  Due to the over-parameterization nature, neural networks are a powerful tool
for nonlinear function approximation. In order to achieve good generalization
on unseen data, a suitable inductive bias is of great importance for neural
networks. One of the most straightforward ways is to regularize the neural
network with some additional objectives. L2 regularization serves as a standard
regularization for neural networks. Despite its popularity, it essentially
regularizes one dimension of the individual neuron, which is not strong enough
to control the capacity of highly over-parameterized neural networks. Motivated
by this, hyperspherical uniformity is proposed as a novel family of relational
regularizations that impact the interaction among neurons. We consider several
geometrically distinct ways to achieve hyperspherical uniformity. The
effectiveness of hyperspherical uniformity is justified by theoretical insights
and empirical evaluations.
