  Neural networks are a powerful class of nonlinear functions that can be
trained end-to-end on various applications. While the over-parametrization
nature in many neural networks renders the ability to fit complex functions and
the strong representation power to handle challenging tasks, it also leads to
highly correlated neurons that can hurt the generalization ability and incur
unnecessary computation cost. As a result, how to regularize the network to
avoid undesired representation redundancy becomes an important issue. To this
end, we draw inspiration from a well-known problem in physics -- Thomson
problem, where one seeks to find a state that distributes N electrons on a unit
sphere as evenly as possible with minimum potential energy. In light of this
intuition, we reduce the redundancy regularization problem to generic energy
minimization, and propose a minimum hyperspherical energy (MHE) objective as
generic regularization for neural networks. We also propose a few novel
variants of MHE, and provide some insights from a theoretical point of view.
Finally, we apply neural networks with MHE regularization to several
challenging tasks. Extensive experiments demonstrate the effectiveness of our
intuition, by showing the superior performance with MHE regularization.
