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Unlike most convolutional\nneural networks, the joint nonlinearity is chosen to implement a form of local\ngain control, inspired by those used to model biological neurons. Using a\nvariant of stochastic gradient descent, we jointly optimize the entire model\nfor rate-distortion performance over a database of training images, introducing\na continuous proxy for the discontinuous loss function arising from the\nquantizer. Under certain conditions, the relaxed loss function may be\ninterpreted as the log likelihood of a generative model, as implemented by a\nvariational autoencoder. Unlike these models, however, the compression model\nmust operate at any given point along the rate-distortion curve, as specified\nby a trade-off parameter. Across an independent set of test images, we find\nthat the optimized method generally exhibits better rate-distortion performance\nthan the standard JPEG and JPEG 2000 compression methods. 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