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Previous literature on unsupervised learning focused on designing structural priors with the aim of learning meaningful features. However, this was done without considering the description length of the learned representations, which is a direct and unbiased measure of the model complexity. In this article, first, we introduce the &#x03C6; metric that evaluates unsupervised models based on their reconstruction accuracy and the degree of compression of their internal representations. We then present and define two activation functions [Identity and rectified linear unit (ReLU)] as a base of reference and three sparse activation functions (top-k absolutes, Extrema-Pool indices, and Extrema) as candidate structures that minimize the previously defined &#x03C6;. We last present sparsely activated networks (SANs) that consist of kernels with shared weights that, during encoding, are convolved with the input and then passed through a sparse activation function. During decoding, the same weights are convolved with the sparse activation map, and subsequently, the partial reconstructions from each weight are summed to reconstruct the input. We compare SANs using the five previously defined activation functions on a variety of data sets (Physionet, UCI-epilepsy, MNIST, and FMNIST) and show that models that are selected using &#x03C6; have small description representation length and consist of interpretable kernels.

Sparsely Activated Networks