We present HEALFormer, a transformer-based neural network architecture for weak gravitational lensing mass mapping that reconstructs convergence maps from incomplete and noisy shear observations on the celestial sphere. The model operates directly on the Hierarchical Equal Area isoLatitude Pixelization and employs learnable mask tokens to handle arbitrary survey geometries without requiring preprocessing. Through a progressive training strategy, HEALFormer efficiently processes high-resolution maps up to $N_{\mathrm{side}}=1024$ and demonstrates excellent performance across diverse survey footprints including KiDS, DES, DECaLS, and Planck. The model generalizes robustly to cosmological parameters beyond its training set, producing nearly unbiased reconstructions with superior noise suppression compared to traditional Kaiser-Squires and Wiener filter methods. Remarkably, HEALFormer exceeds the theoretical phase recovery limits of linear reconstruction methods at small scales, achieving a fundamental breakthrough in weak lensing analysis. The combination of computational efficiency, reconstruction accuracy, and adaptability to varying survey configurations makes HEALFormer well-suited for current and next-generation cosmological surveys. Code is available at GitHub.

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• Dark matter
• Gravitational lenses
• Sky surveys
• Large scale structure of the Universe