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

TL;DR

This paper introduces Sparsely Activated Networks (SANs) that utilize sparse activation functions to improve data decomposition and compression, demonstrating effective reconstruction and interpretability across multiple datasets.

Contribution

The paper proposes a new metric $\

Findings

SANs achieve low description length and high interpretability.

Sparse activation functions improve data reconstruction quality.

Models selected by the $\

Abstract

Recent literature on unsupervised learning focused on designing structural priors with the aim of learning meaningful features, but without considering the description length of the representations. In this thesis, 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 metric $\varphi$. 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.