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: Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges to an unpleasant distance function on the underlying space whose properties are detrimental to machine learning. We also study the behavior of the shortest path distance in weighted kNN graphs.

Output: Shortest path distance in random k-nearest neighbor graphs


Input: Consider Input: Our study identifies sentences in Wikipedia articles that are either identical or highly similar by applying techniques for near-duplicate detection of web pages. This is accomplished with a MapReduce implementation of minhash to identify clusters of sentences with high Jaccard similarity. We show that these clusters can be categorized into six different types, two of which are particularly interesting: identical sentences quantify the extent to which content in Wikipedia is copied and pasted, and near-duplicate sentences that state contradictory facts point to quality issues in Wikipedia.

Output: Identifying Duplicate and Contradictory Information in Wikipedia


Input: Consider Input: During the last years, Convolutional Neural Networks (CNNs) have achieved state-of-the-art performance in image classification. Their architectures have largely drawn inspiration by models of the primate visual system. However, while recent research results of neuroscience prove the existence of non-linear operations in the response of complex visual cells, little effort has been devoted to extend the convolution technique to non-linear forms. Typical convolutional layers are linear systems, hence their expressiveness is limited. To overcome this, various non-linearities have been used as activation functions inside CNNs, while also many pooling strategies have been applied. We address the issue of developing a convolution method in the context of a computational model of the visual cortex, exploring quadratic forms through the Volterra kernels. Such forms, constituting a more rich function space, are used as approximations of the response profile of visual cells. Our proposed second-order convolution is tested on CIFAR-10 and CIFAR-100. We show that a network which combines linear and non-linear filters in its convolutional layers, can outperform networks that use standard linear filters with the same architecture, yielding results competitive with the state-of-the-art on these datasets.


Output: Non-linear Convolution Filters for CNN-based Learning