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Register a new userDeep Hyperspherical Learning
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Added by
Weiyang Liu
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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Convolution as inner product has been the founding basis of convolutional neural networks (CNNs) and the key to end-to-end visual representation learning. Benefiting from deeper architectures, recent CNNs have demonstrated increasingly strong representation abilities. Despite such improvement, the increased depth and larger parameter space have also led to challenges in properly training a network. In light of such challenges, we propose hyperspherical convolution (SphereConv), a novel learning framework that gives angular representations on hyperspheres. We introduce SphereNet, deep hyperspherical convolution networks that are distinct from conventional inner product based convolutional networks. In particular, SphereNet adopts SphereConv as its basic convolution operator and is supervised by generalized angular softmax loss - a natural loss formulation under SphereConv. We show that SphereNet can effectively encode discriminative representation and alleviate training difficulty, leading to easier optimization, faster convergence and comparable (even better) classification accuracy over convolutional counterparts. We also provide some theoretical insights for the advantages of learning on hyperspheres. In addition, we introduce the learnable SphereConv, i.e., a natural improvement over prefixed SphereConv, and SphereNorm, i.e., hyperspherical learning as a normalization method. Experiments have verified our conclusions.
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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.
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.
Valuable training data is often owned by independent organizations and located in multiple data centers. Most deep learning approaches require to centralize the multi-datacenter data for performance purpose. In practice, however, it is often infeasible to transfer all data to a centralized data center due to not only bandwidth limitation but also the constraints of privacy regulations. Model averaging is a conventional choice for data parallelized training, but its ineffectiveness is claimed by previous studies as deep neural networks are often non-convex. In this paper, we argue that model averaging can be effective in the decentralized environment by using two strategies, namely, the cyclical learning rate and the increased number of epochs for local model training. With the two strategies, we show that model averaging can provide competitive performance in the decentralized mode compared to the data-centralized one. In a practical environment with multiple data centers, we conduct extensive experiments using state-of-the-art deep network architectures on different types of data. Results demonstrate the effectiveness and robustness of the proposed method.
Learning curves model a classifiers test error as a function of the number of training samples. Prior works show that learning curves can be used to select model parameters and extrapolate performance. We investigate how to use learning curves to evaluate design choices, such as pretraining, architecture, and data augmentation. We propose a method to robustly estimate learning curves, abstract their parameters into error and data-reliance, and evaluate the effectiveness of different parameterizations. Our experiments exemplify use of learning curves for analysis and yield several interesting observations.
In the low-data regime, it is difficult to train good supervised models from scratch. Instead practitioners turn to pre-trained models, leveraging transfer learning. Ensembling is an empirically and theoretically appealing way to construct powerful predictive models, but the predominant approach of training multiple deep networks with different random initialisations collides with the need for transfer via pre-trained weights. In this work, we study different ways of creating ensembles from pre-trained models. We show that the nature of pre-training itself is a performant source of diversity, and propose a practical algorithm that efficiently identifies a subset of pre-trained models for any downstream dataset. The approach is simple: Use nearest-neighbour accuracy to rank pre-trained models, fine-tune the best ones with a small hyperparameter sweep, and greedily construct an ensemble to minimise validation cross-entropy. When evaluated together with strong baselines on 19 different downstream tasks (the Visual Task Adaptation Benchmark), this achieves state-of-the-art performance at a much lower inference budget, even when selecting from over 2,000 pre-trained models. We also assess our ensembles on ImageNet variants and show improved robustness to distribution shift.
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