Parameter Symmetries Determine Representational Geometry in Overparameterized Nonlinear Networks

원문 초록

Representations are routinely used across machine learning, psychology, and neuroscience to draw inferences about the computations of biological and artificial systems. Such inferences presume that the geometry of these representations reflects the computation being performed. For artificial neural networks, however, the extent to which the function a network computes constrains this geometry remains unclear. One key obstacle is that these networks admit parameter symmetries: changes in parameterization that preserve function exactly while reshaping representational geometry. Here, we show that a broad class of parameter symmetries acts on representations through just three primitive feature transformations: addition, duplication, and scaling. This feature-level characterization yields a closed-form decomposition of representational geometry into essential and auxiliary components, revealing how representational degeneracy can exist without and grows with overparameterization even when function is held fixed. Finally, we establish conditions under which implementation-level selection rules resolve this degeneracy, yielding identifiable geometries in which features are weighted according to their contributions to the network's function. Together, our results delineate when representational geometry can support inferences about computation, and when it cannot.