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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper introduces the idea of deep Gaussian mixture models. A GMM can be seen as consisting of a single isotropic unit norm Gaussian, where each of the components of the mixture consists of applying a different linear transformation to that Gaussian. This idea is extended to the case of a multilayer network, where each node in the network corresponds to a linear transformation, and each route through the network corresponds to a sequence of linear transformations. The number of mixture components is then the number of routes through the network.