435 research outputs found
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Considerations in Representation Selection for Problem Solving: A Review
Choosing how to represent knowledge effectively is a long-standing open problem. Cognitive science has shed light on the taxonomisation of representational systems from the perspective of cognitive processes, but a similar analysis is absent from the perspective of problem solving, where the representations are employed. In this paper we review how representation choices are made for solving problems in the context of theorem proving from three perspectives: cognition, heterogeneity, and computational demands. We contrast the different factors that are most important for each perspective in the context of problem solving to produce a list of considerations for developers of problem solving tools regarding representations that are appropriate for particular users and effective for specific problem domains
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Now you see me (CME): Concept-based model extraction
Deep Neural Networks (DNNs) have achieved remarkable performance on a range
of tasks. A key step to further empowering DNN-based approaches is improving
their explainability. In this work we present CME: a concept-based model
extraction framework, used for analysing DNN models via concept-based extracted
models. Using two case studies (dSprites, and Caltech UCSD Birds), we
demonstrate how CME can be used to (i) analyse the concept information learned
by a DNN model (ii) analyse how a DNN uses this concept information when
predicting output labels (iii) identify key concept information that can
further improve DNN predictive performance (for one of the case studies, we
showed how model accuracy can be improved by over 14%, using only 30% of the
available concepts)
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How to (Re)represent it?
Choosing an effective representation is fundamental to the ability of the representation’s user to exploit it for the intended purpose. The major contribution of this paper is to provide a novel, flexible framework, rep2rep, that can be used by AI systems to recommend effective representations. What makes an effective representation is determined by whether it expresses the necessary information, supports the execution of tasks, and reflects the user’s cognitive abilities. In general, there is no single ‘most effective’ representation for every problem and every user, which makes it difficult to choose one from the plethora of possible representations. To address this, rep2rep includes: a domain-independent language for describing representations, algorithms that compute measures of informational suitability and cognitive cost, and uses these measures to recommend representations. We demonstrate the application of rep2rep in the probability domain. Importantly, our framework provides the foundations for personalised interaction with AI systems in the context of representation choice
Correspondence-based analogies for choosing problem representations
Mathematics and computing students learn new concepts and fortify their expertise by solving problems. The representation of a problem, be it through algebra, diagrams, or code, is key to understanding and solving it. Multiple-representation interactive environments are a promising approach, but the task of choosing an appropriate representation is largely placed on the user. We propose a new method to recommend representations based on correspondences: conceptual links between domains. Correspondences can be used to analyse, identify, and construct analogies even when the analogical target is unknown. This paper explains how correspondences build on probability theory and Gentner's structure-mapping framework; proposes rules for semi-automated correspondence discovery; and describes how correspondences can explain and construct analogies
Inelastic Processes in the Collision of Relativistic Highly Charged Ions with Atoms
A general expression for the cross sections of inelastic collisions of fast
(including relativistic) multicharged ions with atoms which is based on the
genelazition of the eikonal approximation is derived. This expression is
applicable for wide range of collision energy and has the standard
nonrelativistic limit and in the ultrarelativistic limit coincides with the
Baltz's exact solution ~\cite{art13} of the Dirac equation. As an application
of the obtained result the following processes are calculated: the excitation
and ionization cross sections of hydrogenlike atom; the single and double
excitation and ionization of heliumlike atom; the multiply ionization of neon
and argon atoms; the probability and cross section of K-vacancy production in
the relativistic collision. The simple analytic formulae
for the cross sections of inelastic collisions and the recurrence relations
between the ionization cross sections of different multiplicities are also
obtained. Comparison of our results with the experimental data and the results
of other calculations are given.Comment: 25 pages, latex, 7 figures avialable upon request,submitted to PR
Mining State-Based Models from Proof Corpora
Interactive theorem provers have been used extensively to reason about
various software/hardware systems and mathematical theorems. The key challenge
when using an interactive prover is finding a suitable sequence of proof steps
that will lead to a successful proof requires a significant amount of human
intervention. This paper presents an automated technique that takes as input
examples of successful proofs and infers an Extended Finite State Machine as
output. This can in turn be used to generate proofs of new conjectures. Our
preliminary experiments show that the inferred models are generally accurate
(contain few false-positive sequences) and that representing existing proofs in
such a way can be very useful when guiding new ones.Comment: To Appear at Conferences on Intelligent Computer Mathematics 201
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Inspection and Selection of Representations
We present a novel framework for inspecting representations and encoding their formal properties. This enables us to assess and compare the informational and cognitive value of different representations for reasoning. The purpose of our framework is to automate the process of representation selection, taking into account the candidate representation’s match to the problem at hand and to the user’s specific cognitive profile. This requires a language for talking about representations, and methods for analysing their relative advantages. This foundational work is first to devise a computational end-to-end framework where problems, representations, and user’s profiles can be described and analysed. As AI systems become ubiquitous, it is important for them to be more compatible with human reasoning, and our framework enables just that.EPSR
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