X-ray magnetic circular dichroism is a precise tool that has long allowed the separation of spin and orbital magnetic moments. However, the classical approach resembles judging an orchestra by its volume: it relies on sum rules, reducing the entire fine structure of the spectrum to a couple of integrals. Unfortunately, this method is sensitive to background and requires laborious data cleaning.

The breakthrough suggests hearing the spectrum as a symphony of electronic transitions, where machine learning acts as the conductor. It can distinguish the contribution of each 'part'. The task is formulated as an inverse one: recover physical observables from line shapes. A dataset of 3240 XAS and XMCD spectra at the Fe, Co, Ni edges was created for training. They were obtained via numerical simulation, varying crystal field, spin-orbit coupling, and exchange interaction.

A two-layer neural network (256 and 128 neurons) learned to map intensity vectors onto ⟨Sz⟩ and ⟨Lz⟩, computed from wave functions. The model grasped how the crystal field shifts peaks and the exchange field modulates polarized radiation. Accuracy is within 0.02 ℏ. For orbital moment, the result is slightly better: the fine structure of electromagnetic transitions proved more informative. The irony is that the network, trained only on numbers, captures quantum correlations more accurately than analytical approximations.

This method does not reject sum rules but complements them, creating a robust quantum-mechanical measuring tool. It can be extended to light elements, non-collinear structures, paving the way to real-time magnetometry at synchrotrons. Thus, quantum sensing gains an intelligent layer, bringing closer the era of smart spectroscopy.