  The study of di-Higgs events, both resonant and non-resonant, plays a crucial
role in understanding the fundamental interactions of the Higgs boson. In this
work we consider di-Higgs events decaying into four $b$-quarks and propose to
improve the experimental sensitivity by utilizing a novel machine learning
algorithm known as Symmetry Preserving Attention Network (\textsc{Spa-Net}) --
a neural network structure whose architecture is designed to incorporate the
inherent symmetries in particle reconstruction tasks. We demonstrate that the
\textsc{Spa-Net} can enhance the experimental reach over baseline methods such
as the cut-based and the Deep Neural Networks (DNN)-based analyses. At the
Large Hadron Collider, with a 14-TeV centre-of-mass energy and an integrated
luminosity of 300 fb$^{-1}$, the \textsc{Spa-Net} allows us to establish 95\%
C.L. upper limits in resonant production cross-sections that are 10\% to 45\%
stronger than baseline methods. For non-resonant di-Higgs production,
\textsc{Spa-Net} enables us to constrain the self-coupling that is 9\% more
stringent than the baseline method.
