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: 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.

Output: Input Convex Neural Networks


Input: Consider Input: This paper describes a new method for reducing the error in a classifier. It uses a weight adjustment update, but includes the very simple rule of either adding or subtracting the adjustment, based on whether the data point is currently larger or smaller than the desired value, and on a pointby-point basis. This gives added flexibility to the convergence procedure, where through a series of transpositions, values far away can continue towards the desired value, whereas values that are originally much closer can oscillate from one side to the other. Tests show that the method can successfully classify some known datasets. It can also work in a batch mode, with reduced training times and can be used as part of a neural network, or classifiers in general. There are also some updates on an earlier wave shape paper.

Output: A New Oscillating-Error Technique for Classifiers


Input: Consider Input: We introduce the lifted Generalized Belief Propagation (GBP) message passing algorithm, for the computation of sum-product queries in Probabilistic Relational Models (e.g. Markov logic network). The algorithm forms a compact region graph and establishes a modified version of message passing, which mimics the GBP behavior in a corresponding ground model. The compact graph is obtained by exploiting a graphical representation of clusters, which reduces cluster symmetry detection to isomorphism tests on small local graphs. The framework is thus capable of handling complex models, while remaining domain-size independent.


Output: Lifted Message Passing for the Generalized Belief Propagation