2,825 research outputs found

    Discovering Implicational Knowledge in Wikidata

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    Knowledge graphs have recently become the state-of-the-art tool for representing the diverse and complex knowledge of the world. Examples include the proprietary knowledge graphs of companies such as Google, Facebook, IBM, or Microsoft, but also freely available ones such as YAGO, DBpedia, and Wikidata. A distinguishing feature of Wikidata is that the knowledge is collaboratively edited and curated. While this greatly enhances the scope of Wikidata, it also makes it impossible for a single individual to grasp complex connections between properties or understand the global impact of edits in the graph. We apply Formal Concept Analysis to efficiently identify comprehensible implications that are implicitly present in the data. Although the complex structure of data modelling in Wikidata is not amenable to a direct approach, we overcome this limitation by extracting contextual representations of parts of Wikidata in a systematic fashion. We demonstrate the practical feasibility of our approach through several experiments and show that the results may lead to the discovery of interesting implicational knowledge. Besides providing a method for obtaining large real-world data sets for FCA, we sketch potential applications in offering semantic assistance for editing and curating Wikidata

    A Unified View of Piecewise Linear Neural Network Verification

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    The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. Despite the reputation of learned NN models to behave as black boxes and the theoretical hardness of proving their properties, researchers have been successful in verifying some classes of models by exploiting their piecewise linear structure and taking insights from formal methods such as Satisifiability Modulo Theory. These methods are however still far from scaling to realistic neural networks. To facilitate progress on this crucial area, we make two key contributions. First, we present a unified framework that encompasses previous methods. This analysis results in the identification of new methods that combine the strengths of multiple existing approaches, accomplishing a speedup of two orders of magnitude compared to the previous state of the art. Second, we propose a new data set of benchmarks which includes a collection of previously released testcases. We use the benchmark to provide the first experimental comparison of existing algorithms and identify the factors impacting the hardness of verification problems.Comment: Updated version of "Piecewise Linear Neural Network verification: A comparative study

    Mathematical practice, crowdsourcing, and social machines

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    The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend. Mathematical practice is an emerging interdisciplinary field which draws on philosophy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question answering system {\it mathoverflow} contains around 40,000 mathematical conversations, and {\it polymath} collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of "soft" aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal. Crowdsourced mathematical activity is an example of a "social machine", a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.Comment: To appear, Springer LNCS, Proceedings of Conferences on Intelligent Computer Mathematics, CICM 2013, July 2013 Bath, U

    Shaping Attitudes Toward Science in an Introductory Astronomy Class

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    At many universities, astronomy is a popular way for non-science majors to fulfill a general education requirement. Because general-education astronomy may be the only college-level science course taken by these students, it is the last chance to shape the science attitudes of these future journalists, teachers, politicians, and voters. I report on an attempt to measure and induce changes in science attitudes in my general-education astronomy course. I describe construction of the attitude survey, classroom activities designed to influence attitudes, and give numerical results indicating a significant improvement. In contrast, the literature on attitudes in introductory physics courses generally reports stagnation or decline. I briefly comment on some plausible explanations for this difference.Comment: v2 includes a copy of the surve
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