Efficient Learning of Sparse Representations with an Energy-Based Model

We describe a novel unsupervised method for learning sparse, overcomplete features. Themodel uses a linear encoder, and a linear decoder preceded by a sparsifying non-linearitythat turns a code vector into a quasi-binary sparse code vector. Given an input, the optimal code minimizes the distance between the output of the decoder and the input patch while being as similar as possible to the encoder output.Learning proceeds in a two-phase EMlike fashion: (1) compute the minimum-energy code vector, (2) adjust the parameters of the encoder and decoder soas to decrease the energy. The model produces "stroke detectors" when trained on handwritten numerals, and Gabor-like filters when trained on natural image patches. Inference and learning are very fast, requiring no preprocessing, and no expensive sampling. Using the proposed unsupervised method to initialize the first layer of a convolutional network, we achieved an error rate slightly lower than the best reported result on the MNIST dataset. Finally, an extension of the method is described to learn topographical filter maps.