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.

Example Input: We describe a technique to minimize weighted tree automata (WTA), a powerful formalisms that subsumes probabilistic context-free grammars (PCFGs) and latent-variable PCFGs. Our method relies on a singular value decomposition of the underlying Hankel matrix defined by the WTA. Our main theoretical result is an efficient algorithm for computing the SVD of an infinite Hankel matrix implicitly represented as a WTA. We provide an analysis of the approximation error induced by the minimization, and we evaluate our method on real-world data originating in newswire treebank. We show that the model achieves lower perplexity than previous methods for PCFG minimization, and also is much more stable due to the absence of local optima.
Example Output: Weighted Tree Automata Approximation by Singular Value Truncation

Example Input: This manuscript develops the theory of agglomerative clustering with Bregman divergences. Geometric smoothing techniques are developed to deal with degenerate clusters. To allow for cluster models based on exponential families with overcomplete representations, Bregman divergences are developed for nondifferentiable convex functions.
Example Output: Agglomerative Bregman Clustering

Example Input: In Distributional Semantic Models (DSMs), Vector Cosine is widely used to estimate similarity between word vectors, although this measure was noticed to suffer from several shortcomings. The recent literature has proposed other methods which attempt to mitigate such biases. In this paper, we intend to investigate APSyn, a measure that computes the extent of the intersection between the most associated contexts of two target words, weighting it by context relevance. We evaluated this metric in a similarity estimation task on several popular test sets, and our results show that APSyn is in fact highly competitive, even with respect to the results reported in the literature for word embeddings. On top of it, APSyn addresses some of the weaknesses of Vector Cosine, performing well also on genuine similarity estimation.
Example Output:
Testing APSyn against Vector Cosine on Similarity Estimation