Learning a Tree of Neural Nets

Much of the success of deep learning is due to choosing good neural net architectures and being able to train them effectively. A type of architecture that has been long sought is one that combines decision trees and neural nets. This is straightforward if the tree makes soft decisions (i.e., an input instance follows all paths in the tree with different probabilities), because the model is differentiable. However, the optimization is much harder if the tree makes hard decisions, but this produces an architecture that is much faster at inference, since an instance follows a single path in the tree. We show that it is possible to train such architectures, with guaranteed monotonic decrease of the loss, and demonstrate it by learning trees with linear decision nodes and deep nets at the leaves. The resulting architecture improves state-of-the-art deep nets, by achieving comparable or lower classification error but with fewer parameters and faster inference time. In particular, we show that, rather than improving a ResNet by making it deeper, it is better to construct a tree of small ResNets. The resulting tree-net hybrid is also more interpretable.