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Recent literature on unsupervised learning focused on designing structuralpriors with the aim of learning meaningful features, but without consideringthe description length of the representations. In this thesis, first weintroduce the $\varphi$ metric that evaluates unsupervised models based ontheir reconstruction accuracy and the degree of compression of their internalrepresentations. We then present and define two activation functions (Identity,ReLU) as base of reference and three sparse activation functions (top-kabsolutes, Extrema-Pool indices, Extrema) as candidate structures that minimizethe previously defined metric $\varphi$. We lastly present Sparsely ActivatedNetworks (SANs) that consist of kernels with shared weights that, duringencoding, are convolved with the input and then passed through a sparseactivation function. During decoding, the same weights are convolved with thesparse activation map and subsequently the partial reconstructions from eachweight are summed to reconstruct the input. We compare SANs using the fivepreviously defined activation functions on a variety of datasets (Physionet,UCI-epilepsy, MNIST, FMNIST) and show that models that are selected using$\varphi$ have small description representation length and consist ofinterpretable kernels.

Sparsely Activated Networks: A new method for decomposing and compressing data