  The angular momentum of galaxies (galaxy spin) contains rich information
about the initial condition of the Universe, yet it is challenging to
efficiently measure the spin direction for the tremendous amount of galaxies
that are being mapped by the ongoing and forthcoming cosmological surveys. We
present a machine learning based classifier for the Z-wise vs S-wise spirals,
which can help to break the degeneracy in the galaxy spin direction
measurement. The proposed Chirality Equivariant Residual Network (CE-ResNet) is
manifestly equivariant under a reflection of the input image, which guarantees
that there is no inherent asymmetry between the Z-wise and S-wise probability
estimators. We train the model with Sloan Digital Sky Survey (SDSS) images,
with the training labels given by the Galaxy Zoo 1 (GZ1) project. A combination
of data augmentation tricks are used during the training, making the model more
robust to be applied to other surveys. We find a $\sim\!30\%$ increase of both
types of spirals when Dark Energy Spectroscopic Instrument (DESI) images are
used for classification, due to the better imaging quality of DESI. We verify
that the $\sim\!7\sigma$ difference between the numbers of Z-wise and S-wise
spirals is due to human bias, since the discrepancy drops to $<\!1.8\sigma$
with our CE-ResNet classification results. We discuss the potential systematics
that are relevant to the future cosmological applications.
