Parallel computations for controlling an arm

In order to control a reaching movement of the arm and body, several different computational problems must be solved. Some parallel methods that could be implemented in networks of neuron-like processors are described. Each method solves a different part of the overall task. First, a method is described for finding the torques necessary to follow a desired trajectory. The methods is more economical and more versatile than table look-up and requires very few sequential steps. Then a way of generating an internal representation of a desired trajectory is described. This method shows the trajectory one piece at a time by applying a large set of heuristic rules to a "motion blackboard" that represents the static and dynamic parameters of the state of the body at the current point in the trajectory. The computations are simplified by expressing the positions, orientations, and motions of parts of the body in terms of a single, non-accelerating, world-based frame of reference, rather than in terms of the joint-angles or an egocentric frame based on the body itself.     

Primitive computations in speech processing

Previous research suggests that artificial-language learners exposed to quasi-continuous speech can learn that the first and the last syllables of words have to belong to distinct classes (e.g., Endress & Bonatti, 2007; Peña, Bonatti, Nespor, & Mehler, 2002). The mechanisms of these generalizations, however, are debated. Here we show that participants learn such generalizations only when the crucial syllables are in edge positions (i.e., the first and the last), but not when they are in medial positions (i.e., the second and the fourth in pentasyllabic items). In contrast to the generalizations, participants readily perform statistical analyses also in word middles. In analogy to sequential memory, we suggest that participants extract the generalizations using a simple but specific mechanism that encodes the positions of syllables that occur in edges. Simultaneously, they use another mechanism to track the syllable distribution in the speech streams. In contrast to previous accounts, this model explains why the generalizations are faster than the statistical computations, require additional cues, and break down under different conditions, and why they can be performed at all. We also show that that similar edge-based mechanisms may explain many results in artificial-grammar learning and also various linguistic observations.     

Neural computations of decision utility

How are decision alternatives represented in the primate brain? A recent study by Sugrue et al. sought to answer this question by integrating behavioral, computational and physiological methods in examining the choice patterns of monkeys placed in a dynamic foraging environment. They observed specific encoding of the relative value of alternatives by neurons in the parietal cortex, providing an important starting point for researchers interested in how value and probability are combined in the brain to arrive at decision outcomes.     

Cupid: A program for computations with probability distributions

This article describes Cupid, a program that performs computations with univariate probability distributions. Cupid can be useful in stochastic modeling and simulation, hypothesis testing, and examination of statistical procedures. The program runs on IBM-PC compatibles under the DOS operating system, and it is free for educational and noncommercial use.     

Learning nonadjacent dependencies: no need for algebraic-like computations

Is it possible to learn the relation between 2 nonadjacent events? M. Pena, L. L. Bonatti, M. Nespor, and J. Mehler (2002) claimed this to be possible, but only in conditions suggesting the involvement of algebraic-like computations. The present article reports simulation studies and experimental data showing that the observations on which Pena et al. grounded their reasoning were flawed by deep methodological inadequacies. When the invalid data are set aside, the available evidence fits exactly with the predictions of a theory relying on ubiquitous associative mechanisms. Because nonadjacent dependencies are frequent in natural language, this reappraisal has far-reaching implications for the current debate on the need for rule-based computations in human adaptation to complex structures.     

Comparing representations and computations in single neurons versus neural networks

Single-neuron-level explanations have been the gold standard in neuroscience for decades. Recently, however, neural-network-level explanations have become increasingly popular. This increase in popularity is driven by the fact that the analysis of neural networks can solve problems that cannot be addressed by analyzing neurons independently. In this opinion article, I argue that while both frameworks employ the same general logic to link physical and mental phenomena, in many cases the neural network framework provides better explanatory objects to understand representations and computations related to mental phenomena. I discuss what constitutes a mechanistic explanation in neural systems, provide examples, and conclude by highlighting a number of the challenges and considerations associated with the use of analyses of neural networks to study brain function.     

Algorithms for processing spatial information

Pairs of stimuli taken from a psychometric measure of spatial aptitude were shown to 9-year-olds, 13-year-olds, and adults. The stimuli in pairs were (a) either identical or mirror images, and (b) presented in orientations that differed by 0-150 degrees. Individuals judged, as rapidly as possible, if the stimuli in a pair would be identical or mirror images if presented at the same orientation. In Experiment 1, in which the stimuli were letter-like characters, at all ages most persons solved the problems using an algorithm in which an individual encodes the stimuli in working memory, mentally rotates one stimulus to the orientation of the other, compares them to determine if they are identical, and responds. In Experiment 2, the stimuli were multielement flags; here, the modal algorithm for both 9- and 13-year-olds differed from the previously described algorithm in that if the comparison process revealed that the stimuli were dissimilar, individuals did not respond immediately, but continued processing until a self-imposed deadline was reached. Among adults, the modal algorithm was the same one used in Experiment 1. Results are discussed in terms of the roles of encoding in contributing to the use of a particular algorithm.     

A faithful embedding of parallel computations in star-finite models

The purpose of this paper is to show that there exist star-finite tree-structured sets in which the computations of parallel programs can be faithfully embedded, and that the theory of star-finite sets and relations therefore provides a new tool for the analysis of non-deterministic computations.This research was carried out while the author held a Postdoctoral Fellowship from the Natural Sciences and Engineering Research Council of Canada. The author also gratefully acknowledges the support of the Centre inter-universitaire en études catégoriques de Montréal.     

Emotions and their computations: Three computer models

Abstract

Three computational models: a narrative reader (BORIS), an editorial reader (OpEd), and a stream of thought generator (DAYDREAMER), are presented and discussed, with specific focus on the emotion-related processing and representational elements of each. These models exhibit comprehension and/or generation of emotional behaviour through the interaction of cognitive processes (memory retrieval, planning, and reasoning) over intentional constructs (goals and beliefs).     

Statistical computations over a speech stream in a rodent

Statistical learning is one of the key mechanisms available to human infants and adults when they face the problems of segmenting a speech stream (Saffran, Aslin, & Newport, 1996) and extracting long-distance regularities (G6mez, 2002; Pe?a, Bonatti, Nespor, & Mehler, 2002). In the present study, we explore statistical learning abilities in rats in the context of speech segmentation experiments. In a series of five experiments, we address whether rats can compute the necessary statistics to be able to segment synthesized speech streams and detect regularities associated with grammatical structures. Our results demonstrate that rats can segment the streams using the frequency of co-occurrence (not transitional probabilities, as human infants do) among items, showing that some basic statistical learning mechanism generalizes over nonprimate species. Nevertheless, rats did not differentiate among test items when the stream was organized over more complex regularities that involved nonadjacent elements and abstract grammar-like rules.     

Algorithms for fast and precise computation of the normal integral

Five highly accurate algorithms that evaluate the normal distribution function are presented. The algorithms, which are based on either numerical integration or series expansions, are explicated, and applications of Simpson’s rule are discussed. Computer programs that implement the algorithms were compared with respect to accuracy and speed. The programs attain from 11- to 15-decimal-place accuracy in finding one-tailed areas of the normal curve, and most execute very quickly. Recommendations are made for selection of algorithms and programs to approximate the normal distribution.     

Justification and Cognitive Algorithms

In this paper, we offer an alternative interpretation for the claim that ‘S is justified in believing that φ’. First, we present what seems to be a common way of interpreting this claim: as an attribution of propositional justification. According to this interpretation, being justified is just a matter of having confirming evidence. We present a type of case that does not fit well with the standard concept, where considerations about cognition are made relevant. The concept of cognitive algorithm is presented and explained. Finally, the new reading of ‘S is justified in believing that φ’ is fleshed out. According to this interpretation, being justified in believing that φ is not just a matter of having evidence in favor of φ, but also of having a cognitive algorithm available such that it allows one to form belief in φ on the basis of the relevant evidence.     

Algorithms and selective attention

Selective attention is hypothesized to be controlled by intentionally chosen algorithms that specify how stimuli are to be processed. These experiments attempted to measure the time to select such algorithms. Subjects were given a two-choice reaction time task with a variety of different possible stimuli. Prior to each trial, subjects viewed a cue under their control that indicated the two possible stimuli for the upcoming trial. During this interval, subjects presumably selected a stimulus identification algorithm appropriate for that pair of letters; the duration of the interval was used as an index of algorithm selection time. The results indicated that selection time increases with the number of alternative algorithms and that algorithms may consist, in part, of perceptual tests to determine which of the two possible stimuli was presented. A specific model of the selection process was proposed to account for the results.     

Minimal models and canonical neural computations: the distinctness of computational explanation in neuroscience

In a recent paper, Kaplan (Synthese 183:339–373, 2011) takes up the task of extending Craver’s (Explaining the brain, 2007) mechanistic account of explanation in neuroscience to the new territory of computational neuroscience. He presents the model to mechanism mapping (3M) criterion as a condition for a model’s explanatory adequacy. This mechanistic approach is intended to replace earlier accounts which posited a level of computational analysis conceived as distinct and autonomous from underlying mechanistic details. In this paper I discuss work in computational neuroscience that creates difficulties for the mechanist project. Carandini and Heeger (Nat Rev Neurosci 13:51–62, 2012) propose that many neural response properties can be understood in terms of canonical neural computations. These are “standard computational modules that apply the same fundamental operations in a variety of contexts.” Importantly, these computations can have numerous biophysical realisations, and so straightforward examination of the mechanisms underlying these computations carries little explanatory weight. Through a comparison between this modelling approach and minimal models in other branches of science, I argue that computational neuroscience frequently employs a distinct explanatory style, namely, efficient coding explanation. Such explanations cannot be assimilated into the mechanistic framework but do bear interesting similarities with evolutionary and optimality explanations elsewhere in biology.     

Algorithms for randomness in the behavioral sciences: A tutorial

Simulations and experiments frequently demand the generation of random numbers that have specific distributions. This article describes which distributions should be used for. the most common problems and gives algorithms to generate the numbers. It is also shown that a commonly used permutation algorithm (Nilsson, 1978) is deficient.