Journal of Computational Neuroscience

, Volume 28, Issue 1, pp 107–130 | Cite as

Alternative time representation in dopamine models

  • François Rivest
  • John F. Kalaska
  • Yoshua Bengio


Dopaminergic neuron activity has been modeled during learning and appetitive behavior, most commonly using the temporal-difference (TD) algorithm. However, a proper representation of elapsed time and of the exact task is usually required for the model to work. Most models use timing elements such as delay-line representations of time that are not biologically realistic for intervals in the range of seconds. The interval-timing literature provides several alternatives. One of them is that timing could emerge from general network dynamics, instead of coming from a dedicated circuit. Here, we present a general rate-based learning model based on long short-term memory (LSTM) networks that learns a time representation when needed. Using a naïve network learning its environment in conjunction with TD, we reproduce dopamine activity in appetitive trace conditioning with a constant CS-US interval, including probe trials with unexpected delays. The proposed model learns a representation of the environment dynamics in an adaptive biologically plausible framework, without recourse to delay lines or other special-purpose circuits. Instead, the model predicts that the task-dependent representation of time is learned by experience, is encoded in ramp-like changes in single-neuron activity distributed across small neural networks, and reflects a temporal integration mechanism resulting from the inherent dynamics of recurrent loops within the network. The model also reproduces the known finding that trace conditioning is more difficult than delay conditioning and that the learned representation of the task can be highly dependent on the types of trials experienced during training. Finally, it suggests that the phasic dopaminergic signal could facilitate learning in the cortex.


Dopamine Reward Interval-timing Trace conditioning Reinforcement learning Representation learning 



We are grateful to Douglas Eck, Aaron Courville, Doina Precup, and many others for discussion in the development of the present work. This manuscript also profited from the comments of Pascal Fortier-Poisson and Elliot Ludvig, as well as from the anonymous reviewers. F.R. was supported by doctoral studentships from the New Emerging Team Grant in Computational Neuroscience (CIHR) and from the Groupe de recherche sur le système nerveux central (FRSQ). Y.B and J.K. were supported by the CIHR New Emerging Team Grant in Computational Neuroscience and an infrastructure grant from the FRSQ.

Supplementary material

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Supplemental Pseudocode (DOC 71 kb)
10827_2009_191_MOESM2_ESM.doc (820 kb)
Supplemental Tables and Figures (DOC 820 kb)


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • François Rivest
    • 1
    • 2
    • 3
  • John F. Kalaska
    • 1
    • 3
  • Yoshua Bengio
    • 1
    • 2
  1. 1.Groupe de Recherche sur le Système Nerveux Central (FRSQ)Université de MontréalMontréalCanada
  2. 2.Département d’informatique et de recherche opérationnelleUniversité de MontréalMontréalCanada
  3. 3.Département de physiologieUniversité de MontréalMontréalCanada

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