  Calabi-Yau four-folds may be constructed as hypersurfaces in weighted
projective spaces of complex dimension 5 defined via weight systems of 6
weights. In this work, neural networks were implemented to learn the Calabi-Yau
Hodge numbers from the weight systems, where gradient saliency and symbolic
regression then inspired a truncation of the Landau-Ginzburg model formula for
the Hodge numbers of any dimensional Calabi-Yau constructed in this way. The
approximation always provides a tight lower bound, is shown to be dramatically
quicker to compute (with compute times reduced by up to four orders of
magnitude), and gives remarkably accurate results for systems with large
weights. Additionally, complementary datasets of weight systems satisfying the
necessary but insufficient conditions for transversality were constructed,
including considerations of the interior point, reflexivity, and
intradivisibility properties. Overall producing a classification of this weight
system landscape, further confirmed with machine learning methods. Using the
knowledge of this classification, and the properties of the presented
approximation, a novel dataset of transverse weight systems consisting of 7
weights was generated for a sum of weights $\leq 200$; producing a new database
of Calabi-Yau five-folds, with their respective topological properties
computed. Further to this an equivalent database of candidate Calabi-Yau
six-folds was generated with approximated Hodge numbers.
