Several regularization methods have recently been introduced which force the latent activations of an autoencoder or deep neural network to conform to either a Gaussian or hyperspherical distribution, or to minimize the implicit rank of the distribution in latent space. In the present work, we introduce a simple and novel regularizing loss function which simulates a pairwise repulsive force between items and an attractive force of each item toward the origin. We show that minimizing this loss function in isolation achieves a hyperspherical distribution, and demonstrate its effectiveness as a regularizer for an image auto-encoder. Moreover, a reduction in the regularization parameter leads to a modest increase in the eccentricity of the distribution in latent space. This enhances image generation, and allows the eigenvectors of the covariance matrix to be extracted as deep principal components, which can be used for data analysis, image generation, visualization and downstream classification.

In label-noise learning, the transition matrix plays a key role in building statistically consistent classifiers. Existing consistent estimators for the transition matrix have been developed by exploiting anchor points. However, the anchor-point assumption is not always satisfied in real scenarios. In this paper, we propose an end-to-end framework for solving label-noise learning without anchor points, in which we simultaneously optimize two objectives: the cross entropy loss between the noisy label and the predicted probability by the neural network, and the volume of the simplex formed by the columns of the transition matrix. Our proposed framework can identify the transition matrix if the clean class-posterior probabilities are sufficiently scattered. This is by far the mildest assumption under which the transition matrix is provably identifiable and the learned classifier is statistically consistent. Experimental results on benchmark datasets demonstrate the effectiveness and robustness of the proposed method.