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Motivated by engineering vector-like (Higgs) pairs in the spectrum of 4dF-theory compactifications, we combine machine learning and algebraic geometrytechniques to analyze line bundle cohomologies on families of holomorphiccurves. To quantify jumps of these cohomologies, we first generate 1.8 millionpairs of line bundles and curves embedded in $dP_3$, for which we compute thecohomologies. A white-box machine learning approach trained on this dataprovides intuition for jumps due to curve splittings, which we use to constructadditional vector-like Higgs-pairs in an F-Theory toy model. We also find that,in order to explain quantitatively the full dataset, further tools fromalgebraic geometry, in particular Brill--Noether theory, are required. Usingthese ingredients, we introduce a diagrammatic way to express cohomology jumpsacross the parameter space of each family of matter curves, which reflects astratification of the F-theory complex structure moduli space in terms of thevector-like spectrum. Furthermore, these insights provide an algorithmicallyefficient way to estimate the possible cohomology dimensions across the entireparameter space.

Machine Learning and Algebraic Approaches towards Complete Matter Spectra in 4d F-theory