Average gradient outer product as a mechanism for deep neural collapse

Deep Neural Collapse (DNC) refers to the surprisingly rigid structure of the data representations in the final layers of Deep Neural Networks (DNNs). Though the phenomenon has been measured in a wide variety of settings, its emergence is only partially understood. In this work, we provide substantial evidence that DNC formation occurs primarily through deep feature learning with the average gradient outer product (AGOP). This takes a step further compared to efforts that explain neural collapse via feature-agnostic approaches, such as the unconstrained features model. We proceed by providing evidence that the right singular vectors and values of the weights are responsible for the majority of within-class variability collapse in DNNs. As shown in recent work, this singular structure is highly correlated with that of the AGOP. We then establish experimentally and theoretically that AGOP induces neural collapse in a randomly initialized neural network. In particular, we demonstrate that Deep Recursive Feature Machines, a method originally introduced as an abstraction for AGOP feature learning in convolutional neural networks, exhibits DNC.