Training generative adversarial networks (GANs) often suffers from cyclic behaviors of iterates. Based on a simple intuition that the direction of centripetal acceleration of an object moving in uniform circular motion is toward the center of the circle, we present the Simultaneous Centripetal Acceleration (SCA) method and the Alternating Centripetal Acceleration (ACA) method to alleviate the cyclic behaviors. Under suitable conditions, gradient descent methods with either SCA or ACA are shown to be linearly convergent for bilinear games. Numerical experiments are conducted by applying ACA to existing gradientbased algorithms in a GAN setup scenario, which demonstrate the superiority of ACA.
The common task in matrix completion (MC) and robust principle component analysis (RPCA) is to recover a low-rank matrix from a given data matrix. These problems gained great attention from various areas in applied sciences recently, especially after the publication of the pioneering works of Candès et al.. One fundamental result in MC and RPCA is that nuclear norm based convex optimizations lead to the exact low-rank matrix recovery under suitable conditions. In this paper, we extend this result by showing that strongly convex optimizations can guarantee the exact low-rank matrix recovery as well. The result in this paper not only provides sufficient conditions under which the strongly convex models lead to the exact low-rank matrix recovery, but also guides us on how to choose suitable parameters in practical algorithms.
In this paper, aiming at solving the bidiagonal SVD problem, a classical divide-andconquer (DC) algorithm is modified, which needs to compute the SVD of broken arrow matrices by solving secular equations. The main cost of DC lies in the updating of singular vectors, which involves two matrix-matrix multiplications. We find that the singular vector matrices of a broken arrow matrix are Cauchy-like matrices and have an off-diagonal low-rank property, so they can be approximated efficiently by hierarchically semiseparable (HSS) matrices. Hereby, by using the HSS techniques, the complexity of computing singular vectors can be reduced significantly. An accelerated DC algorithm is proposed, denoted by ADC. Furthermore, we use a structured low-rank approximation method to construct these HSS approximations. Numerous experiments show ADC is both fast and numerically stable. When dealing with large matrices with few deflations, ADC can be 3x faster than DC in the optimized LAPACK libraries such as Intel MKL without any degradation in accuracy. These techniques can be used to similarly solve the symmetric tridiagonal eigenvalue problem.
Spoken language understanding (SLU), which is a core component of the task-oriented dialogue system, has made substantial progress in the research of single-turn dialogue. However, the performance in multi-turn dialogue is still not satisfactory in the sense that the existing multi-turn SLU methods have low portability and compatibility for other single-turn SLU models. Further, existing multi-turn SLU methods do not exploit the historical predicted results when predicting the current utterance, which wastes helpful information. To gap those shortcomings, in this paper, we propose a novel Resultbased Portable Framework for SLU (RPFSLU). RPFSLU allows most existing single-turn SLU models to obtain the contextual information from multi-turn dialogues and takes full advantage of predicted results in the dialogue history during the current prediction. Experimental results on the public dataset KVRET have shown that all SLU models in baselines acquire enhancement by RPFSLU on multi-turn SLU tasks.
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