Horizontal magnetic fields dominate the weak-field quiet Sun in Sunrise III observations. Evidence from traditional and transformer-based inversions

The relative prevalence of horizontal and vertical magnetic fields in the quiet-Sun remains debated, owing to the weak linear polarisation signals that make the inferred magnetic inclination distributions sensitive to observational quality and inversion methodology. We investigate the magnetic topology of the quiet-Sun in Sunrise iii observations by independently applying transformer-based and traditional inversion techniques to the same spectropolarimetric dataset. We analysed observations obtained with the Sunrise Chromospheric Infrared spectroPolarimeter (SCIP). Transformer-based inversions (SINN), trained exclusively on synthetic Stokes profiles generated from a large radiative magnetohydrodynamic simulation, were compared with independent inversions performed using the DeSIRe code. We separated the selected pixels into weak- and strong-field populations according to their circular-polarisation amplitudes. Linear polarisation exceeding 4σ is detected in 34.6% of the field of view, enabling the magnetic topology to be constrained over a substantially larger detected population than in typical short-integration Hinode observations. Both inversion methods recover a quiet-Sun magnetic topology in which the weak fields are strongly dominated by the horizontal component, whereas strong fields exhibit a substantially more balanced topology. At łogτ=-1, the median horizontal and unsigned line-of-sight field components in the weak-field population are 63 and 7 G with DeSIRe, and 60 and 6.5 G with SINN, respectively, corresponding to a horizontal-to-line-of-sight ratio of approximately nine for both methods. The agreement between the two fundamentally different optimisation methodologies indicates that the weak-field quiet-Sun in this dataset is characterised by a substantially stronger horizontal than vertical magnetic field component. These results demonstrate that transformer-based inversions can be successfully transferred from synthetic training data to real spectropolarimetric observations, while providing inference orders of magnitude faster than traditional inversion techniques.