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.

Example Input: Consider a setting where selfish agents are to be assigned to coalitions or projects from a set P. Each project k ∈ P is characterized by a valuation function; vk(S) is the value generated by a set S of agents working on project k. We study the following classic problem in this setting: “how should the agents divide the value that they collectively create?”. One traditional approach in cooperative game theory is to study core stability with the implicit assumption that there are infinite copies of one project, and agents can partition themselves into any number of coalitions. In contrast, we consider a model with a finite number of non-identical projects; this makes computing both high-welfare solutions and core payments highly non-trivial. The main contribution of this paper is a black-box mechanism that reduces the problem of computing a near-optimal core stable solution to the purely algorithmic problem of welfare maximization; we apply this to compute an approximately core stable solution that extracts one-fourth of the optimal social welfare for the class of subadditive valuations. We also show much stronger results for several popular sub-classes: anonymous, fractionally subadditive, and submodular valuations, as well as provide new approximation algorithms for welfare maximization with anonymous functions. Finally, we establish a connection between our setting and the well-studied simultaneous auctions with item bidding; we adapt our results to compute approximate pure Nash equilibria for these auctions.
Example Output: Computing Stable Coalitions: Approximation Algorithms for Reward Sharing

Example Input: Auto-encoders are perhaps the best-known non-probabilistic methods for representation learning. They are conceptually simple and easy to train. Recent theoretical work has shed light on their ability to capture manifold structure, and drawn connections to density modeling. This has motivated researchers to seek ways of auto-encoder scoring, which has furthered their use in classification. Gated auto-encoders (GAEs) are an interesting and flexible extension of auto-encoders which can learn transformations among different images or pixel covariances within images. However, they have been much less studied, theoretically or empirically. In this work, we apply a dynamical systems view to GAEs, deriving a scoring function, and drawing connections to Restricted Boltzmann Machines. On a set of deep learning benchmarks, we also demonstrate their effectiveness for single and multi-label classification.
Example Output: Scoring and Classifying with Gated Auto-encoders

Example Input: Many deep Convolutional Neural Networks (CNN) make incorrect predictions on adversarial samples obtained by imperceptible perturbations of clean samples. We hypothesize that this is caused by a failure to suppress unusual signals within network layers. As remedy we propose the use of Symmetric Activation Functions (SAF) in non-linear signal transducer units. These units suppress signals of exceptional magnitude. We prove that SAF networks can perform classification tasks to arbitrary precision in a simplified situation. In practice, rather than use SAFs alone, we add them into CNNs to improve their robustness. The modified CNNs can be easily trained using popular strategies with the moderate training load. Our experiments on MNIST and CIFAR-10 show that the modified CNNs perform similarly to plain ones on clean samples, and are remarkably more robust against adversarial and nonsense samples.
Example Output:
Suppressing the Unusual: towards Robust CNNs using Symmetric Activation Functions