We introduce a principled approach for unsupervised structure learning of deep neural networks. We propose a new interpretation for depth and inter-layer connectivity where conditional independencies in the input distribution are encoded hierarchically in the network structure. Thus, the depth of the network is determined inherently. The proposed method casts the problem of neural network structure learning as a problem of Bayesian network structure learning. Then, instead of directly learning the discriminative structure, it learns a generative graph, constructs its stochastic inverse, and then constructs a discriminative graph. We prove that conditional-dependency relations among the latent variables in the generative graph are preserved in the class-conditional discriminative graph. We demonstrate on image classification benchmarks that the deepest layers (convolutional and dense) of common networks can be replaced by significantly smaller learned structures, while maintaining classification accuracy---state-of-the-art on tested benchmarks. Our structure learning algorithm requires a small computational cost and runs efficiently on a standard desktop CPU.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Understanding the structural relationships among different variables provides critical insights in manyreal-worldapplications, suchasmedicine,economics andeducation [42,62]. Thus,learning graphs from observed data, known as structure learning, has recently made remarkable progress [10,61,63,64]. Formanyapplications, variables inthedata can begathered into semantically meaningful groups, where useful insights are at group level. For example, in finance, one may be interested in how a financial situation influences different industries (i.e.