  This paper investigates the connections between two state of the art
classifiers: decision forests (DFs, including decision jungles) and
convolutional neural networks (CNNs). Decision forests are computationally
efficient thanks to their conditional computation property (computation is
confined to only a small region of the tree, the nodes along a single branch).
CNNs achieve state of the art accuracy, thanks to their representation learning
capabilities. We present a systematic analysis of how to fuse conditional
computation with representation learning and achieve a continuum of hybrid
models with different ratios of accuracy vs. efficiency. We call this new
family of hybrid models conditional networks. Conditional networks can be
thought of as: i) decision trees augmented with data transformation operators,
or ii) CNNs, with block-diagonal sparse weight matrices, and explicit data
routing functions. Experimental validation is performed on the common task of
image classification on both the CIFAR and Imagenet datasets. Compared to state
of the art CNNs, our hybrid models yield the same accuracy with a fraction of
the compute cost and much smaller number of parameters.
