  We present a determination of fragmentation functions (FFs) for the octet
baryon $\Xi ^-/\bar{\Xi}^+$ from data for single inclusive electron-positron
annihilation. Our parametrization in this QCD analysis is provided in terms of
a Neural Network (NN). We determine fragmentation functions for $\Xi
^-/\bar{\Xi}^+$ at next-to-leading order and for the first time at
next-to-next-to-leading order in perturbative QCD. We discuss the improvement
of higher-order QCD corrections, the quality of fit, and the comparison of our
theoretical results with the fitted datasets. As an application of our new set
of fragmentation functions, named SHKS22, we present predictions for $\Xi ^- /
\bar{\Xi}^+$ baryon production in proton-proton collisions at the LHC
experiments.
