Though traditional algorithms could be embedded into neural architectures
with the proposed principle of \cite{xiao2017hungarian}, the variables that
only occur in the condition of branch could not be updated as a special case.
To tackle this issue, we multiply the conditioned branches with Dirac symbol
(i.e. $\mathbf{1}_{x>0}$), then approximate Dirac symbol with the continuous
functions (e.g. $1 - e^{-\alpha|x|}$). In this way, the gradients of
condition-specific variables could be worked out in the back-propagation
process, approximately, making a fully functioned neural graph. Within our
novel principle, we propose the neural decision tree \textbf{(NDT)}, which
takes simplified neural networks as decision function in each branch and
employs complex neural networks to generate the output in each leaf. Extensive
experiments verify our theoretical analysis and demonstrate the effectiveness
of our model.

通过提出的神经图结构来解决在分支条件中只出现变量无法特别更新的问题，并利用 Dirac 符号和连续函数来近似计算条件特定变量的梯度，最终提出了一种使用简化神经网络作为分支条件函数，复杂神经网络作为叶子输出的神经决策树模型，并经过大量实验证实该模型的有效性。