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: The Region Connection Calculus (RCC) [41] is a well-known calculus for representing part-whole and topological relations. It plays an important role in qualitative spatial reasoning, geographical information science, and ontology. The computational complexity of reasoning with RCC5 and RCC8 (two fragments of RCC) as well as other qualitative spatial/temporal calculi has been investigated in depth in the literature. Most of these works focus on the consistency of qualitative constraint networks. In this paper, we consider the important problem of redundant qualitative constraints. For a set Γ of qualitative constraints, we say a constraint (xRy) in Γ is redundant if it is entailed by the rest of Γ. A prime subnetwork of Γ is a subset of Γ which contains no redundant constraints and has the same solution set as Γ. It is natural to ask how to compute such a prime subnetwork, and when it is unique. In this paper, we show that this problem is in general intractable, but becomes tractable if Γ is over a tractable subalgebra S of a qualitative calculus. Furthermore, if S is a subalgebra of RCC5 or RCC8 in which weak composition distributes over nonempty intersections, then Γ has a unique prime subnetwork, which can be obtained in cubic time by removing all redundant constraints simultaneously from Γ. As a byproduct, we show that any path-consistent network over such a distributive subalgebra is weakly globally consistent and minimal. A thorough empirical analysis of the prime subnetwork upon real geographical data sets demonstrates the approach is able to identify significantly more redundant con∗Corresponding Author Email addresses: sanjiang.li@uts.edu.au (Sanjiang Li), zhiguo.long@student.uts.edu.au (Zhiguo Long), liuweiming@baidu.com (Weiming Liu), matt@duckham.org (Matt Duckham), aboth@student.unimelb.edu.au (Alan Both) Preprint submitted to Elsevier February 16, 2015 ar X iv :1 40 3. 06 13 v2 [ cs .A I] 1 3 Fe b 20 15 straints than previously proposed algorithms, especially in constraint networks with larger proportions of partial overlap relations.

Output: On Redundant Topological Constraints


Input: Consider Input: Common activation functions used in neural networks can yield to training difficulties due to the saturation behavior of the activation function, which may hide dependencies which are not visible to first order (using only gradients). Gating mechanisms that use softly saturating activation functions to emulate the discrete switching of digital logic circuits are good examples of this. We propose to exploit the injection of appropriate noise so that some gradients may sometimes flow, even if the noiseless application of the activation function would yield zero gradient. Large noise will dominate the noise-free gradient and allow stochastic gradient descent to be more exploratory. By adding noise only to the problematic parts of the activation function we allow the optimization procedure to explore the boundary between the degenerate (saturating) and the well-behaved parts of the activation function. We also establish connections to simulated annealing, when the amount of noise is annealed down, making it easier to optimize hard objective functions. We find experimentally that replacing such saturating activation functions by by noisy variants helps training in many contexts, yielding state-of-the-art results on several datasets, especially when training seems to be the most difficult, e.g., when curriculum learning is necessary to obtain good results.

Output: Noisy Activation Functions


Input: Consider Input: The continuing development of Semantic Web technologies and the increasing user adoption in the recent years have accelerated the progress incorporating explicit semantics with data on the Web. With the rapidly growing RDF (Resource Description Framework) data on the Semantic Web, processing large semantic graph data have become more challenging. Constructing a summary graph structure from the raw RDF can help obtain semantic type relations and reduce the computational complexity for graph processing purposes. In this paper, we addressed the problem of graph summarization in RDF graphs, and we proposed an approach for building summary graph structures automatically from RDF graph data. Moreover, we introduced a measure to help discover optimum class dissimilarity thresholds and an effective method to discover the type classes automatically. In future work, we plan to investigate further improvement options on the scalability of the proposed method.


Output: Dynamic Discovery of Type Classes and Relations in Semantic Web Data