A drift–diffusion model of interval timing in the peak procedure

Luzardo, Andre; Rivest, François; Alonso, Eduardo; Ludvig, Elliot Andrew

doi:10.1016/j.jmp.2016.10.002

“…Schneider (1969) and subsequently Gibbon and Church (1990) and others Matell et al, 2006) have argued that the pattern of responding is better characterized not by a Gaussian but instead by an approximate squarewave function, with a low-high-low response frequency pattern. It can be shown that by introducing a stop threshold to the timer Ψ i (t), the TDDM timer (used in RWDDM) can fit the data on times of start and stop responding (Luzardo et al, 2017). Alternatively, the accumulator Ψ i (t) itself could be used as the CS representation, replacing x i in equations (9) and (10).…”

Section: Discussionmentioning

confidence: 99%

“…It has been well established experimentally that the CV of time estimates in humans and other animals is approximately constant over a wide timescale (Gibbon, 1977;Gallistel and Gibbon, 2000;Allman et al, 2014). The CV of TDDM's time estimate is (see equation 3 in Luzardo et al, 2017)…”

Section: Modelmentioning

confidence: 99%

A Rescorla-Wagner Drift-Diffusion Model of Conditioning and Timing

Luzardo

¹

,

Alonso

²

,

Mondragón

³

2017

Preprint

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Computational models of classical conditioning have made significant contributions to the theoretic understanding of associative learning, yet they still struggle when the temporal aspects of conditioning are taken into account. Interval timing models have contributed a rich variety of time representations and provided accurate predictions for the timing of responses, but they usually have little to say about associative learning. In this article we present a unified model of conditioning and timing that is based on the influential RescorlaWagner conditioning model and the more recently developed Timing Drift-Diffusion model. We test the model by simulating 10 experimental phenomena and show that it can provide an adequate account for 8, and a partial account for the other 2. We argue that the model can account for more phenomena in the chosen set than these other similar in scope models: CSC-TD, MS-TD, Learning to Time and Modular Theory. A comparison and analysis of the mechanisms in these models is provided, with a focus on the types of time representation and associative learning rule used. Author summaryHow does the time of events affect the way we learn about associations between these events? Computational models have made great contributions to our understanding of associative learning, but they usually do not perform very well when time is taken into account. Models of timing have reached high levels of accuracy in describing timed behaviour, but they usually do not have much to say about associations. A unified approach would involve combining associative learning and timing models into a single framework. This article takes just this approach. It combines the influential Rescorla-Wagner associative model with a timing model based on the Drift-Diffusion process, and shows how the resultant model can account for a number of learning and timing phenomena. The article also compares the new model to others that are similar in scope.PLOS Computational Biology | https://doi

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“…Anticipating when future events will occur is a central component of these predictions and is an important area of research across fields such as psychology and neuroscience, spanning topics including attentional orienting ( Beck et al, 2014 ; Coull et al, 2016 ; Nobre and van Ede, 2018 ), decision-making ( Akdoğan and Balcı, 2017 ; Jazayeri and Shadlen, 2010 ; Luzardo et al, 2017 ; Simen et al, 2016 ), reinforcement learning ( Lau et al, 2017 ; Rivest et al, 2014 ; Sutton, 1988 ), memory storage ( Gallistel, 2017 ; Johansson et al, 2015 ), and treatments for cognitive impairments in disease ( Emmons et al, 2017 ; Gu et al, 2015 ). Temporal expectations can be guided by local sources of information.…”

Section: Introductionmentioning

confidence: 99%

Recalibrating timing behavior via expected covariance between temporal cues

Corte

¹

,

Valle

²

,

Matell

³

2018

eLife

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Individuals must predict future events to proactively guide their behavior. Predicting when events will occur is a critical component of these expectations. Temporal expectations are often generated based on individual cue-duration relationships. However, the durations associated with different environmental cues will often co-vary due to a common cause. We show that timing behavior may be calibrated based on this expected covariance, which we refer to as the ‘common cause hypothesis’. In five experiments using rats, we found that when the duration associated with one temporal cue changes, timed-responding to other cues shift in the same direction. Furthermore, training subjects that expecting covariance is not appropriate in a given situation blocks this effect. Finally, we confirmed that this transfer is context-dependent. These results reveal a novel principle that modulates timing behavior, which we predict will apply across a variety of magnitude-expectations.

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“…Schneider [ 117 ] and subsequently Gibbon and Church [ 118 ] and others [ 119 , 120 ] have argued that the pattern of responding is better characterized not by a Gaussian but instead by an approximate square-wave function, with a low-high-low response frequency pattern. It can be shown that by introducing a stop threshold to the timer Ψ i ( t ), the TDDM timer (used in RWDDM) can fit the data on times of start and stop responding [ 68 ]. Alternatively, the accumulator Ψ i ( t ) itself could be used as the CS representation, replacing x i in eqs (9) and (10) .…”

Section: Discussionmentioning

confidence: 99%

“…It has been well established experimentally that the CV of time estimates in humans and other animals is approximately constant over a wide timescale [ 35 , 67 , 36 ]. The CV of TDDM’s time estimate is [see equation 3 in 68 ] which depends only on the choice of threshold θ and noise factor m . As these are constant, the CV of TDDM’s time estimate is also constant.…”

Section: Modelmentioning

confidence: 99%

A Rescorla-Wagner drift-diffusion model of conditioning and timing

Luzardo

¹

,

Alonso

²

,

Mondragón

³

2017

Self Cite

View full text Add to dashboard Cite

Computational models of classical conditioning have made significant contributions to the theoretic understanding of associative learning, yet they still struggle when the temporal aspects of conditioning are taken into account. Interval timing models have contributed a rich variety of time representations and provided accurate predictions for the timing of responses, but they usually have little to say about associative learning. In this article we present a unified model of conditioning and timing that is based on the influential Rescorla-Wagner conditioning model and the more recently developed Timing Drift-Diffusion model. We test the model by simulating 10 experimental phenomena and show that it can provide an adequate account for 8, and a partial account for the other 2. We argue that the model can account for more phenomena in the chosen set than these other similar in scope models: CSC-TD, MS-TD, Learning to Time and Modular Theory. A comparison and analysis of the mechanisms in these models is provided, with a focus on the types of time representation and associative learning rule used.

show abstract

A drift–diffusion model of interval timing in the peak procedure

Cited by 16 publications

References 40 publications

A Rescorla-Wagner Drift-Diffusion Model of Conditioning and Timing

A Rescorla-Wagner Drift-Diffusion Model of Conditioning and Timing

Recalibrating timing behavior via expected covariance between temporal cues

A Rescorla-Wagner drift-diffusion model of conditioning and timing

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