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:
This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of) the inputs. The networks allow for efficient inference via optimization over some inputs to the network given others, and can be applied to settings including structured prediction, data imputation, reinforcement learning, and others. In this paper we lay the basic groundwork for these models, proposing methods for inference, optimization and learning, and analyze their representational power. We show that many existing neural network architectures can be made input-convex with only minor modification, and develop specialized optimization algorithms tailored to this setting. Finally, we highlight the performance of the methods on multi-label prediction, image completion, and reinforcement learning problems, where we show improvement over the existing state of the art in many cases.

Ex Output:
Input Convex Neural Networks


Ex Input:
As food becomes an important part of modern life, recipes shared on the web are a great indicator of civilizations and culinary attitudes in different countries. Similarly, ingredients, flavors, and nutrition information are strong signals of the taste preferences of individuals from various parts of the world. Yet, we do not have a thorough understanding of these palate varieties. In this paper, we present a large-scale study of recipes published on the Web and their content, aiming to understand cuisines and culinary habits around the world. Using a database of more than 157K recipes from over 200 different cuisines, we analyze ingredients, flavors, and nutritional values which distinguish dishes from different regions, and use this knowledge to assess the predictability of recipes from different cuisines. We then use country health statistics to understand the relation between these factors and health indicators of different nations, such as obesity, diabetes, migration, and health expenditure. Our results confirm the strong effects of geographical and cultural similarities on recipes, health indicators, and culinary preferences between countries around the world.

Ex Output:
Kissing Cuisines: Exploring Worldwide Culinary Habits on the Web


Ex Input:
Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or singular vectors) induced by the sparsity or noise. In this work, we propose a general method to solve the localization problem by learning a regularization matrix from the localized eigenvectors. Using matrix perturbation analysis, we demonstrate that the learned regularizations suppress down the eigenvalues associated with localized eigenvectors and enable us to recover the informative eigenvectors representing the global structure. We show applications of our method in several inference problems: community detection in networks, clustering from pairwise similarities, rank estimation and matrix completion problems. Using extensive experiments, we illustrate that our method solves the localization problem and works down to the theoretical detectability limits in different kinds of synthetic data. This is in contrast with existing spectral algorithms based on data matrix, non-backtracking matrix, Laplacians and those with rank-one regularizations, which perform poorly in the sparse case with noise.

Ex Output:

Robust Spectral Detection of Global Structures in the Data by Learning a Regularization