Michael C. Mozer, Michael Colagrosso, David Huber
We are interested in the mechanisms by which individuals monitor and adjust their performance of simple cognitive tasks. We model a speeded discrimination task in which individuals are asked to classify a sequence of stimuli (Jones & Braver, 2001). Response conﬂict arises when one stimulus class is infrequent relative to another, resulting in more errors and slower reaction times for the infrequent class. How do control pro- cesses modulate behavior based on the relative class frequencies? We explain performance from a rational perspective that casts the goal of individuals as minimizing a cost that depends both on error rate and re- action time. With two additional assumptions of rationality—that class prior probabilities are accurately estimated and that inference is optimal subject to limitations on rate of information transmission—we obtain a good ﬁt to overall RT and error data, as well as trial-by-trial variations in performance.
Consider the following scenario: While driving, you approach an intersection at which the trafﬁc light has already turned yellow, signaling that it is about to turn red. You also notice that a car is approaching you rapidly from behind, with no indication of slowing. Should you stop or speed through the intersection? The decision is difﬁcult due to the presence of two conﬂicting signals. Such response conﬂict can be produced in a psychological labo- ratory as well. For example, Stroop (1935) asked individuals to name the color of ink on which a word is printed. When the words are color names incongruous with the ink color— e.g., “blue” printed in red—reaction times are slower and error rates are higher. We are in- terested in the control mechanisms underlying performance of high-conﬂict tasks. Conﬂict requires individuals to monitor and adjust their behavior, possibly responding more slowly if errors are too frequent.
In this paper, we model a speeded discrimination paradigm in which individuals are asked to classify a sequence of stimuli (Jones & Braver, 2001). The stimuli are letters of the alphabet, A–Z, presented in rapid succession. In a choice task, individuals are asked to press one response key if the letter is an X or another response key for any letter other than X (as a shorthand, we will refer to non-X stimuli as Y). In a go/no-go task, individuals
are asked to press a response key when X is presented and to make no response otherwise. We address both tasks because they elicit slightly different decision-making behavior. In both tasks, Jones and Braver (2001) manipulated the relative frequency of the X and Y stimuli; the ratio of presentation frequency was either 17:83, 50:50, or 83:17. Response conﬂict arises when the two stimulus classes are unbalanced in frequency, resulting in more errors and slower reaction times. For example, when X’s are frequent but Y is presented, individuals are predisposed toward producing the X response, and this predisposition must be overcome by the perceptual evidence from the Y.
Jones and Braver (2001) also performed an fMRI study of this task and found that anterior cingulate cortex (ACC) becomes activated in situations involving response conﬂict. Specif- ically, when one stimulus occurs infrequently relative to the other, event-related fMRI re- sponse in the ACC is greater for the low frequency stimulus. Jones and Braver also ex- tended a neural network model of Botvinick, Braver, Barch, Carter, and Cohen (2001) to account for human performance in the two discrimination tasks. The heart of the model is a mechanism that monitors conﬂict—the posited role of the ACC—and adjusts response biases accordingly. In this paper, we develop a parsimonious alternative account of the role of the ACC and of how control processes modulate behavior when response conﬂict arises.
1 A RATIONAL ANALYSIS
Our account is based on a rational analysis of human cognition, which views cognitive processes as being optimized with respect to certain task-related goals, and being adaptive to the structure of the environment (Anderson, 1990). We make three assumptions of ratio- nality: (1) perceptual inference is optimal but is subject to rate limitations on information transmission, (2) response class prior probabilities are accurately estimated, and (3) the goal of individuals is to minimize a cost that depends both on error rate and reaction time.
The heart of our account is an existing probabilistic model that explains a variety of fa- cilitation effects that arise from long-term repetition priming (Colagrosso, in preparation; Mozer, Colagrosso, & Huber, 2000), and more broadly, that addresses changes in the na- ture of information transmission in neocortex due to experience. We give a brief overview of this model; the details are not essential for the present work.
The model posits that neocortex can be characterized by a collection of information- processing pathways, and any act of cognition involves coordination among pathways. To model a simple discrimination task, we might suppose a perceptual pathway to map the visual input to a semantic representation, and a response pathway to map the semantic representation to a response. The choice and go/no-go tasks described earlier share a per- ceptual pathway, but require different response pathways. The model is framed in terms of probability theory: pathway inputs and outputs are random variables and microinference in a pathway is carried out by Bayesian belief revision.