A series of findings in machine learning (ML) and decay theory are captured while exploring the role of deformation and preformation factors in $\alpha$ decay. We provide a novel and practical paradigm for developing physics-driven ML in nuclear physics research by introducing known decay theory and statistical correlation analysis. Furthermore, this analysis verifies the Geiger-Nuttall law, and the relationship between the decay energy and $\alpha$ formation amplitude, also releases a signal that nuclei with hexadecapole deformation are more likely to form $\alpha$ clusters. In particular, we identify two novel phenomena, shape inheritance, in which the deformation properties are partially transmitted from parent to daughter nuclei; and half-life inversion due to shape staggering of adjacent even-even nuclei. This phenomenon occurs frequently in neutron-deficient nuclei near lead isotopes, which is consistent with shape coexistence in experiments. Surprisingly, it reappeared within the predicted half-life of the 119 and 120 isotope chains in the eighth period of the periodic table. The half-life considering the inversion effect is preferable for the study of new nuclides and shape coexistence in experiments.

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• Nuclear structure & decays