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 representation. We show that this picture is incomplete. In regression problems with clustered data, we demonstrate that multilayer perceptrons (MLPs) develop specialized neurons: individual neurons become strongly aligned with specific features relevant to a particular region of the input space. A substantial fraction of these neurons exhibit monosemanticity: they activate predominantly on inputs from the corresponding cluster. Thus, rather than learning a single global low-dimensional representation, MLPs learn a collection of local low-dimensional representations. Furthermore, we show that this ability to specialize gives MLPs a provable data-efficiency advantage over feature-learning methods based on a global low-dimensional representation.

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