Field-Level Baryon Acoustic Oscillation Reconstruction of the DESI DR1 Luminous Red Galaxies with Linear Field Transformer (LiFT)

We present the first application of neural field-level baryon-acoustic oscillation (BAO) reconstruction to real spectroscopic survey data. We develop Linear Field Transformer (LiFT), a 3D vision transformer that takes as input the observed galaxy field, its standard reconstruction, and a set of context channels encoding local line of sight, survey coverage, and redshift, and learns to correct standard reconstruction toward the linear density field. We construct a forward-modeling pipeline to produce mock lightcones similar to the DESI Data Release 1 (DR1) luminous red galaxy (LRG) sample, and train LiFT on these. We validate LiFT on held-out simulations, as well as on additional mocks which differ in gravity solver, halo finder, HOD, cosmology, and fiber-assignment history, as well as on mocks analyzed with a distorted distance-redshift relation; ultimately, we find unbiased dilation parameters with consistently tighter constraints than standard reconstruction. Applied to the DESI DR1 LRGs, LiFT improves errors on α iso by 13%, 24%, and 30% and on α AP by 5%, 22%, and 30% relative to the DESI DR1 standard reconstruction analysis in the LRG1, LRG2, and LRG3 bins respectively; meanwhile, our DR1 central values remain consistent with DR1 and DR2. This equates to a factor of 1.2, 1.7 and 2.0 increase in Figure of Merit (or effective survey volume) if one were to only use standard reconstruction. Ultimately, these results establish LiFT as a validated, survey-ready tool for current and upcoming galaxy surveys.