Probability Relations within Response Sequences under Ratio Reinforcement.
01 Apr 1958-Journal of the Experimental Analysis of Behavior (Society for the Experimental Analysis of Behavior)-Vol. 1, Iss: 2, pp 109-121
About: This article is published in Journal of the Experimental Analysis of Behavior.The article was published on 1958-04-01 and is currently open access. It has received 264 citations till now. The article focuses on the topics: Reinforcement.
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01 Jan 2007
TL;DR: Results showed that during shaping, run length on the left key increased and then, for some pigeons, it stabilized, whereas for others pigeons it remained variable, and in extinction, before the pigeons ceased to respond altogether, they emitted the same distribution of run lengths as during the last sessions of shaping.
Abstract: The experiment examined how pigeons differentiate response patterns along the dimension of number. Seven pigeons received food after pecking the left key at least N times and then switching to the right key (Mechner’s Fixed Consecutive Number schedule). Parameter N was set according to a percentile schedule, which is a form of automatic shaping. Our aim was twofold: on the empirical side to determine how run length on the left key would evolve under this shaping procedure and how it would change during a subsequent extinction phase; and on the theoretical side to compare the data with the predictions of a theoretical model of response differentiation. Results showed that during shaping, run length on the left key increased and then, for some pigeons, it stabilized, whereas for others pigeons it remained variable. Some pigeons ceased to respond when average run length reached a high value. There were substantial within-session trends in run length. In extinction, before the pigeons ceased to respond altogether, they emitted the same distribution of run lengths as during the last sessions of shaping with the exception, in some birds, of a large number of runs of length zero. These results are interpreted at the light of the theoretical model of numerosity differentiation.
Cites background or methods from "Probability Relations within Respon..."
...In particular, when the population follows a Gaussian distribution, as is typically the case with run length (see Laties, 1972; Machado & Rodrigues, 2007; Mechner, 1958; Platt & Johnson, 1971), the 50 sample percentile estimates the mean of the distribution, μ....
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...The reinforcement rule was as follows (see Mechner, 1958): With probability p, a reinforcer was delivered after the Nth peck on the left key (Fixed Ratio N schedule); with probability 1-p, a reinforcer was delivered after one peck on the right key provided that peck was preceded by at least N pecks…...
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...Whereas we found no systematic changes, Mechner (1958b) reported greater variability using rats in a FCN 8 schedule....
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...A stimulus presented a given number of times may control an operant response (Alsop & Honig, 1991; Emmerton, 2001; Keen & Machado, 1999) and, similarly, animals can learn to emit a response a given number of times (Laties, 1972; Hobson & Newman, 1981; Mechner, 1958; Platt & Johnson, 1971)....
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...In particular, when the population follows a Gaussian distribution, as is typically the case with run length (see Laties, 1972; Machado & Rodrigues, 2007; Mechner, 1958; Platt & Johnson, 1971), the 50th sample percentile estimates the mean of the distribution, µ....
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TL;DR: In this paper , the authors developed an online evidence accumulation game and nonverbal training pipeline for humans inspired by pulse-based evidence accumulation tasks for rodents, and used this game to evaluate how perceptual noise scales with accumulated evidence and found that participants trained using feedback alone learned the game rules rapidly and used similar strategies to those who received explicit instructions.
Abstract: Evidence accumulation, how the brain integrates sensory information over time, is an essential component of perception and decision making. In humans, evidence accumulation is commonly modeled as a diffusion process in which noise accumulates linearly with the incoming evidence. However, recent studies in rodents have shown that during perceptual decision making, noise scales non-linearly with the strength of accumulated evidence. The question of whether nonlinear noise scaling also holds for humans has been clouded by differences in the methodologies typically used to collect and analyze human and rodent data. For example, whereas humans are typically given explicit instructions in these tasks, rodents are trained using feedback. Therefore, to evaluate how perceptual noise scales with accumulated evidence, we developed an online evidence accumulation game and nonverbal training pipeline for humans inspired by pulse-based evidence accumulation tasks for rodents. Using this game, we collected and analyzed behavioral data from hundreds of participants trained either with an explicit description of the relevant decision rule or merely with experiential feedback. Across all participants, performance was well described by an accumulation process, in which stimuli were integrated equally across time. Participants trained using feedback alone learned the game rules rapidly and used similar strategies to those who received explicit instructions. Decisions in both groups were influenced in similar ways by biases and perceptual noise, suggesting that explicit instructions did not reduce bias or noise in pulse-based accumulation tasks. Finally, by leveraging data across all participants, we show that perceptual noise during evidence accumulation was best described by a non-linear model of noise scaling, consistent with previous animal studies, but inconsistent with diffusion models widely used in human studies. These results challenge the conventional description of humans’ accumulation process and suggest that online games inspired by evidence accumulation tasks provide a valuable large-scale behavioral assessment platform to examine perceptual decision making and learning in humans. In addition, the feedback-based training pipeline developed for this game may be useful for evaluating perceptual decision making in human populations with difficulty following verbal instructions. Highlights Development and validation of an online video game to measure perceptual decision making. Humans trained using a feedback-based pipeline exhibit similar strategies and performance compared with those receiving instructions. Perceptual noise increases superlinearly with sensory evidence.
TL;DR: There is a relatively strong representational control over counting behavior even in conditions that afford strong stimulus control, according to the frequency but not the probability-sensitive parametrization of switching behavior changed when the discriminative stimulus became non-informative in testing.
01 Jan 2018
TL;DR: It can be assumed that during human history, the development of new numerical abilities was correlated with the involvement of new brain areas during the performance of progressively more complex numerical tasks.
Abstract: The ability to calculate represents a complex cognitive process including verbal, spatial, somatic, memory, and executive functions. The origin of mathematical concepts can be traced to subhuman species. The immediate recognition of certain small quantities without counting – subitizing – is found not only in animals but also in small children. During child development, different stages in the acquisition of numerical knowledge are observed, including global quantification, recognition of small quantities, enumeration, correspondence construction, counting, and finally permutability (arithmetic). Some numerical abilities, such as correspondence construction, probably existed in prehistoric man. In human history, as well as in child development, counting begins with sequencing the fingers; this may be the reason for the frequent use of a decimal system. Written numbers appeared in history before written language. Neuroimaging techniques have demonstrated that different brain areas are active during arithmetical tasks, but the specific pattern of brain activity depends on the particular type of task that is performed. It can be assumed that during human history, the development of new numerical abilities was correlated with the involvement of new brain areas during the performance of progressively more complex numerical tasks. Mediators used in numerical cognition continue evolving with the introduction of new contemporary technologies.
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TL;DR: I am indebted to Professor Lighthill for some further illuminating remarks regarding this point and his comments on Heisenberg's Theory of Isotropic Turbulence are highly illuminating.
Abstract: 1 G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge: At the University Press, 1954). 2 G. K. Batchelor and A. A. Townsend, \"Decay of Turbulence in the Final Period of Decay,\" Proc. Roy. Soc. London, A, 194, 527-543, 1948. 3 W. Heisenberg, \"Zur statistischen Theorie der Turbulenz,\" Z. Physik, 124, 628-657, 1948. 4W. H. Reid, \"Two Remarks on Heisenberg's Theory of Isotropic Turbulence,\" Quart. Appl. Math. 14, 201-205, 1956. 6 Cf. M. J. Lighthill, Nature, 173, 746, 1954. I am indebted to Professor Lighthill for some further illuminating remarks regarding this point.
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