  The spin characteristics of black holes offer valuable insights into the
evolutionary pathways of their progenitor stars, crucial for understanding the
broader population properties of black holes. Traditional Hierarchical Bayesian
inference techniques employed to discern these properties often entail
substantial time investments, and consensus regarding the spin distribution of
Binary Black Hole (BBH) systems remains elusive. In this study, leveraging
observations from GWTC-3, we adopt a machine learning approach to infer the
spin distribution of black holes within BBH systems. Specifically, we develop a
Deep Neural Network (DNN) and train it using data generated from a Beta
distribution. Our training strategy, involving the segregation of data into 10
bins, not only expedites model training but also enhances the DNN's versatility
and adaptability to accommodate the burgeoning volume of gravitational wave
observations. Utilizing Monte Carlo-bootstrap (MC-bootstrap) to generate
observation-simulated samples, we derive spin distribution parameters:
$\alpha=1.3^{+0.25}_{-0.18},\beta=1.70^{+0.24}_{-0.29}$ for the larger BH
sample and $\alpha=1.37^{+0.31}_{-0.20},\beta=1.63^{+0.30}_{-0.20}$ for the
smaller BH sample. Within our constraints, the distributions of component spin
magnitudes suggest the likelihood of both black holes in the BBH merger
possessing non-zero spin.
