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We apply machine-learning to the study of dessins d'enfants. Specifically, weinvestigate a class of dessins which reside at the intersection of theinvestigations of modular subgroups, Seiberg-Witten curves and extremalelliptic K3 surfaces. A deep feed-forward neural network with simple structureand standard activation functions without prior knowledge of the underlyingmathematics is established and imposed onto the classification of extensiondegree over the rationals, known to be a difficult problem. The classificationsreached 0.92 accuracy with 0.03 standard error relatively quickly. TheSeiberg-Witten curves for those with rational coefficients are also tabulated.

Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curves