Revenge of Monosemanticity: Specialized Neurons Improve Data Efficiency in MLPs

Understanding how neural networks learn and organize features is central to understanding their behavior. Much existing theory of feature learning has focused on the emergence of a global low-dimensional predictive geometry. We show that this picture is incomplete. In regression problems with clustered data, we demonstrate that multilayer perceptrons (MLPs) naturally develop monosemantic specialized neurons: individual neurons become strongly aligned with a specific predictive feature relevant to a particular region of the input space. Rather than learning a single global low-dimensional representation, MLPs learn a collection of local low-dimensional representations that can collectively span a high-dimensional space. This specialization provably gives MLPs a data-efficiency advantage over feature-learning methods based on a global low-dimensional representation.