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.

Ex Input:
Encoding finite linear CSPs as Boolean formulas and solving them by using modern SAT solvers has proven to be highly effective, as exemplified by the award-winning sugar system. We here develop an alternative approach based on ASP. This allows us to use first-order encodings providing us with a high degree of flexibility for easy experimentation with different implementations. The resulting system aspartame re-uses parts of sugar for parsing and normalizing CSPs. The obtained set of facts is then combined with an ASP encoding that can be grounded and solved by off-the-shelf ASP systems. We establish the competitiveness of our approach by empirically contrasting aspartame and sugar.

Ex Output:
Aspartame: Solving Constraint Satisfaction Problems with Answer Set Programming


Ex Input:
We propose new methods to speed up convergence of the Alternating Direction Method of Multipliers (ADMM), a common optimization tool in the context of large scale and distributed learning. The proposed method accelerates the speed of convergence by automatically deciding the constraint penalty needed for parameter consensus in each iteration. In addition, we also propose an extension of the method that adaptively determines the maximum number of iterations to update the penalty. We show that this approach effectively leads to an adaptive, dynamic network topology underlying the distributed optimization. The utility of the new penalty update schemes is demonstrated on both synthetic and real data, including a computer vision application of distributed structure from motion.

Ex Output:
Fast ADMM Algorithm for Distributed Optimization with Adaptive Penalty


Ex Input:
The EM-algorithm is a general procedure to get maximum likelihood estimates if part of the observations on the variables of a network are missing. In this paper a stochastic version of the algorithm is adapted to probabilistic neural networks describing the associative dependency of variables. These networks have a proba­ bility distribution, which is a special case of the distribution generated by proba­ bilistic inference networks. Hence both types of networks can be combined al­ lowing to integrate probabilistic rules as well as unspecified associations in a sound way. The resulting network may have a number of interesting features including cycles of probabilistic rules, hidden 'un­ observable' variables, and uncertain and contradictory evidence.

Ex Output:

Integrating Probabilistic Rules into Neural Networks: A Stochastic EM Learning Algorithm