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Model-based methods and deep neural networks have both been tremendouslysuccessful paradigms in machine learning. In model-based methods, problemdomain knowledge can be built into the constraints of the model, typically atthe expense of difficulties during inference. In contrast, deterministic deepneural networks are constructed in such a way that inference isstraightforward, but their architectures are generic and it is unclear how toincorporate knowledge. This work aims to obtain the advantages of bothapproaches. To do so, we start with a model-based approach and an associatedinference algorithm, and \emph{unfold} the inference iterations as layers in adeep network. Rather than optimizing the original model, we \emph{untie} themodel parameters across layers, in order to create a more powerful network. Theresulting architecture can be trained discriminatively to perform accurateinference within a fixed network size. We show how this framework allows us tointerpret conventional networks as mean-field inference in Markov randomfields, and to obtain new architectures by instead using belief propagation asthe inference algorithm. We then show its application to a non-negative matrixfactorization model that incorporates the problem-domain knowledge that soundsources are additive. Deep unfolding of this model yields a new kind ofnon-negative deep neural network, that can be trained using a multiplicativebackpropagation-style update algorithm. We present speech enhancementexperiments showing that our approach is competitive with conventional neuralnetworks despite using far fewer parameters.

Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures