  The precise measurement of the top-Higgs coupling is crucial in particle
physics, offering insights into potential new physics Beyond the Standard Model
(BSM) carrying CP Violation (CPV) effects. In this paper, we explore the CP
properties of a Higgs boson coupling with a top quark pair, focusing on events
where the Higgs state decays into a pair of $b$-quarks and the top-antitop
system decays leptonically. The novelty of our analysis resides in the
exploitation of two conditional Deep Learning (DL) networks: a Multi-Layer
Perceptron (MLP) and a Graph Convolution Network (GCN). These models are
trained for selected CPV phase values and then used to interpolate all possible
values ranging from $0 \text{ to } \pi/2$. This enables a comprehensive
assessment of sensitivity across all CP phase values, thereby streamlining the
process as the models are trained only once. Notably, the conditional GCN
exhibits superior performance over the conditional MLP, owing to the nature of
graph-based Neural Network (NN) structures. Our Machine Learning (ML) informed
findings indicate that assessment of the CP properties of the Higgs coupling to
the $t\bar{t}$ pair can be within reach of the HL-LHC, quantitatively
surpassing the sensitivity of more traditional approaches.
