  Recently proposed budding tree is a decision tree algorithm in which every
node is part internal node and part leaf. This allows representing every
decision tree in a continuous parameter space, and therefore a budding tree can
be jointly trained with backpropagation, like a neural network. Even though
this continuity allows it to be used in hierarchical representation learning,
the learned representations are local: Activation makes a soft selection among
all root-to-leaf paths in a tree. In this work we extend the budding tree and
propose the distributed tree where the children use different and independent
splits and hence multiple paths in a tree can be traversed at the same time.
This ability to combine multiple paths gives the power of a distributed
representation, as in a traditional perceptron layer. We show that distributed
trees perform comparably or better than budding and traditional hard trees on
classification and regression tasks.
