Temporal Generalization Gradients Research Articles

Asymmetry in updating long-term memory for time.

The present study evaluates the updating of long-term memory for duration. After learning a temporal discrimination associating one lever with a standard duration (4 sec) and another lever with both a shorter (1-sec) and a longer (16-sec) duration, rats underwent a single session for learning a new standard duration. The temporal generalization gradient obtained 24 h later showed a modification in long-term memory for durations longer than the standard but only when the new duration was longer than the one initially learned. The effect was confirmed for another set of durations (0.5–2–8 sec). Our study demonstrates asymmetry in updating long-term memory for time.

Increased generalization in a peak procedure after delayed reinforcement

Temporal control of behavior might be impaired by reinforcement devaluation and other motivational operations such as delaying reinforcement of the instrumental response. Here, we report an experiment that assessed the effect of delayed reinforcement on a timing peak procedure. Using a within-subject design with a multiple two-component schedule of reinforcement, we found evidence of flat temporal generalization gradients, along with degraded response-reinforcer contingency, lower response rates and changes in the responding patterns due to delayed reinforcement. This result is consistent with the Learning to Time (LeT) and some versions of Scalar Expectancy Theory (SET).

Modelling Chronometric Counting

Participants performed on a temporal generalization task with standard durations being either 4 or 8 s, and comparison durations ranging from 2.5 to 5.5, or 5 to 11 s. They were required to count during all stimulus presentations, and counts were recorded as spacebar presses. Generalization gradients around both standard values peaked at the standard, but the gradient from the 8-s condition was steeper. Measured counts had low variance, both within trials and between trials, and a start process, which was different from the counting sequence, could also be identified in data. A computer model assuming that a comparison duration was identified as the standard when the count value for the comparison was one that had previously occurred for a standard fitted the temporal generalization gradients well. The model was also applied to some published data on temporal reproduction with counting, and generally fitted data adequately. The model makes a distinction between the variance of the count unit from one trial to another, and the counts within the trial, and this distinction was related to the overall variance of behaviours resulting from counting, and the ways in which variability of timing measures change with the duration timed.

Temporal generalization gradients following an interdimensional discrimination protocol.

We investigated the effects of interdimensional discrimination training in the temporal generalization gradient. In a matching-to-sample task, pigeons learned to choose key S after a T-s houselight sample and key NS in the absence of the houselight sample. For one group of pigeons, T = 20 s; for another, T = 10 s. Subsequently, houselight duration was varied to obtain temporal generalization gradients. Results showed that (a) proportion S increased as houselight duration ranged from 0 s to T s and then remained high for houselight durations longer than T; (b) the gradients were well described by negative-exponential functions; (c) these non-flat gradients were present from the beginning of testing, and; (d) the average gradients obtained with T = 20 s and T = 10 s overlapped when plotted in relative time. We conclude that temporal control does not require explicit discrimination training along the temporal dimension, and that temporal generalization gradients obtained with an interdimensional protocol show the scalar property of timing. We discuss how these findings challenge current models of timing.

Animal timing: a synthetic approach.

Inspired by Spence's seminal work on transposition, we propose a synthetic approach to understanding the temporal control of operant behavior. The approach takes as primitives the temporal generalization gradients obtained in prototypical concurrent and retrospective timing tasks and then combines them to synthetize more complex temporal performances. The approach is instantiated by the learning-to-time (LeT) model. The article is divided into three parts. In the first part, we review the basic findings concerning the generalization gradients observed in fixed-interval schedules, the peak procedure, and the temporal generalization procedure and then describe how LeT explains them. In the second part, we use LeT to derive by gradient combination the typical performances observed in mixed fixed-interval schedules, the free-operant psychophysical procedure, the temporal bisection task, and the double temporal bisection task. We also show how the model plays the role of a useful null hypothesis to examine whether temporal control in the bisection task is relative or absolute. In the third part, we identify a set of issues that must be solved to advance our understanding of temporal control, including the shape of the generalization gradients outside the range of trained stimulus durations, the nature of temporal memories, the influence of context on temporal learning, whether temporal control can be inhibitory, and whether temporal control is also relational. These issues attest to the heuristic value of a Spencean approach to temporal control.

The context effect as interaction of temporal generalization gradients: Testing the fundamental assumptions of the Learning-to-Time model

To test the Learning-to-Time model, six pigeons learned two temporal bisection tasks. In one task they learned to choose a Red key over a Green key following 2-s samples and the Green key over the Red key following 6-s samples; in another task, they learned to choose a Blue key over a Yellow key following 6-s samples and the Yellow key over the Blue key following 18-s samples. After each task was learned, temporal generalization gradients were obtained with samples ranging from 0.7s to 51.4s. Finally, preference for Green over Blue – the keys associated with the common 6-s duration, was determined as a function of sample duration. Two issues were examined, whether the preference for Green over Blue increased with sample duration, a transposition-like effect reported before, and whether the preference for Green over Blue could be predicted from the generalization gradients for Green and Blue previously obtained. Results showed that preference for Green over Blue increased with sample duration and that the general shape of the function could be predicted from the generalization gradients. The Learning-to-Time model accounted well for the major trends in the data.This article is part of a Special Issue entitled: SQAB 2012.

THE INTERACTION OF TEMPORAL GENERALIZATION GRADIENTS PREDICTS THE CONTEXT EFFECT

In a temporal double bisection task, animals learn two discriminations. In the presence of Red and Green keys, responses to Red are reinforced after 1-s samples and responses to Green are reinforced after 4-s samples; in the presence of Blue and Yellow keys, responses to Blue are reinforced after 4-s samples and responses to Yellow are reinforced after 16-s samples. Subsequently, given a choice between Green and Blue, the probability of choosing Green increases with the sample duration-the context effect. In the present study we asked whether this effect could be predicted from the stimulus generalization gradients induced by the two basic discriminations. Six pigeons learned to peck Green following 4-s samples (S(+)) but not following 1-s samples (S(-)) and to peck Red following 4-s samples (S(+)) but not following 16-s samples (S(-)). Temporal generalization gradients for Green and Red were then obtained. Finally, the pigeons were given a choice between Green and Red following sample durations ranging from 1 to 16 s. Results showed that a) the two generalization gradients had the minimum at the S(-) duration, an intermediate value between the S(-) and the S(+) durations, and the maximum at the S(+) as well as more extreme durations; b) on choice trials, preference for Green over Red increased with sample duration, the context effect; and c) the two generalization gradients predicted the average context effect well. The Learning-to-Time model accounts for the major trends in the data.

The Effects of Acute Exercise on Temporal Generalization

Sixteen healthy college students performed a multiple-trial referenced temporal generalization task and an episodic temporal generalization task before and during moderate-intensity aerobic exercise. The same tasks were performed in a resting control condition. Working memory tasks were also administered before, during, and after exercise to determine whether exercise affected working memory processes. Temporal generalization gradients demonstrated leftward shifts during exercise when compared to rest, indicating that the subject perceived intervals to elapse more slowly. This finding is consistent with an increased pacemaker speed. Subjective lengthening of stimuli as the task progressed did not occur during exercise or rest. No significant differences were observed on the episodic timing task, nor were any differences found on the working memory tasks. These findings provide support for the notion that exercise influences the internal clock in a manner similar to other arousal-inducing manipulations.

Why Do Temporal Generalization Gradients Change When People Make Decisions as Quickly as Possible?

Three experiments investigated temporal generalization performance under conditions in which participants were instructed to make their decisions as quickly as possible (speed), or were allowed to take their time (accuracy). A previous study (Klapproth & Müller, 2008) had shown that under speeded conditions people were more likely to confuse durations shorter than the standard with the standard than in the accuracy conditions, and a possible explanation of this result is that longer stimulus durations are "truncated" (i.e., people make a judgement about them before they have terminated, thereby shortening their effective duration) and that these truncated durations affect the standard used for the task. Experiment 1 investigated performance under speed and accuracy conditions when comparison durations were close to the standard or further away. No performance difference was found as a function of stimulus spacing, even though responses occurred on average before the longest durations had terminated, but this lack of effect was attributed to "task difficulty" effects changing decision thresholds. In Experiment 2, the standard duration was either the longest or the shortest duration in the comparison set, and differences between speed and accuracy groups occurred only when the comparisons were longer than the standard, supporting the "truncation" hypothesis. A third experiment showed that differences between speed and accuracy groups only occurred if some memory of the standard that was valid for more than one trial was used. In general, the results suggest that the generalization gradient shifts in speeded conditions occur because of truncation of longer comparison durations, which influences the effective standard used for the task.

Timing with opportunity cost: Concurrent schedules of reinforcement improve peak timing

The temporal generalization gradient produced by the peak-interval (PI) procedure reflects behavior under the control of positive reinforcement for responding after the criterial time, but shows negligible discouragement for early responses. The lack of consequences for premature responding may affect estimates of timing accuracy and precision in the PI procedure. In two experiments, we sought to encourage more accurate timing in pigeons by establishing an opportunity cost for such responding. Concurrent ratio and interval schedules of reinforcement reduced the dispersion of keypecking around the target time. A sequence of three response-rate states (low-high-low) characterized performance in individual trials. Opportunity cost substantially reduced the mean and standard deviation of the duration of the middle-high state that typically enveloped the target time, indicating improved temporal acuity. We suggest a model as a first-order approximation to timing with opportunity cost.

More is Still not Better: Testing the Perturbation Model of Temporal Reference Memory across Different Modalities and Tasks

The ability of the perturbation model (Jones & Wearden, 2003) to account for reference memory function in a visual temporal generalization task and auditory and visual reproduction tasks was examined. In all tasks the number of presentations of the standard was manipulated (1, 3, or 5), and its effect on performance was compared. In visual temporal generalization the number of presentations of the standard did not affect the number of times the standard was correctly identified, nor did it affect the overall temporal generalization gradient. In auditory reproduction there was no effect of the number of times the standard was presented on mean reproductions. In visual reproduction mean reproductions were shorter when the standard was only presented once; however, this effect was reduced when a visual cue was provided before the first presentation of the standard. Whilst the results of all experiments are best accounted for by the perturbation model there appears to be some attentional benefit to multiple presentations of the standard in visual reproduction.

Stimulus timing by people with Parkinson’s disease

Previous literature suggests that Parkinson’s disease is marked by deficits in timed behaviour. However, the majority of studies of central timing mechanisms in patients with Parkinson’s disease have used timing tasks with a motor component. Since the motor abnormalities are a defining feature of the condition, the status of timing in Parkinson’s disease remains uncertain. Data are reported from patients with mild to moderate Parkinson’s disease (both on and off medication) and age- and IQ-matched controls on a range of stimulus timing tasks without counting. Tasks used were temporal generalization, bisection, threshold determination, verbal estimation, and a memory for duration task. Performance of patients was generally “normal” on all tasks, but significant differences from performance of controls were found on the memory for duration task. Among the “normal” effects noted were arithmetic mean bisection, asymmetric temporal generalization gradients, and subjective shortening on the memory for duration task. The results suggest (a) that some previous reports of timing “deficits” in Parkinson’s patients were possibly due to the use of tasks requiring a timed manual response and (b) small differences between patients and controls may be found on tasks where two stimuli are presented on each trial, whether patients are on medication or off it.

Detectability and criterion measures in temporal generalization

Computer simulation of performance on "normal" and "episodic" temporal generalization tasks was used to examine the relations between the theoretical parameters of models which fit temporal generalization data ("timing sensitivity" and "threshold"), and the d' (detectability) and beta (decision criterion) measures of signal-detection theory. In general, changes in timing sensitivity altered d', whereas threshold changes affected beta, supporting the assertion that the two sorts of variables ("sensitivity/detectability" and "threshold/criterion") were psychologically equivalent. Cases where temporal generalization gradients were apparently contaminated by "random responding" could be treated by changes in beta, but cases in which temporal generalization gradients were not peaked at the standard posed severe problems for a simple signal-detection account, although existing models of temporal generalization performance could deal with them.

The remembrance of times past: Interference in temporal reference memory.

Six experiments examined human performance on a modified temporal generalization task when either 1 or 2 standard durations were encoded. In most conditions, participants were presented with a 1st standard duration (A), then judged whether a number of comparison stimuli had the same duration as A. They were then presented with a 2nd standard (B) and again judged whether other comparison stimuli had the same duration as B. Then, after a delay period of 0-45 s, further comparison stimuli were presented, and participants judged whether those stimuli had the same duration as A, without A being represented. A was either the same length as B or shorter or longer than it, so potential retroactive interference effects of B on A could be examined. After a short delay before retesting of A comparisons, the peak of the temporal generalization gradient shifted toward the shortest of the comparisons when A < B and the longest when A > B. The results suggest that certain combinations of delay and interference might render the memory of A unusable, so that a new standard is constructed on the basis of the remembered relationship between A and B, a kind of "false memory" for duration.

The Effect of Feedback on Timing in Children and Adults: The Temporal Generalization Task

Children aged 5 and 8 years and adults were tested on a temporal generalization task with a standard duration of 600 ms in a condition with or without corrective feedback. In all conditions, the participants produced orderly temporal generalization gradients, although these were flatter in the younger children, especially in the no-feedback condition. Nevertheless, the results show that the feedback increased the steepness of the generalization gradient in all age groups and in a greater extent in the younger children. Our clock-based model suggested that feedback reduces the variability of the memory representation of the standard duration but also the probability of random responses in the 5-year-olds.

The effect of study-test modalities on the remembrance of subjective duration from long-term memory

It was examined whether stimulus modality (auditory vs. visual) affects the retrieval of subjective duration from memory. In two experiments the temporal generalization paradigm was used. Participants had to decide whether the previously learned standard duration (400 ms) occurred in the context of comparison stimuli. Two major results were found. (1) Discrimination was more accurate if the training and testing stimuli were of the same modality than if they were of opposite modalities. (2) If both modality of learning and modality of testing were different, subjects systematically underestimated the test durations, i.e. temporal generalization gradients (the proportion of identifications of a stimulus as the standard, plotted against stimulus duration) shifted to the right. The observed shift is interpreted as a result of a delayed timing process.

Scalar timing without reference memory? Episodic temporal generalization and bisection in humans.

Three experiments tested whether the scalar property of timing could occur when humans timed short durations under conditions in which it was unlikely that they developed reference memories of temporal "standards". Experiment 1 used an episodic version of a temporal generalization task where judgements were made of the potential equality of two durations presented on each trial. Unknown to the subject, one of these was always 200, 400, 600, or 800 ms, and the other was of variable duration. Temporal generalization gradients showed the scalar property of superimposition at standard values greater than 200 ms. Experiment 2 used a variant of the "roving bisection" method invented by Rodriguez-Girones and Kacelnik (1998) modified so that the scalar property of timing could be observed empirically. Data from bisection with short/long standard pairs of 100/400, 200/800, and 300/1,200 ms showed nearly perfect scalar-type superimposition. Experiment 3 again used episodic temporal generalization, but durations were never repeated and came from three distinct time ranges. Superimposition was found across these ranges except for the shortest visual stimuli timed. The data suggested that scalar timing could occur in humans in conditions where the formation of reference memories of temporal standards was highly improbable.

‘Subjective lengthening’ during repeated testing of a simple temporal discrimination

Three experiments investigated behavioural changes, using a temporal generalization paradigm with human subjects, resulting from repeated testing without feedback. In Experiment 1, different groups received five initial presentations of a 400 ms 500 Hz tone, or a 400 ms 14×14 cm blue square, identified as having a standard duration, then received blocks of testing where stimuli with durations shorter than, longer than, or equal to the standard were presented. Subjects had to judge whether each presented stimulus was the standard duration, but no feedback was given. Temporal generalization gradients (proportion of identifications of a stimulus as being the standard, plotted against stimulus duration) shifted progressively to the right during the test phase (i.e. longer stimuli tended to be identified as the standard as testing proceeded) in the visual stimulus condition. Experiment 2 used a generalization procedure to examine, with different subject groups, behavioural changes when either the duration, or the length, of a blue bar presented on the computer screen was the basis of judgement. Across trials, both length and duration could vary, but for one group only duration was relevant whereas for the other group only length was. Generalization gradients shifted systematically to the right only in duration judgements. Experiment 3 replicated the rightward shift in generalization gradients when the duration of visual stimuli was measured, and in addition used a self-rating scale derived from Thayer [Thayer, R.E., 1967. Measurement of activation through self-report. Psych. Rep. 20, 663–678.) to measure subjects’ arousal. This declined systematically as testing proceeded, suggesting that the shift in temporal generalization gradient was probably caused by an arousal-induced change in internal clock speed.

Scalar timing in temporal generalization in humans with longer stimulus durations.

Three experiments investigated temporal generalization performance in humans by using stimulus durations similar to those previously used with rats. In most conditions, chronometric counting was prevented by concurrent shadowing of temporally irregular numbers. Experiment 1 examined performance with visual stimuli, when the standard was 4.0 s long and nonstandard stimuli were spaced either linearly or logarithmically around the standard. Generalization gradients were asymmetrical with linear spacing but symmetrical with logarithmic spacing, a result obtained previously with humans. Experiment 2 used auditory stimuli and varied the standard across values of 2.0, 4.0, 6.0, and 8.0 s. All gradients were asymmetrical, and good superposition was obtained, indicating conformity to scalar timing. Experiment 3 prevented or encouraged chronometric counting by changing instructions, and temporal generalization gradients differed when counting was and was not used.

Temporal generalization in humans.

In 3 experiments, humans were tested on an analogue of the temporal generalization procedure used by Church and Gibbon (1982) with rats. In Experiment 1, a 400-ms tone was the standard duration, with 6 nonstandard durations spaced in equal arithmetic of logarithmic steps around it. Temporal generalization gradients peaked at the standard, with asymmetry in real time, as stimuli that were longer than the standard produced more yes responses than stimuli that were shorter by the same amount