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Neurobiological Models of Two-Choice Decision Making Can Be Reduced to a One-Dimensional Nonlinear Diffusion Equation

By Alex Roxin and Anders Ledberg

Abstract

The response behaviors in many two-alternative choice tasks are well described by so-called sequential sampling models. In these models, the evidence for each one of the two alternatives accumulates over time until it reaches a threshold, at which point a response is made. At the neurophysiological level, single neuron data recorded while monkeys are engaged in two-alternative choice tasks are well described by winner-take-all network models in which the two choices are represented in the firing rates of separate populations of neurons. Here, we show that such nonlinear network models can generally be reduced to a one-dimensional nonlinear diffusion equation, which bears functional resemblance to standard sequential sampling models of behavior. This reduction gives the functional dependence of performance and reaction-times on external inputs in the original system, irrespective of the system details. What is more, the nonlinear diffusion equation can provide excellent fits to behavioral data from two-choice decision making tasks by varying these external inputs. This suggests that changes in behavior under various experimental conditions, e.g. changes in stimulus coherence or response deadline, are driven by internal modulation of afferent inputs to putative decision making circuits in the brain. For certain model systems one can analytically derive the nonlinear diffusion equation, thereby mapping the original system parameters onto the diffusion equation coefficients. Here, we illustrate this with three model systems including coupled rate equations and a network of spiking neurons

Topics: Research Article
Publisher: Public Library of Science
OAI identifier: oai:pubmedcentral.nih.gov:2268007
Provided by: PubMed Central
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    1. (1886) The time taken up by cerebral operations.
    2. (1890) The time-relations of mental phenomena.
    3. (2006). A biophysically based neural model of matching law behavior: melioration by stochastic synapses.
    4. (2003). A comparison of macaque behavior and superior colliculus neuronal activity to predictions from models of twochoice decisions.
    5. (2004). A comparison of sequential sampling sampling models for two-choice reaction time.
    6. (2007). A neural circuit model of flexible sensorimotor mapping: learing and forgetting on multiple timescales.
    7. (2006). A recurrent network mechanism of time integration in perceptual decisions.
    8. (1995). Applied nonlinear dynamics.
    9. (1999). Connectionist and diffusion models of reaction time.
    10. (2006). Cortico-basal ganglia circuit mechanism for a decision threshold in reaction time tasks.
    11. (2001). Effects of synaptic noise and filtering on the frequency response of spiking neurons.
    12. (1999). Fast global oscillations in networks of integrate-andfire neurons with low firing rates.
    13. (2005). Flexible control of mutual inhibition: A neural model of two-interval discrimination.
    14. (2006). Integrated neural processes for defining potential actions and deciding between them: A computational model.
    15. (1995). Introduction to perturbation methods.
    16. (2001). Making choices: the neurophysiology of visual-saccadic decision making.
    17. (2003). Microstimulation of visual cortex affects the speed of perceptual decisions.
    18. (1997). Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex.
    19. (1998). Modeling response times for two-choice decisions.
    20. (2001). Modelling a simple choice task: Stochastic dynamics of mutually inhibitory neural groups.
    21. (1960). Models for choice reaction time.
    22. (1996). Motion perception: Seeing and deciding.
    23. (2005). Neural activity in macaque parietal cortex reflects temporal integration of visual motion signals during perceptual decision making.
    24. (2001). Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey.
    25. (2001). Neural basis of deciding, choosing and acting.
    26. (2007). Neural circuit dynamics underlying accumulation of time-varying evidence during perceptual decisionmaking. Frontiers Comput Neurosci; In press.
    27. (2001). Neural computations that underlie decisions about sensory stimuli.
    28. (1999). Neural correlates of a decision in the dorsolateral prefrontal cortex of the macaque.
    29. (1994). Nonlinear dynamics and chaos.
    30. (1992). Numerical recipes in C. Cambridge: Cambridge University Press. A Nonlinear Diffusion Equation for Decision Making PLoS
    31. (1981). Oculomotor procrastination.
    32. (1969). On the speed of mental processes.
    33. (2007). Optimal decision-making theories: linking neurobiology with behaviour.
    34. (1993). Pattern formation outside of equilibrium.
    35. (2002). Probabilistic decision making by slow reverberation in cortical circuits.
    36. (2004). Psychology and neurobiology of simple decisions.
    37. (2002). Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task.
    38. (1986). Response times, 1st edition.
    39. (1993). Responses of neurons in macaque mt to stochastic motion signals. Vis Neurosci 10: 1157–1169. A Nonlinear Diffusion Equation for Decision Making PLoS
    40. (1999). Separate signals for target selection and movement specification in the superior colliculus.
    41. (2005). Simple neural networks that optimize decisions.
    42. (1983). Synergetics.
    43. (2001). Target selection for saccadic eye movements: Prelude activity in the superior colliculus during a directiondiscrimination task.
    44. (2007). The basal ganglia and cortex implement optimal decision making between alternative options.
    45. (2005). The effect of stimulus strength on the speed and accuracy of a perceptual decision.
    46. (2006). The physics of optimal decision making: a formal analysis of models of performance in twoalternative forced-choice tasks.
    47. (2001). The time course of perceptual choice: The leaky, competing accumulator model.
    48. (1978). Theory of memory retrieval.
    49. (2001). Touch and go: Decision-making mechanisms in somatosensation.

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