TASK DEFINITION: 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.
PROBLEM: In this paper, we describe a system for generating threedimensional visual simulations of natural language motion expressions. We use a rich formal model of events and their participants to generate simulations that satisfy the minimal constraints entailed by the associated utterance, relying on semantic knowledge of physical objects and motion events. This paper outlines technical considerations and discusses implementing the aforementioned semantic models into such a system.

SOLUTION: Multimodal Semantic Simulations of Linguistically Underspecified Motion Events

PROBLEM: We describe a technique to minimize weighted tree automata (WTA), a powerful formalisms that subsumes probabilistic context-free grammars (PCFGs) and latent-variable PCFGs. Our method relies on a singular value decomposition of the underlying Hankel matrix defined by the WTA. Our main theoretical result is an efficient algorithm for computing the SVD of an infinite Hankel matrix implicitly represented as a WTA. We provide an analysis of the approximation error induced by the minimization, and we evaluate our method on real-world data originating in newswire treebank. We show that the model achieves lower perplexity than previous methods for PCFG minimization, and also is much more stable due to the absence of local optima.

SOLUTION: Weighted Tree Automata Approximation by Singular Value Truncation

PROBLEM: Given a graphical model, one essential problem is MAP inference, that is, finding the most likely configuration of states according to the model. Although this problem is NP-hard, large instances can be solved in practice. A major open question is to explain why this is true. We give a natural condition under which we can provably perform MAP inference in polynomial time. We require that the number of fractional vertices in the LP relaxation exceeding the optimal solution is bounded by a polynomial in the problem size. This resolves an open question by Dimakis, Gohari, and Wainwright. In contrast, for general LP relaxations of integer programs, known techniques can only handle a constant number of fractional vertices whose value exceeds the optimal solution. We experimentally verify this condition and demonstrate how efficient various integer programming methods are at removing fractional solutions.

SOLUTION:
Exact MAP Inference by Avoiding Fractional Vertices