Compressive Hyperspherical Energy Minimization

Recent work on minimum hyperspherical energy (MHE) has demonstrated its potential in regularizing neural networks and improving their generalization. MHE was inspired by the Thomson problem in physics, where the distribution of multiple propelling electrons on a unit sphere can be modeled via minimizing some potential energy. Despite the practical effectiveness, MHE suffers from local minima as their number increases dramatically in high dimensions, limiting MHE from unleashing its full potential in improving network generalization. To address this issue, we propose compressive minimum hyperspherical energy (CoMHE) as an alternative regularization for neural networks. Specifically, CoMHE utilizes a projection mapping to reduce the dimensionality of neurons and minimizes their hyperspherical energy. According to different constructions for the projection matrix, we propose two major variants: random projection CoMHE and angle-preserving CoMHE. Furthermore, we provide theoretical insights to justify its effectiveness. We show that CoMHE consistently outperforms MHE by a significant margin in comprehensive experiments, and demonstrate its diverse applications to a variety of tasks such as image recognition and point cloud recognition.