  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 paper, first
we introduce the $\varphi$ 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,
ReLU) as base of reference and three sparse activation functions (top-k
absolutes, Extrema-Pool indices, Extrema) as candidate structures that minimize
the previously defined $\varphi$. We lastly 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 datasets (Physionet, UCI-epilepsy, MNIST,
FMNIST) and show that models that are selected using $\varphi$ have small
description representation length and consist of interpretable kernels.
