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:
Recent works on word representations mostly rely on predictive models. Distributed word representations (aka word embeddings) are trained to optimally predict the contexts in which the corresponding words tend to appear. Such models have succeeded in capturing word similarities as well as semantic and syntactic regularities. Instead, we aim at reviving interest in a model based on counts. We present a systematic study of the use of the Hellinger distance to extract semantic representations from the word co-occurrence statistics of large text corpora. We show that this distance gives good performance on word similarity and analogy tasks, with a proper type and size of context, and a dimensionality reduction based on a stochastic low-rank approximation. Besides being both simple and intuitive, this method also provides an encoding function which can be used to infer unseen words or phrases. This becomes a clear advantage compared to predictive models which must train these new words.

Ex Output:
Rehabilitation of Count-based Models for Word Vector Representations


Ex Input:
There are already quite a few tools for solving the Satisfiability Modulo Theories (SMT) problems. In this paper, we present VolCE, a tool for counting the solutions of SMT constraints, or in other words, for computing the volume of the solution space. Its input is essentially a set of Boolean combinations of linear constraints, where the numeric variables are either all integers or all reals, and each variable is bounded. The tool extends SMT solving with integer solution counting and volume computation/estimation for convex polytopes. Effective heuristics are adopted, which enable the tool to deal with high-dimensional problem instances efficiently and accurately.

Ex Output:
A Tool for Computing and Estimating the Volume of the Solution Space of SMT(LA) Constraints


Ex Input:
The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of Constraint Satisfaction Problems (#CSP). We consider the random model, i.e. RB model. We prove that phase transition of #CSP does exist as the number of variables approaches infinity and the critical values where phase transitions occur are precisely located. Preliminary experimental results also show that the critical point coincides with the theoretical derivation. Moreover, we propose an approximate algorithm to estimate the expectation value of the solutions number of a given CSP instance of RB model.

Ex Output:

Counting Solutions of Constraint Satisfiability Problems: Exact Phase Transitions and Approximate Algorithm