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We introduce a novel approach for building language models based on a systematic, recursive exploration of skip n-gram models which are interpolated using modified Kneser-Ney smoothing. Our approach generalizes language models as it contains the classical interpolation with lower order models as a special case. In this paper we motivate, formalize and present our approach. In an extensive empirical experiment over English text corpora we demonstrate that our generalized language models lead to a substantial reduction of perplexity between 3.1% and 12.7% in comparison to traditional language models using modified Kneser-Ney smoothing. Furthermore, we investigate the behaviour over three other languages and a domain specific corpus where we observed consistent improvements. Finally, we also show that the strength of our approach lies in its ability to cope in particular with sparse training data. Using a very small training data set of only 736 KB text we yield improvements of even 25.7% reduction of perplexity.

Making a payment in a privacy-aware payment channel network is achieved by trying several payment paths until one succeeds. With a large network, such as the Lightning Network, a completion of a single payment can take up to several minutes. We introduce a network imbalance measure and formulate the optimization problem of improving the balance of the network as a sequence of rebalancing operations of the funds within the channels along circular paths within the network. As the funds and balances of channels are not globally known, we introduce a greedy heuristic with which every node despite the uncertainty can improve its own local balance. In an empirical simulation on a recent snapshot of the Lightning Network we demonstrate that the imbalance distribution of the network has a Kolmogorov-Smirnoff distance of 0.74 in comparison to the imbalance distribution after the heuristic is applied. We further show that the success rate of a single unit payment increases from 11.2% on the imbalanced network to 98.3% in the balanced network. Similarly, the median possible payment size across all pairs of participants increases from 0 to 0.5 mBTC for initial routing attempts on the cheapest possible path. We provide an empirical evidence that routing fees should be dropped for proactive rebalancing operations. Executing 4 different strategies for selecting rebalancing cycles lead to similar results indicating that a collaborative approach within the friend of a friend network might be preferable from a practical point of view.

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