained directly on electronic spectra can predict spin--orbit-driven properties, yet models with comparable predictive accuracy may learn different electronic dependencies. We examine this problem using magnetic anisotropy in atomic-scale magnets and a validation strategy designed to assess the physical relevance of learned spectral relationships. We compare a bidirectional gated recurrent unit and a one-dimensional convolutional neural network, both trained to predict magnetic anisotropy energy (MAE) from spin- and orbital-resolved scalar-relativistic densities of states (SR-DOS). Despite comparable in-domain (ID) accuracy, the architectures learn only partly overlapping spectral dependencies. Shapley additive explanations identify spectral features shared between the two architectures that can be associated with plausible spin--orbit-coupling pathways consistent with second-order perturbation theory (PT2). Adding PT2-derived MAE contributions to the model inputs has little effect on ID performance but can improve transfer beyond the training domain, with gains differing between architectures. Controlled spectral perturbations further demonstrate that similar attribution patterns do not imply the same functional dependence of the predicted MAE on spectral weight. The contrasting responses provide a functional context for architecture-dependent out-of-domain transfer. End-to-end learning can identify candidate electronic signatures of magnetic anisotropy. Their credible microscopic interpretation, however, rests on convergent evidence from predictive performance, model comparison, physical theory, controlled spectral interventions, and evaluation under distribution shift.
ER  -

Abstract

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