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.

Normalized graph cut (NGC) has become a popular research topic due to its wide applications in a large variety of areas like machine learning and very large scale integration (VLSI) circuit design. Most of traditional NGC methods are based on pairwise relationships (similarities). However, in real-world applications relationships among the vertices (objects) may be more complex than pairwise, which are typically represented as hyperedges in hypergraphs. Thus, normalized hypergraph cut (NHC) has attracted more and more attention. Existing NHC methods cannot achieve satisfactory performance in real applications. In this paper, we propose a novel relaxation approach, which is called relaxed NHC (RNHC), to solve the NHC problem. Our model is defined as an optimization problem on the Stiefel manifold. To solve this problem, we resort to the Cayley transformation to devise a feasible learning algorithm. Experimental results on a set of large hypergraph benchmarks for clustering and partitioning in VLSI domain show that RNHC can outperform the state-of-the-art methods.
A New Relaxation Approach to Normalized Hypergraph Cut

Understanding a long document requires tracking how entities are introduced and evolve over time. We present a new type of language model, ENTITYNLM, that can explicitly model entities, dynamically update their representations, and contextually generate their mentions. Our model is generative and flexible; it can model an arbitrary number of entities in context while generating each entity mention at an arbitrary length. In addition, it can be used for several different tasks such as language modeling, coreference resolution, and entity prediction. Experimental results with all these tasks demonstrate that our model consistently outperforms strong baselines and prior work.
Dynamic Entity Representations in Neural Language Models

Language learning is thought to be a highly complex process. One of the hurdles in learning a language is to learn the rules of syntax of the language. Rules of syntax are often ordered in that before one rule can applied one must apply another. It has been thought that to learn the order of n rules one must go through all n! permutations. Thus to learn the order of 27 rules would require 27! steps or 1.08889x10 steps. This number is much greater than the number of seconds since the beginning of the universe! In an insightful analysis the linguist Block ([Block 86], pp. 62-63, p.238) showed that with the assumption of transitivity this vast number of learning steps reduces to a mere 377 steps. We present a mathematical analysis of the complexity of Block’s algorithm. The algorithm has a complexity of order n given n rules. In addition, we improve Block’s results exponentially, by introducing an algorithm that has complexity of order less than n log n.

On the complexity of learning a language: An improvement of Block’s algorithm