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Register a new userLearning towards Minimum Hyperspherical Energy
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Added by
Weiyang Liu
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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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.
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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.
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.
Supervised learning requires a large amount of training data, limiting its application where labeled data is scarce. To compensate for data scarcity, one possible method is to utilize auxiliary tasks to provide additional supervision for the main task. Assigning and optimizing the importance weights for different auxiliary tasks remains an crucial and largely understudied research question. In this work, we propose a method to automatically reweight auxiliary tasks in order to reduce the data requirement on the main task. Specifically, we formulate the weighted likelihood function of auxiliary tasks as a surrogate prior for the main task. By adjusting the auxiliary task weights to minimize the divergence between the surrogate prior and the true prior of the main task, we obtain a more accurate prior estimation, achieving the goal of minimizing the required amount of training data for the main task and avoiding a costly grid search. In multiple experimental settings (e.g. semi-supervised learning, multi-label classification), we demonstrate that our algorithm can effectively utilize limited labeled data of the main task with the benefit of auxiliary tasks compared with previous task reweighting methods. We also show that under extreme cases with only a few extra examples (e.g. few-shot domain adaptation), our algorithm results in significant improvement over the baseline.
Convolution is one of the most essential components of architectures used in computer vision. As machine learning moves towards reducing the expert bias and learning it from data, a natural next step seems to be learning convolution-like structures from scratch. This, however, has proven elusive. For example, current state-of-the-art architecture search algorithms use convolution as one of the existing modules rather than learning it from data. In an attempt to understand the inductive bias that gives rise to convolutions, we investigate minimum description length as a guiding principle and show that in some settings, it can indeed be indicative of the performance of architectures. To find architectures with small description length, we propose $beta$-LASSO, a simple variant of LASSO algorithm that, when applied on fully-connected networks for image classification tasks, learns architectures with local connections and achieves state-of-the-art accuracies for training fully-connected nets on CIFAR-10 (85.19%), CIFAR-100 (59.56%) and SVHN (94.07%) bridging the gap between fully-connected and convolutional nets.
Almost all neural architecture search methods are evaluated in terms of performance (i.e. test accuracy) of the model structures that it finds. Should it be the only metric for a good autoML approach? To examine aspects beyond performance, we propose a set of criteria aimed at evaluating the core of autoML problem: the amount of human intervention required to deploy these methods into real world scenarios. Based on our proposed evaluation checklist, we study the effectiveness of a random search strategy for fully automated multimodal neural architecture search. Compared to traditional methods that rely on manually crafted feature extractors, our method selects each modality from a large search space with minimal human supervision. We show that our proposed random search strategy performs close to the state of the art on the AV-MNIST dataset while meeting the desirable characteristics for a fully automated design process.
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