  Galaxy morphologies provide valuable insights into their formation processes,
tracing the spatial distribution of ongoing star formation and encoding
signatures of dynamical interactions. While such information has been
extensively investigated at low redshift, it is crucial to develop a robust
system for characterising galaxy morphologies at earlier cosmic epochs. Relying
solely on the nomenclature established for low-redshift galaxies risks
introducing biases that hinder our understanding of this new regime. In this
paper, we employ variational auto-encoders to perform feature extraction on
galaxies at z $>$ 2 using JWST/NIRCam data. Our sample comprises 6869 galaxies
at z $>$ 2, including 255 galaxies z $>$ 5, which have been detected in both
the CANDELS/HST fields and CEERS/JWST, ensuring reliable measurements of
redshift, mass, and star formation rates. To address potential biases, we
eliminate galaxy orientation and background sources prior to encoding the
galaxy features, thereby constructing a physically meaningful feature space. We
identify 11 distinct morphological classes that exhibit clear separation in
various structural parameters, such as CAS-$M_{20}$, S\'ersic indices, specific
star formation rates, and axis ratios. We observe a decline in the presence of
spheroidal-type galaxies with increasing redshift, indicating a dominance of
disk-like galaxies in the early universe. We demonstrate that conventional
visual classification systems are inadequate for high-redshift morphology
classification and advocate the need for a more detailed and refined
classification scheme. Leveraging machine-extracted features, we propose a
solution to this challenge and illustrate how our extracted clusters align with
measured parameters, offering greater physical relevance compared to
traditional methods.
