2,825 research outputs found
Discovering Implicational Knowledge in Wikidata
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
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
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
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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