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Register a new userRegularizing Neural Networks via Minimizing Hyperspherical Energy
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Weiyang Liu
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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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, hyperspherical energy minimization has demonstrated its potential in regularizing neural networks and improving their generalization power. In this paper, we first study the important role that hyperspherical energy plays in neural network training by analyzing its training dynamics. Then we show that naively minimizing hyperspherical energy suffers from some difficulties due to highly non-linear and non-convex optimization as the space dimensionality becomes higher, therefore limiting the potential to further improve the generalization. To address these problems, we propose the compressive minimum hyperspherical energy (CoMHE) as a more effective regularization for neural networks. Specifically, CoMHE utilizes projection mappings to reduce the dimensionality of neurons and minimizes their hyperspherical energy. According to different designs for the projection mapping, we propose several distinct yet well-performing variants and provide some theoretical guarantees to justify their effectiveness. Our experiments show that CoMHE consistently outperforms existing regularization methods, and can be easily applied to different neural networks.
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Effective regularization techniques are highly desired in deep learning for alleviating overfitting and improving generalization. This work proposes a new regularization scheme, based on the understanding that the flat local minima of the empirical risk cause the model to generalize better. This scheme is referred to as adversarial model perturbation (AMP), where instead of directly minimizing the empirical risk, an alternative AMP loss is minimized via SGD. Specifically, the AMP loss is obtained from the empirical risk by applying the worst norm-bounded perturbation on each point in the parameter space. Comparing with most existing regularization schemes, AMP has strong theoretical justifications, in that minimizing the AMP loss can be shown theoretically to favour flat local minima of the empirical risk. Extensive experiments on various modern deep architectures establish AMP as a new state of the art among regularization schemes. Our code is available at https://github.com/hiyouga/AMP-Regularizer.
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We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various practical strategies. Specifically, this perspective (i) provides a common umbrella for many existing regularization principles, including spectral norm and gradient penalties, or adversarial training, (ii) leads to new effective regularization penalties, and (iii) suggests hybrid strategies combining lower and upper bounds to get better approximations of the RKHS norm. We experimentally show this approach to be effective when learning on small datasets, or to obtain adversarially robust models.
Data augmentation is widely known as a simple yet surprisingly effective technique for regularizing deep networks. Conventional data augmentation schemes, e.g., flipping, translation or rotation, are low-level, data-independent and class-agnostic operations, leading to limited diversity for augmented samples. To this end, we propose a novel semantic data augmentation algorithm to complement traditional approaches. The proposed method is inspired by the intriguing property that deep networks are effective in learning linearized features, i.e., certain directions in the deep feature space correspond to meaningful semantic transformations, e.g., changing the background or view angle of an object. Based on this observation, translating training samples along many such directions in the feature space can effectively augment the dataset for more diversity. To implement this idea, we first introduce a sampling based method to obtain semantically meaningful directions efficiently. Then, an upper bound of the expected cross-entropy (CE) loss on the augmented training set is derived by assuming the number of augmented samples goes to infinity, yielding a highly efficient algorithm. In fact, we show that the proposed implicit semantic data augmentation (ISDA) algorithm amounts to minimizing a novel robust CE loss, which adds minimal extra computational cost to a normal training procedure. In addition to supervised learning, ISDA can be applied to semi-supervised learning tasks under the consistency regularization framework, where ISDA amounts to minimizing the upper bound of the expected KL-divergence between the augmented features and the original features. Although being simple, ISDA consistently improves the generalization performance of popular deep models (e.g., ResNets and DenseNets) on a variety of datasets, i.e., CIFAR-10, CIFAR-100, SVHN, ImageNet, and Cityscapes.
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