  Track reconstruction algorithms are critical for polarization measurements.
In addition to traditional moment-based track reconstruction approaches,
convolutional neural networks (CNN) are a promising alternative. However,
hexagonal grid track images in gas pixel detectors (GPD) for better anisotropy
do not match the classical rectangle-based CNN, and converting the track images
from hexagonal to square results in loss of information. We developed a new
hexagonal CNN algorithm for track reconstruction and polarization estimation in
X-ray polarimeters, which was used to extract emission angles and absorption
points from photoelectron track images and predict the uncertainty of the
predicted emission angles. The simulated data of PolarLight test were used to
train and test the hexagonal CNN models. For individual energies, the hexagonal
CNN algorithm produced 15-30% improvements in modulation factor compared to
moment analysis method for 100% polarized data, and its performance was
comparable to rectangle-based CNN algorithm newly developed by IXPE team, but
at a much less computational cost.
