Riemannian Optimization for Skip-Gram Negative Sampling

Skip-Gram Negative Sampling (SGNS) word embedding model, well known by its implementation in "word2vec" software, is usually optimized by stochastic gradient descent. However, the optimization of SGNS objective can be viewed as a problem of searching for a good matrix with the low-rank constraint. The most standard way to solve this type of problems is to apply Riemannian optimization framework to optimize the SGNS objective over the manifold of required low-rank matrices. In this paper, we propose an algorithm that optimizes SGNS objective using Riemannian optimization and demonstrates its superiority over popular competitors, such as the original method to train SGNS and SVD over SPPMI matrix.Comment: 9 pages, 4 figures, ACL 201

Russian energy policies revisited: assessing the impact of the crisis in Ukraine on Russian energy policies and specifying the implications for German and EU energy policies

The analysis of Russian energy policies after the political crisis in and around Ukraine offers important insights with respect to the economic and geopolitical repercussions. The structural changes made in the Russian energy sector have been significant and include both internal and external dimensions. The Russian energy sector is under stress and has to adapt to low oil and gas prices, economic sanctions and increasing competition on international energy markets. Against the background of this turbulence on the energy markets, Russian energy companies are pursuing various strategies: a shift to Asia and asset swaps with Chinese and Indian companies, stronger integration within the Eurasian Union and changing strategies on the European energy markets. The structural changes have been reinforced by recent geopolitical developments, which have led to the deterioration of EU-Russia energy relations and the securitisation of energy questions. However, despite immediate intentions to diversify away from one another, the EU and Russia will remain dependent on each other in the gas and oil sectors at least for the next 10 years. The current study provides insights into current changes in the Russian gas, oil and electricity sectors, highlights potential implications for the European energy market, considers the current status of EU-Russia energy relations and presents some recommendations for further bilateral cooperation and energy dialogue." (author's abstract