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Summary: International Journal of Bifurcation and Chaos, Vol. 15, No. 3 (2005) 803826
c World Scientific Publishing Company
SIMPLE NEURAL NETWORKS THAT
OPTIMIZE DECISIONS
ERIC BROWN, JUAN GAO, PHILIP HOLMES,, RAFAL BOGACZ,,
MARK GILZENRAT, and JONATHAN D. COHEN
Program in Applied and Computational Mathematics,
Department of Mechanical and Aerospace Engineering,
Department of Psychology,
Princeton University, Princeton, NJ 08544, USA
Received April 2, 2004; Revised July 7, 2004
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 ordi-
nary 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 parame-
ter is gain: the maximum slope of the sigmoidal activation function. We develop piecewise-linear
and purely linear models, and one-dimensional reductions to OrnsteinUhlenbeck 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 OrnsteinUhlenbeck processes, finding explicit gain schedules that minimize error rates for
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