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.

To reduce the redundancy in representation, this paper extends some recent work on diversity regularization in neural networks by proposing the so-called hyperspherical potential energy defined on the Euclidean distance or the angular distance, which, when minimized, helps to increase the diversity of the input weights of different neurons and hence reduce the redundancy. The regularized loss function contains two regularization terms corresponding to the hidden units and the output units, respectively.

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.

In recent years, deep learning has surpassed traditional approaches to the problem of singing voice separation. The Wave-U-Net is a recent deep network architecture that operates directly on the time domain. The standard Wave-U-Net is trained with data augmentation and early stopping to prevent overfitting. Minimum hyperspherical energy (MHE) regularization has recently proven to increase generalization in image classification problems by encouraging a diversified filter configuration. In this work, we apply MHE regularization to the 1D filters of the Wave-U-Net. We evaluated this approach for separating the vocal part from mixed music audio recordings on the MUSDB18 dataset. We found that adding MHE regularization to the loss function consistently improves singing voice separation, as measured in the Signal to Distortion Ratio on test recordings, leading to the current best time-domain system for singing voice extraction.