Application of a trace model to the retention of information in a recognition task

A stochastic model is proposed to account for the behavior of subjects in recognition tasks in which stimuli are presented, one at a time, in a protracted sequence. The basic assumption is that the memory trace resulting from the presentation of a particular stimulus not only fades away during the presentation of subsequent stimuli but also diffuses in such a way as to become decreasingly stimulus specific. An account is thereby provided for both (a) the increase in the probability of false recognition with the total number of stimulus presentations and (b) the departure of curves of forgetting from the previously proposed simple exponential decay functions. An expression for the amount of information carried along when the number of stimulus presentations becomes large is then derived for subjects who conform with the model.The author has benefited from discussions of this work with J. W. Tukey, J. R. Pierce, E. N. Gilbert, and D. Slepian of the Bell Telephone Laboratories and with G. A. Miller of Harvard University.     

A generalization of Thurstone's learning function

Thurstone's equation giving the probability of a correct response (p) as a function of practice time (t) when punishment and reward have equal effects has been generalized to the case where the effect of punishment is not necessarily equal to the effect of reward. Since the general equation is somewhat unwieldy, three special cases are considered, where reward has no effect, where punishment has no effect, and where these effects are equal. Equations are given together with tables for making a rectified plot for each of the three special cases.This study was supported in part by contract N6onr 270-20 between the Office of Naval Research and Princeton University. The opinions expressed are, of course, those of the author and do not represent attitudes or policies of the Office of Naval Research.     

The generalized universal law of generalization

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 perceived as similar. Specifically, this probability 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 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 probabilities concerned are computable. We also give a mathematically more appealing form of the Universal Law.     

Asymmetrical stimulus generalization following differential fear conditioning

Rodent ultrasonic vocalizations (USVs) are ethologically critical social signals. Rats emit 22 kHz USVs and 50 kHz USVs, respectively, in conjunction with negative and positive affective states. Little is known about what controls emotional reactivity to these social signals. Using male Sprague–Dawley rats, we examined unconditional and conditional freezing behavior in response to the following auditory stimuli: three 22 kHz USVs, a discontinuous tone whose frequency and on–off pattern matched one of the USVs, a continuous tone with the same or lower frequencies, a 4 kHz discontinuous tone with an on–off pattern matched to one of the USVs, and a 50 kHz USV. There were no differences among these stimuli in terms of the unconditional elicitation of freezing behavior. Thus, the stimuli were equally neutral before conditioning. During differential fear conditioning, one of these stimuli (the CS⁺) always co-terminated with a footshock unconditional stimulus (US) and another stimulus (the CS⁻) was explicitly unpaired with the US. There were no significant differences among these cues in CS⁺-elicited freezing behavior. Thus, the stimuli were equally salient or effective as cues in supporting fear conditioning. When the CS⁺ was a 22 kHz USV or a similar stimulus, rats discriminated based on the principal frequency and/or the temporal pattern of the stimulus. However, when these same stimuli served as the CS⁻, discrimination failed due to generalization from the CS⁺. Thus, the stimuli differed markedly in the specificity of conditioning. This strikingly asymmetrical stimulus generalization is a novel bias in discrimination.     

On the discriminative control of concurrent responses: the relations among response frequency, latency, and topography in auditory generalization

Human subjects were used in a study of auditory generalization following multiple-response discrimination training. The relations observed among stimulus intensity, response probability, and response latency were invariant with respect to whether the two vocal responses conditioned were topographically discrete, as in one experiment, or topographically continuous, as in another. The major findings were:

1. The probabilities associated with a specific response were maximal over several stimulus values at the extreme ends of the continuum, then dropped sharply at stimuli intermediate to the initial S^D's as the probability of the alternative response increased.

2. Overall response latency was inversely related to the relative frequency of the two responses at each stimulus value. When the two responses were most nearly equal in probability, latencies were maximal; when one response had close to unit or zero probability, latencies were minimal.

3. Analysis of the latencies of the two responses, taken separately, revealed: (a) an increase in latency as the difference between the test stimulus and the initial S^D increased; (b) a sharp discontinuity in the latency gradient and reversal in trend at intermediate stimulus intensities; and (c) at a given stimulus value, latencies associated with the stochastically dominant response were consistently shorter than those of the nondominant response.

4. No changes in response topography (fundamental frequency) were correlated with the characteristic changes in probability and latency during stimulus generalization.

     

Dissociation of binding and learning processes

A single encounter of a stimulus together with a response can result in a short-lived association between the stimulus and the response [sometimes called an event file, see Hommel, Müsseler, Aschersleben, & Prinz, (2001) Behavioral and Brain Sciences, 24, 910–926]. The repetition of stimulus–response pairings typically results in longer lasting learning effects indicating stimulus–response associations (e.g., Logan & Etherton, (1994) Journal of Experimental Psychology: Learning, Memory, and Cognition, 20, 1022–1050]. An important question is whether or not what has been described as stimulus–response binding in action control research is actually identical with an early stage of incidental learning (e.g., binding might be seen as single-trial learning). Here, we present evidence that short-lived binding effects can be distinguished from learning of longer lasting stimulus–response associations. In two experiments, participants always responded to centrally presented target letters that were flanked by response irrelevant distractor letters. Experiment 1 varied whether distractors flanked targets on the horizontal or vertical axis. Binding effects were larger for a horizontal than for a vertical distractor-target configuration, while stimulus configuration did not influence incidental learning of longer lasting stimulus–response associations. In Experiment 2, the duration of the interval between response n – 1 and presentation of display n (500 ms vs. 2000 ms) had opposing influences on binding and learning effects. Both experiments indicate that modulating factors influence stimulus–response binding and incidental learning effects in different ways. We conclude that distinct underlying processes should be assumed for binding and incidental learning effects.

     

On the time course of perceptual information that results from a brief visual presentation.

A briefly presented visual stimulus engenders an available-information function that lags behind the physical stimulus. We report two experiments that focus on the iconic-decay portion of this function, which falls to 0 over a 200-300 ms period following stimulus offset. In each experiment, to-be-reported digit strings were shown for varying durations followed by a noise mask at varying poststimulus intervals. We found the shape of the performance curve relating digit-report probability to stimulus exposure duration to be independent of stimulus-mask interstimulus interval. This finding is consistent with the proposition that the iconic-decay function's shape is independent of stimulus duration and allows us to identify this shape. We rejected exponential iconic decay for 6 of 8 observers; however, all observers' decay functions could be adequately fit by gamma decay, a generalization of exponential decay.     

Bayesian generalization with circular consequential regions

Generalization–deciding whether to extend a property from one stimulus to another stimulus–is a fundamental problem faced by cognitive agents in many different settings. Shepard (1987) provided a mathematical analysis of generalization in terms of Bayesian inference over the regions of psychological space that might correspond to a given property. He proved that in the unidimensional case, where regions are intervals of the real line, generalization will be a negatively accelerated function of the distance between stimuli, such as an exponential function. These results have been extended to rectangular consequential regions in multiple dimensions, but not for circular consequential regions, which play an important role in explaining generalization for stimuli that are not represented in terms of separable dimensions. We analyze Bayesian generalization with circular consequential regions, providing bounds on the generalization function and proving that this function is negatively accelerated.     

Shepard's universal law supported by honeybees in spatial generalization

An animal that is rewarded for a response in one situation (the S+) is likely to respond to similar but recognizably different stimuli, the ubiquitous phenomenon of stimulus generalization. On the basis of functional analyses of the probabilistic structure of the world, Shepard formulated a universal law of generalization, claiming that generalization gradients, as a function of the appropriately scaled distance of a stimulus from S+, should be exponential in shape. This law was tested in spatial generalization in honeybees. Based on theoretically derived scales, generalization along both the dimensions of the distance from a landmark and the direction to a landmark followed Shepard's law. Support in an invertebrate animal increases the scope of the law, and suggests that the ecological structure of the world may have driven the evolution of cognitive structures in diverse animals.     

Single-letter recognition as a function of exposure duration

The time course of visual letter recognition was investigated in a single-stimulus identification experiment. On each trial, a randomly chosen stimulus letter was presented at 1 of 12 equiprobable positions that were equally spaced around the circumference of an imaginary circle centered on fixation. Exposure duration was varied from 10 to 200 ms, and the letter was followed by a pattern mask. The subject's task was to report the identity of the stimulus letter but refrain from guessing. For the briefest exposures, correct reports never occurred. For longer exposures, the function relating the probability p of recognizing the letter to the duration t of the stimulus exposure was well approximated by an exponential distribution function: p(t) = 1 − exp[−v·(t−t ₀)], where v is the rate of processing and t ₀ is the minimum effective exposure duration. The generality of this finding may be limited to cases in which stimuli are highly discriminable and response criteria are conservative. Extensions to Poisson counter or random walk models are considered for cases in which stimuli are confusable. Received: 1 July 1997 / Accepted: 2 July 1998     

Finite and infinite state confusion models

A confusion model is defined as a model that decomposes response probabilities in stimulus identification experiments into perceptual parameters and response parameters. Historically, confusion models fall into two groups. Models in Group I, which includes Townsend's (Perception and Psychophysics, 1971, 9, 40–50) overlap model, were developed on the basis of the notion that stimulus identification is mediated by a finite number of internal states. We call the general class of models that have this processing interpretation finite state confusion models. Models in Group II, which includes Luce's (R. O. Luce et al., Eds., Handbook of Mathematical Psychology (Vol. I), New York: Wiley, 1963) biased choice model, were not developed on the basis of an explicit processing interpretation. It is shown here that models in Group II are not finite state confusion models. We prove in addition that except for Falmagne's (Journal of Mathematical Psychology, 1972, 9, 206–224) simply biased model models in Group II belong to a certain class of infinite state confusion models, namely, models asserting that stimulus identification is mediated by a continuous space of vectors representing detector activation levels.     

Decay functions and criminal spatial processes: geographical offender profiling of volume crime

Although it is now well established across diverse samples that the frequency of offending ‘decays’ as distance from the home/base increases, it remains unclear what form of decay function best characterises this relationship. Different forms of decay function reflect different patterns and rates of decrease in the likelihood of offending as distance from the home/base increases. These different patterns imply rather different underlying psychological processes. Therefore, considerations of the particular function characterising distance decay elucidate explanations of offender spatial behaviour. To bring to light the possible psychological and behavioural processes inherent in offending distance decay, the present study examined the fit of logarithmic, negative exponential, and quadratic decay functions to the distribution of the distances travelled to offend by a sample of 70 prolific burglars from the UK. It is argued that these functions are consistent with the operation of perceptual processes of magnitude estimation, friction or effort effects, and the influences of cost‐benefit assessments, respectively. The results indicate that offending distance decay patterns most closely fit the logarithmic function, consistent with Stevens' perceptual processes of distortion in magnitude estimation, whilst not ruling out additional processes relating to the increased effort required in travelling greater distances to offend. Because most geographical profiling systems are built upon the distance decay function, the impact of utilising the different forms of function on the accuracy of geographic profiles was also assessed utilising ‘search cost’ calculations. The results showed little impact of applying different decay functions. Thus, whilst the decay function does have important theoretical implications for understanding offender spatial behaviour, it is noted that the particular variant used does not significantly impact on the effectiveness of geographical profiling systems as they currently exist. Copyright © 2011 John Wiley & Sons, Ltd.     

Temporal generalization under time pressure in humans

In two experiments, participants performed a temporal generalization task in which they were asked to decide whether or not the durations of comparison stimuli were different from those of standard stimuli (750 ms, 1,000 ms, or 1,250 ms). One half of the participants was instructed to respond as quickly as possible, while the other half received no instruction concerning the speed of response. The relationship between stimulus duration and the time of response and the effect of time pressure on duration discrimination were examined. Response time increased as a linear function of the duration of the to-be-judged stimuli until a certain instant, which was defined as T ₂ = s/(1 – b), where s refers to the internal representation of the standard duration and b to the decision threshold. Moreover, the participants systematically overestimated the presented intervals if they were asked to respond as fast as possible when the standard duration was either 1,000 ms or 1,250 ms, but not when the standard duration was 750 ms.     

Two Theories of Visual Speed

A measure of clustering in free recall based upon the parameters of the original stimulus list (R/Opt. R) was proposed and compared with five other measures for eight recall protocols. The R/Opt. R measure was shown to be relatively independent of the length of the recall protocol, but yielded higher scores where fewer categories were utilized. Optimum clustering was defined not simply in terms of perfect ordering of elements within the protocol but also in terms of the number of categories and items within those categories in the original stimulus list.     

The psychological growth of women in a short-term inpatient group

This paper identifies ways in which a short-term inpatient group can support psychological growth of women. A four-stage developmental model of women's work in an inpatient group is described. In each stage, women achieve greater comfort in new modes of relating. Women also gain greater appreciation of their interpersonal strengths. In the first stage, women face issues related to autonomy and connection. In the second stage, women focus upon conflictual feelings in relation to authority. In the third stage, women address obstacles to the achievement of satisfying, intimate, peer-based relationships. In the fourth stage, women focus upon the issues of separation and loss that are precipitated by the termination of the group. At each stage, the developmental tasks women perform are contrasted with related but nonidentical tasks performed by men.The author wishes to thank Drs. Joan Cooper and Francine Deutsch for their comments on an earlier draft of this paper.     

The pseudodiagnosticity trap: Should participants consider alternative hypotheses?

The pseudodiagnosticity task has been used as an example of the tendency on the part of participants to incorrectly assess Bayesian constraints in assessing data, and as a failure to consider alternative hypotheses in a probabilistic inference task. In the task, participants are given one value, the anchor value, corresponding to P(D1|H) and may choose one other value, either P(D1|¬!H), P(D2|H), or P(D2|not;!H). Most participants select P(D2|H), or P(D2|¬!H) which have been considered inappropriate (and called pseudodiagnostic) because only P(D1|¬!H) allows use of Bayes' theorem. We present a new analysis based on probability intervals and show that selection of either P(D2|H), or P(D2|¬!H) is in fact pseudodiagnostic, whereas choice of P(D1|¬!H) is diagnostic. Our analysis shows that choice of the pseudodiagnostic values actually increases uncertainty regarding the posterior probability of H, supporting the original interpretation of the experimental findings on the pseudodiagnosticity task. The argument illuminates the general proposition that evolutionarily adaptive heuristics for Bayesian inference can be misled in some task situations.     

Effect of Injected Adrenalin on an Avoidance Response in the Rat

It was hypothesized that slight modifications in word association test (WAT) instructions would have no discernable effect on the responses of college students, but would produce significantly different response hierarchies generated by young children. Seventy-five adults and 375 children gave WAT responses to 32 stimulus words. One-third of the Ss, at each of six grade levels, was given standard WAT instructions; one-third was given a practice session with 10 additional words; and the remainder were instructed to respond to stimulus words with the “first thing” that came to mind. Although the different instructional sets had no discernable effect on the adult Ss, they had a significant effect (ps < .05) upon the number of (a) multiple-word and nonword responses, (b) paradigmatic responses, and (c) idiosyncratic responses produced by the children. These differences suggest that caution be used in the interpretation of WAT responses provided by young Ss.     

A note on keats' generalization of the rasch model

An alternative derivation is given for a simple test model which incorporates anability parameter for the subject anddifficulty level andguessing parameters for the problem. The probability of a correct response to the problem is a projective transformation of the problem difficulty. The ability and difficulty parameters separate into additive components.     

Semantic similarity of labels and inductive generalization: Taking a second look

Prior research suggests that preschoolers can generalize object properties based on category information conveyed by semantically-similar labels. However, previous research did not control for co-occurrence probability of labels in natural speech. The current studies re-assessed children’s generalization with semantically-similar labels. Experiment 1 indicated that adults made category-based inferences regardless of co-occurrence probability; however, 4-year-olds generalized with semantically-similar labels that co-occurred in child-directed speech (e.g., bunny–rabbit) but not with non-co-occurring labels (e.g., crocodile–alligator). Experiment 2 indicated that generalization with semantically-similar labels increased gradually between 4- and 6-years of age. These results are discussed in relation to theories of early learning.     

Some preliminary postulates on stimulus-perception,and consequent probability distributions for behavior

A stimulus (or stimulus-complex) is pictured as giving rise to a random series of sensory nerve pulses, which manifest themselves in contractions of individual muscle fibers. Assuming the expected time-frequency of these pulses to be proportional to the intensity of the stimulus, probability distributions are computed representing the cumulative effect of these pulses on the state of the organism, that is, on its degree ofawareness of the stimulus. Preliminary results suggest a modification of the Weber-Fechner formula for intensity discrimination for certain types of stimuli: the psychological scale to be measured byI ⁱ instead of logI.Contributions from the Scripps Institution of Oceanography, New Series, No. 54.