instruction:
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.
question:
Sentences are important semantic units of natural language. A generic, distributional representation of sentences that can capture the latent semantics is beneficial to multiple downstream applications. We observe a simple geometry of sentences – the word representations of a given sentence (on average 10.23 words in all SemEval datasets with a standard deviation 4.84) roughly lie in a low-rank subspace (roughly, rank 4). Motivated by this observation, we represent a sentence by the low-rank subspace spanned by its word vectors. Such an unsupervised representation is empirically validated via semantic textual similarity tasks on 19 different datasets, where it outperforms the sophisticated neural network models, including skip-thought vectors, by 15% on average.
answer:
Representing Sentences as Low-Rank Subspaces


question:
A two–step Christoffel function based solution is proposed to distribution regression problem. On the first step, to model distribution of observations inside a bag, build Christoffel function for each bag of observations. Then, on the second step, build outcome variable Christoffel function, but use the bag’s Christoffel function value at given point as the weight for the bag’s outcome. The approach allows the result to be obtained in closed form and then to be evaluated numerically. While most of existing approaches minimize some kind an error between outcome and prediction, the proposed approach is conceptually different, because it uses Christoffel function for knowledge representation, what is conceptually equivalent working with probabilities only. To receive possible outcomes and their probabilities Gauss quadrature for second–step measure can be built, then the nodes give possible outcomes and normalized weights – outcome probabilities. A library providing numerically stable polynomial basis for these calculations is available, what make the proposed approach practical.
answer:
Multiple–Instance Learning: Christoffel Function Approach to Distribution Regression Problem


question:
Texts are complex structures emerging from an intricate system consisting of syntactical constraints and semantical relationships. While the complete modeling of such structures is impractical owing to the high level of complexity inherent to linguistic constructions, under a limited domain, certain tasks can still be performed. Recently, statistical techniques aiming at analysis of texts, referred to as text analytics, have departed from the use of simple word count statistics towards a new paradigm. Text mining now hinges on a more sophisticate set of methods, including the representation of texts as complex networks. In this perspective, networks represent a set of textual elements, typically words; and links are established via adjacency relationships. While current word-adjacency (co-occurrence) methods successfully grasp syntactical and stylistic features of written texts, they are unable to represent important aspects of textual data, such as its topical structure. As a consequence, the mesoscopic structure of texts is often overlooked by current methodologies. In order to grasp mesoscopic characteristics of semantical content in written texts, we devised a network approach which is able to analyze documents in a multi-scale, mesoscopic fashion. In the proposed model, a limited amount of adjacent paragraphs are represented as nodes, which are connected whenever they share a minimum semantical content. To illustrate the capabilities of our model, we present, as a use case, a qualitative analysis of “Alice’s Adventures in Wonderland”, a novel by Lewis Carroll. We show that the mesoscopic structure of documents modeled as networks reveals many semantic traits of texts, a feature that could be explored in a myriad of semantic-based applications.
answer:

Mesoscopic representation of texts as complex networks