Sparsely Activated Networks
This work addresses the need for better evaluation metrics in unsupervised learning, though it is incremental as it builds on existing activation functions and network structures.
The authors tackled the problem of evaluating unsupervised learning models by introducing the φ metric, which balances reconstruction accuracy with representation compression, and demonstrated that Sparsely Activated Networks (SANs) using sparse activation functions selected by φ achieve small description lengths and interpretable kernels across multiple datasets.
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.