Neural (Tangent Kernel) Collapse

Published: 21 Sept 2023, Last Modified: 07 Jan 2024NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: Neural Collapse, Neural Tangent Kernel, NTK alignment, Local Elasticity, Gradient Flow
TL;DR: The Neural Tangent Kernel alignment drives Neural Collapse.
Abstract: This work bridges two important concepts: the Neural Tangent Kernel (NTK), which captures the evolution of deep neural networks (DNNs) during training, and the Neural Collapse (NC) phenomenon, which refers to the emergence of symmetry and structure in the last-layer features of well-trained classification DNNs. We adopt the natural assumption that the empirical NTK develops a block structure aligned with the class labels, i.e., samples within the same class have stronger correlations than samples from different classes. Under this assumption, we derive the dynamics of DNNs trained with mean squared (MSE) loss and break them into interpretable phases. Moreover, we identify an invariant that captures the essence of the dynamics, and use it to prove the emergence of NC in DNNs with block-structured NTK. We provide large-scale numerical experiments on three common DNN architectures and three benchmark datasets to support our theory.
Supplementary Material: zip
Submission Number: 2136