  Ab-initio calculations of nuclear masses, the binding energy and the $\alpha$
decay half-lives are intractable for heavy nucleus, because of the curse of
dimensionality in many body quantum simulations as proton number($\mathrm{N}$)
and neutron number($\mathrm{Z}$) grow. We take advantage of the powerful
non-linear transformation and feature representation ability of deep neural
network(DNN) to predict the nuclear masses and $\alpha$ decay half-lives. For
nuclear binding energy prediction problem we achieve standard deviation
$\sigma=0.263$ MeV on 10-fold cross validation on 2149 nuclei. Word-vectors
which are high dimensional representation of nuclei from the hidden layers of
mass-regression DNN help us to calculate $\alpha$ decay half-lives. For this
task, we get $\sigma=0.797$ on 100 times 10-fold cross validation on 350 nuclei
on $log_{10}T_{1/2}$ and $\sigma=0.731 $ on 486 nuclei. We also find physical a
priori such as shell structure, magic numbers and augmented inputs inspired by
Finite Range Droplet Model are important for this small data regression task.
