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We develop piecewise-linear and purely linear models, and one-dimensional reductions to Ornstein\u2013Uhlenbeck 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\u2013Uhlenbeck 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. <\/jats:p>","DOI":"10.1142\/s0218127405012478","type":"journal-article","created":{"date-parts":[[2005,5,31]],"date-time":"2005-05-31T12:20:40Z","timestamp":1117542040000},"page":"803-826","source":"Crossref","is-referenced-by-count":80,"title":["SIMPLE NEURAL NETWORKS THAT OPTIMIZE DECISIONS"],"prefix":"10.1142","volume":"15","author":[{"given":"ERIC","family":"BROWN","sequence":"first","affiliation":[{"name":"Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JUAN","family":"GAO","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PHILIP","family":"HOLMES","sequence":"additional","affiliation":[{"name":"Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA"},{"name":"Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"RAFAL","family":"BOGACZ","sequence":"additional","affiliation":[{"name":"Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA"},{"name":"Department of Psychology, Princeton University, Princeton, NJ 08544, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MARK","family":"GILZENRAT","sequence":"additional","affiliation":[{"name":"Department of Psychology, Princeton University, Princeton, NJ 08544, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JONATHAN D.","family":"COHEN","sequence":"additional","affiliation":[{"name":"Department of Psychology, Princeton University, Princeton, NJ 08544, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","unstructured":"L.\u00a0Abbott, Neural Networks: From Biology to High-Energy Physics, eds. 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