In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: The paper addresses the problem of learning a regression model parameterized by a fixedrank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixed-rank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks.

A: Regression on fixed-rank positive semidefinite matrices: a Riemannian approach
****
Q: In neural machine translation (NMT), generation of a target word depends on both source and target contexts. We find that source contexts have a direct impact on the adequacy of a translation while target contexts on the fluency. Intuitively, generation of a content word should rely more on the source context and generation of a functional word should rely more on the target context. Due to lack of effective control on the influence from source and target contexts, conventional NMT tends to yield fluent but inadequate translations. To address this problem, we propose to use context gates to dynamically control the ratios at which source and target contexts contribute to the generation of target words. In this way, we can enhance the adequacy of NMT while keeping the fluency unchanged. Experiments show that our approach significantly improves upon a standard attention-based NMT system by +2.3 BLEU points.

A: Context Gates for Neural Machine Translation
****
Q: Conditional independence and Markov prop­ erties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As mul­ tidimensional possibilistic models have been studied for several years, the demand for analogous tools in possibility theory seems to be quite natural. This paper is intended to be a promotion of de Cooman's measure­ theoretic approach to possibility theory, as this approach allows us to find analogies to many important results obtained in prob­ abilistic framework. First we recall semi­ graphoid properties of conditional possibilis­ tic independence, parameterized by a contin­ uous t-norm, and find sufficient conditions for a class of Archimedean t-norms to have the graphoid property. Then we introduce Markov properties and factorization of possi­ bility distributions (again parameterized by a continuous t-norm) and find the relation­ ships between them. These results are ac­ companied by a number of counterexamples, which show that the assumptions of specific theorems are substantial.

A:
Conditional Independence and Markov Properties in Possibility Theory
****