Simple neural networks that optimize decisions

Eric Brown, Juan Gao, Philip Holmes, Rafal Bogacz, Mark Gilzenrat, Jonathan D. Cohen

Research output: Contribution to journalArticlepeer-review

80 Scopus citations


We review simple connectionist and firing rate models for mutually inhibiting pools of neurons that discriminate between pairs of stimuli. Both are two-dimensional nonlinear stochastic ordinary differential equations, and although they differ in how inputs and stimuli enter, we show that they are equivalent under state variable and parameter coordinate changes. A key parameter is gain: the maximum slope of the sigmoidal activation function. We develop piecewise-linear and purely linear models, and one-dimensional reductions to Ornstein-Uhlenbeck processes that can be viewed as linear filters, and show that reaction time and error rate statistics are well approximated by these simpler models. We then pose and solve the optimal gain problem for the Ornstein-Uhlenbeck processes, finding explicit gain schedules that minimize error rates for time-varying stimuli. We relate these to time courses of norepinephrine release in cortical areas, and argue that transient firing rate changes in the brainstem nucleus locus coeruleus may be responsible for approximate gain optimization.

Original languageEnglish (US)
Pages (from-to)803-826
Number of pages24
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number3
StatePublished - Mar 2005

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics


  • Decision task
  • Gain
  • Locus coeruleus
  • Matched filter
  • Neural network model
  • Optimal speed and accuracy
  • Reaction time
  • Stochastic differential equation


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