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:
In this paper we study lifted inference for the Weighted First-Order Model Counting problem (WFOMC), which counts the assignments that satisfy a given sentence in firstorder logic (FOL); it has applications in Statistical Relational Learning (SRL) and Probabilistic Databases (PDB). We present several results. First, we describe a lifted inference algorithm that generalizes prior approaches in SRL and PDB. Second, we provide a novel dichotomy result for a non-trivial fragment of FO CNF sentences, showing that for each sentence the WFOMC problem is either in PTIME or #P-hard in the size of the input domain; we prove that, in the first case our algorithm solves the WFOMC problem in PTIME, and in the second case it fails. Third, we present several properties of the algorithm. Finally, we discuss limitations of lifted inference for symmetric probabilistic databases (where the weights of ground literals depend only on the relation name, and not on the constants of the domain), and prove the impossibility of a dichotomy result for the complexity of probabilistic inference for the entire language FOL.

Ex Output:
Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting

Ex Input:
We introduce a parametric form of pooling, based on a Gaussian, which can be optimized alongside the features in a single global objective function. By contrast, existing pooling schemes are based on heuristics (e.g. local maximum) and have no clear link to the cost function of the model. Furthermore, the variables of the Gaussian explicitly store location information, distinct from the appearance captured by the features, thus providing a what/where decomposition of the input signal. Although the differentiable pooling scheme can be incorporated in a wide range of hierarchical models, we demonstrate it in the context of a Deconvolutional Network model (Zeiler et al. [22]). We also explore a number of secondary issues within this model and present detailed experiments on MNIST digits.

Ex Output:
Differentiable Pooling for Hierarchical Feature Learning

Ex Input:
Two popular approaches for distributed training of SVMs on big data are parameter averaging and ADMM. Parameter averaging is efficient but suffers from loss of accuracy with increase in number of partitions, while ADMM in the feature space is accurate but suffers from slow convergence. In this paper, we report a hybrid approach called weighted parameter averaging (WPA), which optimizes the regularized hinge loss with respect to weights on parameters. The problem is shown to be same as solving SVM in a projected space. We also demonstrate an O( 1 N ) stability bound on final hypothesis given by WPA, using novel proof techniques. Experimental results on a variety of toy and real world datasets show that our approach is significantly more accurate than parameter averaging for high number of partitions. It is also seen the proposed method enjoys much faster convergence compared to ADMM in features space.

Ex Output:
Distributed Weighted Parameter Averaging for SVM Training on Big Data