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.

Ex Input:
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.

Ex Output:
Truthful Mechanisms for Matching and Clustering in an Ordinal World

Ex Input:
Dropout and other feature noising schemes control overfitting by artificially cor-<lb>rupting the training data. For generalized linear models, dropout performs a form<lb>of adaptive regularization. Using this viewpoint, we show that the dropout regular-<lb>izer is first-order equivalent to an L2 regularizer applied after scaling the features<lb>by an estimate of the inverse diagonal Fisher information matrix. We also establish<lb>a connection to AdaGrad, an online learning algorithm, and find that a close rel-<lb>ative of AdaGrad operates by repeatedly solving linear dropout-regularized prob-<lb>lems. By casting dropout as regularization, we develop a natural semi-supervised<lb>algorithm that uses unlabeled data to create a better adaptive regularizer. We ap-<lb>ply this idea to document classification tasks, and show that it consistently boosts<lb>the performance of dropout training, improving on state-of-the-art results on the<lb>IMDB reviews dataset.

Ex Output:
Dropout Training as Adaptive Regularization

Ex Input:
Increasing the capacity of recurrent neural networks (RNN) usually involves augmenting the size of the hidden layer, resulting in a significant increase of computational cost. An alternative is the recurrent neural tensor network (RNTN), which increases capacity by employing distinct hidden layer weights for each vocabulary word. The disadvantage of RNTNs is that memory usage scales linearly with vocabulary size, which can reach millions for word-level language models. In this paper, we introduce restricted recurrent neural tensor networks (r-RNTN) which reserve distinct hidden layer weights for frequent vocabulary words while sharing a single set of weights for infrequent words. Perplexity evaluations using the Penn Treebank corpus show that r-RNTNs improve language model performance over standard RNNs using only a small fraction of the parameters of unrestricted RNTNs.

Ex Output:
Restricted Recurrent Neural Tensor Networks