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.
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Question: 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

Answer: Multilinear Grammar: Ranks and Interpretations


Question: We study truthful mechanisms for matching and related problems in a partial information<lb>setting, where the agents’ true utilities are hidden, and the algorithm only has access to ordi-<lb>nal preference information. Our model is motivated by the fact that in many settings, agents<lb>cannot express the numerical values of their utility for different outcomes, but are still able<lb>to rank the outcomes in their order of preference. Specifically, we study problems where the<lb>ground truth exists in the form of a weighted graph of agent utilities, but the algorithm can<lb>only elicit the agents’ private information in the form of a preference ordering for each agent<lb>induced by the underlying weights. Against this backdrop, we design truthful algorithms to<lb>approximate the true optimum solution with respect to the hidden weights. Our techniques<lb>yield universally truthful algorithms for a number of graph problems: a 1.76-approximation<lb>algorithm for Max-Weight Matching, 2-approximation algorithm for Max k-matching, a 6-<lb>approximation algorithm for Densest k-subgraph, and a 2-approximation algorithm for Max<lb>Traveling Salesman as long as the hidden weights constitute a metric. We also provide im-<lb>proved approximation algorithms for such problems when the agents are not able to lie about<lb>their preferences. Our results are the first non-trivial truthful approximation algorithms for<lb>these problems, and indicate that in many situations, we can design robust algorithms even<lb>when the agents may lie and only provide ordinal information instead of precise utilities.

Answer: Truthful Mechanisms for Matching and Clustering in an Ordinal World


Question: When training deep neural networks, it is typically assumed that the training examples are uniformly difficult to learn. Or, to restate, it is assumed that the training error will be uniformly distributed across the training examples. Based on these assumptions, each training example is used an equal number of times. However, this assumption may not be valid in many cases. “Oddball SGD” (novelty-driven stochastic gradient descent) was recently introduced to drive training probabilistically according to the error distribution – training frequency is proportional to training error magnitude. In this article, using a deep neural network to encode a video, we show that oddball SGD can be used to enforce uniform error across the training set.

Answer:
Uniform Learning in a Deep Neural Network via "Oddball" Stochastic Gradient Descent