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The Generalized Universal Law of Generalization
TL;DR: 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 form
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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.
464 citations
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.
Abstract: The advent of multiple-point geostatistics (MPS) gave rise to the integration of complex subsurface geological structures and features into the model by the concept of training images Initial algorithms generate geologically realistic realizations by using these training images to obtain conditional probabilities needed in a stochastic simulation framework More recent pattern-based geostatistical algorithms attempt to improve the accuracy of the training image pattern reproduction In these approaches, the training image is used to construct a pattern database Consequently, sequential simulation will be carried out by selecting a pattern from the database and pasting it onto the simulation grid One of the shortcomings of the present algorithms is the lack of a unifying framework for classifying and modeling the patterns from the training image In this paper, an entirely different approach will be taken toward geostatistical modeling 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 In the developed methodology, patterns scanned from the training image are represented as points in a Cartesian space using multidimensional scaling The idea behind this mapping is to use distance functions as a tool for analyzing variability between all the patterns in a training image These distance functions can be tailored to the application at hand Next, by significantly reducing the dimensionality of the problem and using kernel space mapping, an improved pattern classification algorithm is obtained This paper discusses the various implementation details to accomplish these ideas Several examples are presented and a qualitative comparison is made with previous methods An improved pattern continuity and data-conditioning capability is observed in the generated realizations for both continuous and categorical variables We show how the proposed methodology is much less sensitive to the user-provided parameters, and at the same time has the potential to reduce computational time significantly
287 citations
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.
215 citations
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.
205 citations
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.
Abstract: In recent years, there has been rapidly growing interest in embodied cognition, a multifaceted theoretical proposition that (1) cognitive processes are influenced by the body, (2) cognition exists in the service of action, (3) cognition is situated in the environment, and (4) cognition may occur without internal representations. Many proponents view embodied cognition as the next great paradigm shift for cognitive science. In this article, we critically examine the core ideas from embodied cognition, taking a "thought exercise" approach. We first note that the basic principles from embodiment theory are either unacceptably vague (e.g., the premise that perception is influenced by the body) or they offer nothing new (e.g., cognition evolved to optimize survival, emotions affect cognition, perception-action couplings are important). We next suggest that, for the vast majority of classic findings in cognitive science, embodied cognition offers no scientifically valuable insight. In most cases, the theory has no logical connections to the phenomena, other than some trivially true ideas. Beyond classic laboratory findings, embodiment theory is also unable to adequately address the basic experiences of cognitive life.
125 citations
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TL;DR: A critical examination of the extensive literature about the effects on symmetry detection of several major factors such as the orientation of the symmetry axis, the location of the stimulus in the visual field, grouping, and perturbations is carried out.
Abstract: This paper reviews empirical evidence for the detection of visual symmetries and explanatory theories and models of symmetry detection. First, mirror symmetry is compared to other types of symmetry. The idea that symmetry detection is preattentive is then discussed and other roles that attention might play in symmetry detection are considered. The major part of the article consists of a critical examination of the extensive literature about the effects on symmetry detection of several major factors such as the orientation of the symmetry axis, the location of the stimulus in the visual field, grouping, and perturbations. Constraints on plausible models of symmetry detection are derived from this rich database and several proposals are evaluated against it. As a result of bringing this research together, open questions and remaining gaps to be filled by future research are identified.
323 citations
309 citations