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.

Input: Consider Input: 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.

Output: Multiple–Instance Learning: Christoffel Function Approach to Distribution Regression Problem


Input: Consider Input: 1 Ranks, processes and flat grammar ....................................................................................... 2 2 The Rank-Interpretation Architecture for Multilinear Grammars ......................................... 6 2.1 Outline of the Rank-Interpretation Architecture framework .............................................. 6 2.2 A preliminary note on linearity and hierarchy at the phrasal rank ..................................... 7 2.3 Characterisation of the Rank-Interpretation Architecture .................................................. 9 2.3.1 Background ..................................................................................................................... 9 2.3.2 Formal summary ........................................................................................................... 10 2.3.3 Contrast with traditional views of language architecture .............................................. 11 2.3.4 Search for sui generis properties of ranks ..................................................................... 11 2.4 Procedural perspectives on the rank hierarchy ................................................................. 12 3 The discourse rank .............................................................................................................. 15 3.1 The primacy of discourse patterning ................................................................................ 15 3.2 Intonation of an adjacency pair ........................................................................................ 16 3.3 Chanted ‘call’ intonation .................................................................................................. 18 4 The utterance or text rank ................................................................................................... 20 5 The phrase rank ................................................................................................................... 22 5.1 Characteristics of phrasal structure .................................................................................. 22 5.2 Linear sequences, iteration: regular and subregular grammars ........................................ 23 5.3 A note on long-distance and cross-serial dependencies ................................................... 26 5.4 Prosodic-phonetic interpretation at the phrasal rank ........................................................ 27 6 The word rank ..................................................................................................................... 30 6.1 Flat words ......................................................................................................................... 30 6.2 Flat derivations ................................................................................................................. 30 6.3 Flat compounds ................................................................................................................ 31 6.4 Prosodic-phonetic interpretation at the word rank ........................................................... 31 7 Summary and conclusion .................................................................................................... 33 7.1 From Duality to Multilinear Grammar and Rank Interpretation Architecture ................. 33 7.2 Generalisation to stochastic flat linear models ................................................................. 34 7.3 Future work ...................................................................................................................... 35 8 References ........................................................................................................................... 36

Output: Multilinear Grammar: Ranks and Interpretations


Input: Consider Input: We propose Neural Reasoner , a framework for neural network-based reasoning over natural language sentences. Given a question, Neural Reasoner can infer over multiple supporting facts and find an answer to the question in specific forms. Neural Reasoner has 1) a specific interaction-pooling mechanism, allowing it to examine multiple facts, and 2) a deep architecture, allowing it to model the complicated logical relations in reasoning tasks. Assuming no particular structure exists in the question and facts, Neural Reasoner is able to accommodate different types of reasoning and different forms of language expressions. Despite the model complexity, Neural Reasoner can still be trained effectively in an end-to-end manner. Our empirical studies show that Neural Reasoner can outperform existing neural reasoning systems with remarkable margins on two difficult artificial tasks (Positional Reasoning and Path Finding) proposed in [8]. For example, it improves the accuracy on Path Finding(10K) from 33.4% [6] to over 98%.


Output: Towards Neural Network-based Reasoning