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: In this paper we formulate the framework of recovering a hidden orthonormal basis given access to a<lb>certain “Basis Encoding Function”. We describe the class of Basis Encoding Functions (BEF), such that<lb>their local maxima on the unit sphere are in one-to-one correspondence with the basis elements. This<lb>description relies on a certain “hidden convexity” property of these functions. A number of theoretical<lb>and practical problems of recent interest can be interpreted as recovering a hidden basis from potentially<lb>noisy observations. Specifically, we show how our simple and general framework applies to Independent<lb>Component Analysis (ICA), tensor decompositions, spectral clustering and Gaussian mixture learning.<lb>We describe a new algorithm, “gradient iteration”, for provable recovery of the hidden basis. We<lb>provide a complete theoretical analysis of Gradient Iteration both for the exact case as well as for the<lb>case when the observed function is a perturbation of the “true” underlying BEF. In both cases we show<lb>convergence and complexity bounds polynomial in dimension and other relevant parameters, such as<lb>perturbation size. Our perturbation results can be considered as a very general non-linear version of<lb>the classical Davis-Kahan theorem for eigenvectors of perturbations of symmetric matrices. In addition<lb>we show that in the exact case the algorithm converges superlinearly and give conditions relating the<lb>degree of convergence to properties of the Basis Encoding Function. Our algorithm can be viewed as a<lb>generalization of the classical power iteration method for eigenanalysis of symmetric matrices as well as<lb>a generalization of power iterations for tensors. Moreover, the Gradient Iteration algorithm can be easily<lb>and efficiently implemented in practice.
Example Output: Learning a Hidden Basis Through Imperfect Measurements: An Algorithmic Primitive

Example 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.
Example Output: Aspartame: Solving Constraint Satisfaction Problems with Answer Set Programming

Example Input: Traditional information retrieval systems rely on keywords to index documents and queries. In such systems, documents are retrieved based on the number of shared keywords with the query. This lexicalfocused retrieval leads to inaccurate and incomplete results when different keywords are used to describe the documents and queries. Semantic-focused retrieval approaches attempt to overcome this problem by relying on concepts rather than on keywords to indexing and retrieval. The goal is to retrieve documents that are semantically relevant to a given user query. This paper addresses this issue by proposing a solution at the indexing level. More precisely, we propose a novel approach for semantic indexing based on concepts identified from a linguistic resource. In particular, our approach relies on the joint use of WordNet and WordNetDomains lexical databases for concept identification. Furthermore, we propose a semantic-based concept weighting scheme that relies on a novel definition of concept centrality. The resulting system is evaluated on the TIME test collection. Experimental results show the effectiveness of our proposition over traditional IR approaches.
Example Output:
CONCEPT-BASED INDEXING IN TEXT INFORMATION RETRIEVAL