Automatic Translating Between Ancient Chinese and Contemporary Chinese with Limited Aligned Corpora

The Chinese language has evolved a lot during the long-term development. Therefore, native speakers now have trouble in reading sentences written in ancient Chinese. In this paper, we propose to build an end-to-end neural model to automatically translate between ancient and contemporary Chinese. However, the existing ancient-contemporary Chinese parallel corpora are not aligned at the sentence level and sentence-aligned corpora are limited, which makes it difficult to train the model. To build the sentence level parallel training data for the model, we propose an unsupervised algorithm that constructs sentence-aligned ancient-contemporary pairs by using the fact that the aligned sentence pair shares many of the tokens. Based on the aligned corpus, we propose an end-to-end neural model with copying mechanism and local attention to translate between ancient and contemporary Chinese. Experiments show that the proposed unsupervised algorithm achieves 99.4% F1 score for sentence alignment, and the translation model achieves 26.95 BLEU from ancient to contemporary, and 36.34 BLEU from contemporary to ancient.Comment: Acceptted by NLPCC 201

Conversions between barycentric, RKFUN, and Newton representations of rational interpolants

We derive explicit formulas for converting between rational interpolants in barycentric, rational Krylov (RKFUN), and Newton form. We show applications of these conversions when working with rational approximants produced by the AAA algorithm [Y. Nakatsukasa, O. S\`ete, L. N. Trefethen, arXiv preprint 1612.00337, 2016] within the Rational Krylov Toolbox and for the solution of nonlinear eigenvalue problems

Point defects in 2-D liquid crystals with singular potential: profiles and stability

We study radial symmetric point defects with degree $\frac {k}{2}$ in 2D disk or $\mathbb{R}^2$ in $Q$-tensor framework with singular bulk energy, which is defined by Bingham closure. First, we obtain the existence of solutions for the profiles of radial symmetric point defects with degree $\frac k2$ in 2D disk or $\mathbb{R}^2$. Then we prove that the solution is stable for $|k|=1$ and unstable for $|k|>1$. Some identities are derived and used throughout the proof of existence and stability/instability

The Inefficiencies of Legislative Centralization: Evidence from Provincial Tax Rate-Setting

Legislative power in China is centralized to an unusual degree. This arrangement is both positively and normatively significant, but has received little attention in prior scholarship. We devise a novel method for analyzing the consequence of centralization by examining provincial rate setting for the vehicle and vessel tax (VVT). Because all provinces have assigned VVT revenue and VVT administration to sub-provincial governments, provincial rate-setting represents centralized, not decentralized, decision-making. Using spatio-econometric analyses, we find that provincial tax rate choices fail to reflect local economic and demographic conditions and display traces of tax mimicking. Both support the hypothesis that provincial officials lack information and incentives to make effective policy

Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks

Recent works have cast some light on the mystery of why deep nets fit any data and generalize despite being very overparametrized. This paper analyzes training and generalization for a simple 2-layer ReLU net with random initialization, and provides the following improvements over recent works: (i) Using a tighter characterization of training speed than recent papers, an explanation for why training a neural net with random labels leads to slower training, as originally observed in [Zhang et al. ICLR'17]. (ii) Generalization bound independent of network size, using a data-dependent complexity measure. Our measure distinguishes clearly between random labels and true labels on MNIST and CIFAR, as shown by experiments. Moreover, recent papers require sample complexity to increase (slowly) with the size, while our sample complexity is completely independent of the network size. (iii) Learnability of a broad class of smooth functions by 2-layer ReLU nets trained via gradient descent. The key idea is to track dynamics of training and generalization via properties of a related kernel.Comment: In ICML 201