The ALPHA-g experiment at CERN aims to perform the first-ever direct measurement of the effect of gravity on antimatter, determining its weight to within 1% precision. This measurement requires an accurate prediction of the vertical position of annihilations within the detector. In this work, we present a novel approach to annihilation position reconstruction using an ensemble of models based on the PointNet deep learning architecture. The newly developed model, PointNet Ensemble for Annihilation Reconstruction (PEAR) outperforms the standard approach to annihilation position reconstruction, providing more than twice the resolution while maintaining a similarly low bias. This work may also offer insights for similar efforts applying deep learning to experiments that require high resolution and low bias.