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The Generalized Universal Law of Generalization
Nick Chater,Paul M. B. Vitányi +1 more
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In this paper, the authors show that the universal law of generalization holds with probability going to one-provided the confusion probabilities are computable, and they also give a mathematically more appealing form.Abstract:
It has been argued by Shepard that there is a robust psychological law that relates the distance between a pair of items in psychological space and the probability that they will be confused with each other. Specifically, the probability of confusion is a negative exponential function of the distance between the pair of items. In experimental contexts, distance is typically defined in terms of a multidimensional Euclidean space-but this assumption seems unlikely to hold for complex stimuli. We show that, nonetheless, the Universal Law of Generalization can be derived in the more complex setting of arbitrary stimuli, using a much more universal measure of distance. This universal distance is defined as the length of the shortest program that transforms the representations of the two items of interest into one another: the algorithmic information distance. It is universal in the sense that it minorizes every computable distance: it is the smallest computable distance. We show that the universal law of generalization holds with probability going to one-provided the confusion probabilities are computable. We also give a mathematically more appealing formread more
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Probabilistic models of cognition: exploring representations and inductive biases
TL;DR: It is argued that the top-down approach to modeling cognition yields greater flexibility for exploring the representations and inductive biases that underlie human cognition.
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Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling
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TL;DR: A novel, principled and unified technique for pattern analysis and generation that ensures computational efficiency and enables a straightforward incorporation of domain knowledge will be presented and has the potential to reduce computational time significantly.
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The Tractable Cognition Thesis
TL;DR: How and why the P-Cognition thesis may be overly restrictive is explained, risking the exclusion of veridical computational-level theories from scientific investigation, and an argument is made to replace the Tractable Cognition thesis by the FPT-Cognitive thesis as an alternative formalization.
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The differential role of phonological and distributional cues in grammatical categorisation
TL;DR: This paper presents a series of analyses of phonological cues and distributional cues and their potential for distinguishing grammatical categories of words in corpus analyses and indicates that phonological and Distributional cues contribute differentially towards grammatical categorisation.
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The poverty of embodied cognition
TL;DR: It is suggested that, for the vast majority of classic findings in cognitive science, embodied cognition offers no scientifically valuable insight and is also unable to adequately address the basic experiences of cognitive life.
References
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An Information Measure for Classification
Chris S. Wallace,D. M. Boulton +1 more
TL;DR: It is suggested that the best classification is that which results in the briefest recording of all the attribute information, and the measurements of each thing are regarded as being a message about that thing.
Book
Classical recursion theory
TL;DR: Theories of Recursive functions, Hierarchies of recursive functions, and Arithmetical sets: Recursively enumerable sets.
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Stochastic Complexity and Modeling
TL;DR: In this article, the stochastic complexity of a string of data, relative to a class of probabilistic models, is defined to be the fewest number of binary digits with which the data can be encoded by taking advantage of the selected models.
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Fisher information and stochastic complexity
TL;DR: A sharper code length is obtained as the stochastic complexity and the associated universal process are derived for a class of parametric processes by taking into account the Fisher information and removing an inherent redundancy in earlier two-part codes.
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