Investigate the interaction between dark matter and dark energy

In this paper we investigate the interaction between dark matter and dark energy by considering two different interacting scenarios, i.e. the cases of constant interaction function and variable interaction function. By fitting the current observational data to constrain the interacting models, it is found that the interacting strength is non-vanishing, but weak for the case of constant interaction function, and the interaction is not obvious for the case of variable interaction function. In addition, for seeing the influence from interaction we also investigate the evolutions of interaction function, effective state parameter for dark energy and energy density of dark matter. At last some geometrical quantities in the interacting scenarios are discussed.Comment: 14 pages, 6 figure

Tighter Information-Theoretic Generalization Bounds from Supersamples

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.Comment: Accepted to ICML 202

Two Facets of SDE Under an Information-Theoretic Lens: Generalization of SGD via Training Trajectories and via Terminal States

Stochastic differential equations (SDEs) have been shown recently to well characterize the dynamics of training machine learning models with SGD. This provides two opportunities for better understanding the generalization behaviour of SGD through its SDE approximation. First, under the SDE characterization, SGD may be regarded as the full-batch gradient descent with Gaussian gradient noise. This allows the application of the generalization bounds developed by Xu & Raginsky (2017) to analyzing the generalization behaviour of SGD, resulting in upper bounds in terms of the mutual information between the training set and the training trajectory. Second, under mild assumptions, it is possible to obtain an estimate of the steady-state weight distribution of SDE. Using this estimate, we apply the PAC-Bayes-like information-theoretic bounds developed in both Xu & Raginsky (2017) and Negrea et al. (2019) to obtain generalization upper bounds in terms of the KL divergence between the steady-state weight distribution of SGD with respect to a prior distribution. Among various options, one may choose the prior as the steady-state weight distribution obtained by SGD on the same training set but with one example held out. In this case, the bound can be elegantly expressed using the influence function (Koh & Liang, 2017), which suggests that the generalization of the SGD is related to the stability of SGD. Various insights are presented along the development of these bounds, which are subsequently validated numerically

Information-Theoretic Analysis of Unsupervised Domain Adaptation

This paper uses information-theoretic tools to analyze the generalization error in unsupervised domain adaptation (UDA). We present novel upper bounds for two notions of generalization errors. The first notion measures the gap between the population risk in the target domain and that in the source domain, and the second measures the gap between the population risk in the target domain and the empirical risk in the source domain. While our bounds for the first kind of error are in line with the traditional analysis and give similar insights, our bounds on the second kind of error are algorithm-dependent, which also provide insights into algorithm designs. Specifically, we present two simple techniques for improving generalization in UDA and validate them experimentally

Belief or Leisure: The Evolution of Miaofeng Mountain Temple Festival in the Last Century

The Miaofeng Mountain temple festival is based on Bixia Yuanjun 碧霞元君, known as Laoniangniang 老娘娘, belief in Beijing-Tianjin area. The paper discusses its historical changes and transformation through methods of text analysis and fieldwork. The historical changes of Miaofeng Mountain temple festival are organized as follow: 1) its origin, 2) the space-time distribution, 3) the ritualized behavior and interactive mode of incense organizations (Xianghui, 香会) and unorganized discrete pilgrims when offering incense and sacrifices, and 4) the impact brought by the participation of special forces represented by the Bannermen and the royal family of Qing dynasty. The driving force behind the contemporary transformation of Miaofeng Mountain temple festival is mainly tourism economy, leisure culture and the decline of the sanctity of the goddess beliefs. Changes were found in temples, managers, the time of the temple festival, the roads to the mountain, the composition and mind set of the Xianghui, etc