A Computational Model of Prefrontal 
Cortex Function 
Todd S. Braver 
Dept. of Psychology 
Carnegie Mellon Univ. 
Pittsburgh, PA 15213 
Jonathan D. Cohen 
Dept. of Psychology 
Carnegie Mellon Univ. 
Pittsburgh, PA 15213 
D avid Servan- S chreib er 
Dept. of Psychiatry 
Univ. of Pittsburgh 
Pittsburgh, PA 15232 
Abstract 
Accumulating data from neurophysiology and neuropsychology 
have suggested two information processing roles for prefrontal cor- 
tex (PFC): 1) short-term active memory; and 2) inhibition. We 
present a new behavioral task and a computational model which 
were developed in parallel. The task was developed to probe both 
of these prefrontal functions simultaneously, and produces a rich 
set of behavioral data that act as constraints on the model. The 
model is implemented in continuous-time, thus providing a natural 
framework in which to study the temporal dynamics of processing 
in the task. We show how the model can be used to examine the be- 
havioral consequences of neuromodulation in PFC. Specifically, we 
use the model to make novel and testable predictions regarding the 
behavioral performance of schizophrenics, who are hypothesized to 
suffer from reduced dopaminergic tone in this brain area. 
I Introduction 
Prefrontal cortex (PFC) is an area of the human brain which is significantly ex- 
panded relative to other animals. There is general consensus that the PFC is cen- 
trally involved in higher cognitive activities such as planning, problem solving and 
language. Recently, the PFC has been associated with two specific information pro- 
cessing mechanisms: short-term active memory and inhibition. Active memory is 
the capacity of the nervous system to maintain information in the form of sustained 
activation states (e.g., cell firing) for short periods of time. This can be distin- 
guished from forms of memory that are longer in duration and are instantiated as 
142 Todd $. Braver, Jonathan D. Cohen, David Servan-Schreiber 
modified values of physiological parameters (e.g., synaptic strength). Over the last 
two decades, there have been a large number of neurophysiological studies focusing 
on the cellular basis of active memory in prefrontal cortex. These studies have re- 
vealed neurons in PFC that fire selectively to specific stimuli and response patterns, 
and that remain active during a delay between these. Investigators such as Fuster 
(1989) and Goldman-Rakic (1987) have argued from this data that PFC maintains 
temporary information needed to guide behavioral responses through sustained pat- 
terns of neural activity. This hypothesis is consistent with behavioral findings from 
both animal and human lesion studies, which suggest that PFC is required for tasks 
involving delayed responses to prior stimuli (Fuster, 1989; Stuss g Benson, 1986). 
In addition to its role in active memory, many investigators have focused on the 
inhibitory functions of PFC. It has been argued that PFC representations are re- 
quired to overcome reflexive or previously reinforced response tendencies in order 
to mediate a contextually appropriate - but otherwise weaker - response (Cohen &: 
Servan-Schreiber, 1992). Clinically, it has been observed that lesions to PFC are of- 
ten associated with a syndrome of behavioral disinhibition, in which patients act in 
impulsive and often socially inappropriate ways (Stuss &: Benson, 1986). This syn- 
drome has often been cited as evidence that PFC plays an important role inhibiting 
behaviors which are compelling but socially inappropriate. 
While the involvement of PFC in both active memory and inhibition is generally 
agreed upon, computational models can play an important role in providing mech- 
anisms by which to explain how these two information processing functions arise. 
There are several computational models now in the literature which have focused 
on either the active memory (Zipser, 1991), or inhibitory (Levine &: Pruiett, 1989) 
functions of PFC, or both functions together (Dehaene g Changeux, 1989; Co- 
hen &: Servan-Schreiber, 1992). These models have been instrumental in explaining 
the role of PFC in a variety of behavioral tasks (e.g., the Wisconsin Card Sort and 
Stroop). However, these earlier models are limited by their inability to fully cap- 
ture the dynamical processes underlying active memory and inhibition. Specifically, 
none of the simulations have been tightly constrained by the temporal parameters 
found in the behavioral tasks (e.g., durations of stimuli, delay periods, and response 
latencies). This limitation is not found solely in the models, but is also a feature of 
the behavioral tasks themselves. The tasks simulated were not structured in ways 
that could facilitate a dynamical analysis of processing. 
In this paper we address the limitations of the previous work by describing both a 
new behavioral task and a computational model of PFC. These have been developed 
in parallel and, together, provide a useful framework for exploring the temporal 
dynamics of active memory and inhibition and their consequences for behavior. We 
then go on to describe how this framework can be used to examine neuromodulatory 
effects in PFC, which are believed to play a critical role in both normal functioning 
and in psychiatric disorders, such as schizophrenia. 
2 Behavioral Assessment of Human PFC Function 
We have developed a task paradigm which incorporates two components central to 
the function of prefrontal cortex - short-term active memory and inhibition - and 
that can be used to study the dynamics of processing. The task is a variant of the 
continuous performance test (CPT), which is commonly used to study attention in 
A Computational Model of Prefrontal Cortex Function 143 
behavioral and clinical research. In a standard version of the task (the CPT-AX), 
letters are presented one at a time in the middle of a computer screen. Subjects are 
instructed to press the target button to the letter X (probe stimulus) but only when 
it is preceded by an A (the cue stimulus). In previous versions of the CPT, subjects 
only responded on target trials. In the present version of the task, a two response 
forced-choice procedure is employed; on non-A-X trials subjects are asked to press 
the non-target button. This procedure allows for response latencies to be evaluated 
on every trial, thus providing more information about the temporal dimensions of 
processing in the task. 
Two additional modifications were made to the standard paradigm in order to 
maximally engage PFC activity. The memory function of PFC is tapped by ma- 
nipulating the delay between stimuli. In the CPT-AX, the prior stimulus (cue or 
non-cue) provides the context necessary to decide how to respond to the probe let- 
ter. However, with a short delay (750 msec.), there is little demand on memory 
for the prior stimulus. This is supported by evidence that PFC lesions have been 
shown to have no effect on performance when there is only a short delay (Stuss & 
Benson, 1986). With a longer delay (5000 msec.), however, it becomes necessary to 
maintain a representation of the prior stimulus in order for it to be used as context 
for responding to the current one. The ability of the PFC to sustain contextual 
representations over the delay period can be determined behaviorally by comparing 
performance on short delay trials (50%) against those with long delays (50%). 
The inhibitory function of PFC is probed by introducing a prepotent response 
tendency that must be overcome to respond correctly. This tendency is introduced 
into the task by increasing the frequency of target trials (A followed by X). In the 
remaining trials, there are three types of distractors: 1) a cue followed by a non- 
target probe letter (e.g., A-Y); 2) a non-cue followed by the target probe letter (e.g., 
B-X); and a non-cue followed by a non-target probe letter (e.g., B-Y). Target trials 
occur 70% of the time, while each type of distractor trial occurs only 10% of the 
time. The frequency of targets promotes the development of a strong tendency to 
respond to the target probe letter whenever it occurs, regardless of the identity of 
the cue (since a response to the X itself is correct 7 out of 8 times). 
The ability to inhibit this response tendency can be examined by comparing accu- 
racy on trials when the target occurs in the absence of the cue (B-X trials), with 
those made when neither the cue nor target occurs (i.e., B-Y trials, which provide a 
measure of non-specific response bias and random responding). Trials in which the 
cue but not the target probe appears (A-Y trials) are also particularly interesting 
with respect to PFC function. These trials measure the cumulative influence of 
active representations of context in guiding responses. In a normally functioning 
system, context representations should stabilize and increase in strength as time 
progresses. Thus, it is expected that A-Y accuracy will tend to decrease for long 
delay trials relative to short ones. 
As mentioned above, the primary benefit of this paradigm is that it provides a 
framework in which to simultaneously probe the inhibitory and memory functions 
associated with PFC. This is supported by preliminary neuroimaging data from 
our laboratory (using PET) which suggests that PFC is, in fact, activated during 
performance of the task. Although it is simple in structure, the task also generates 
a rich set of behavioral data. There are four stimulus conditions crossed with two 
delay conditions for which both accuracy and reaction time performance can be 
144 Todd S. Braver, Jonathan D. Cohen, David Servan-Schreiber 
lOO 
 80 
 70 
6o 
750 
Accuracy (Short Delay) Accuracy (Long Delay) 
 MODEL (Acc) I 
ODATA (Acc) 
RT (Short Delay) RT (Long Delay) 
650 
550 
dS0 
350 
250 ' ' BX BJY L ' * B'Y 
AX AY AX AY BX 
Trial Condition Trial Condition 
 MODEL (Correct) 
--- MODEL (Incorrect) 
 DATA (Correct) 
V DATA (Incorrect) 
Figure 1: Subject behavioral data with model performance superimposed. Top Panels: Accuracy across 
both delays in all four conditions. Bottom Panels: Reaction times for both correct and incorrect responses in 
all conditions. Bars represent standard error of measurement for the empirical data. 
measured. Figure 1 shows data gathered from 36 college-age subjects performing 
this task. 
In brief, we found that: 1) Accuracy was relatively unchanged in the long delays 
compared to the short, demonstrating that active memory was adequately support- 
ing performance; 2) A-Y accuracy, however, did slightly decrease at long delays, 
reflecting the normal build-up of context representations over time; 3) Accuracy 
on B-X trials was relatively high, supporting the assumption that subjects could 
effectively use context representations to inhibit prepotent responses; 4) A distinct 
pattern emerged in the latencies of correct and incorrect responses, providing in- 
formation on the temporal dynamics of processing (i.e., responses to A-Y trials are 
slow on correct trials and fast on incorrect ones; the pattern is reversed for B-X tri- 
als). Taken together, the data provides specific, detailed information about normal 
PFC functioning, which act as constraints on the development and evaluation of a 
computational model. 
3 A Computational Model of the CPT-AX 
We have developed a recurrent network model which produces detailed information 
regarding the temporal course of processing in the CPT-AX task. The network is 
composed of three modules: an input module, a memory module, and an output 
module. The memory module implements the memory and inhibitory functions 
believed to be carried out by PFC. Figure 2 shows a diagram of the model. 
Each unit in the input module represents a different stimulus condition: A, B, X & 
A Computational Model of Prefrontal Cortex Function 145 
OUTPUT LAYER 
INPUT LAYER 
Figure 2: A diagram of the CPT-AX model. 
Y. Units in the input module make excitatory connections on the response module, 
both directly and indirectly through the memory module. Lateral inhibition within 
each layer produces competition for representations. Activity from the cue stimulus 
flows to the memory module, which is responsible for maintaining a trace of the 
relevant context in each trial. Units in the memory module have self-excitatory 
connections, which allow for the activity generated by the cue to be sustained in 
the absence of input. The recurrent connectivity utilized by each unit in this module 
is assumed to be a simpler, but formally equivalent analogue of a fully connected 
recurrent cell assembly. Further, Zipser (1991) has used this type of connectivity to 
produce temporal activity patterns which are highly similar to the firing patterns 
of neurons in memory-associated areas of cortex, such as PFC. Activity from the 
input and memory modules is integrated in the output module. The output of this 
module determines whether a target (T) or non-target (N) response is made. 
To simulate the CPT-AX task we have purposefifily kept the network architecture 
and size as simple as possible in order to maximize the model's interpretability. We 
have therefore not attempted to simulate neural information processing in a neuron- 
by-neuron manner. Rather, the populations of a few units are seen as capturing the 
information processing characteristics of much larger populations of real neurons. 
In this way, it is possible to capture the stochastic, distributed, and dynamical 
properties of real neural networks with small and analytically tractable simulations. 
The simulation is run in a temporally continuous framework in which processing is 
governed by the following difference equation: 
Ij(t -t- 1) = (7 E wijyi -t- fl- Ij(t))dt (1) 
i 
where 
1 
= 1 + (2) 
is the state of unit j, Ij is the total input to j, dt is the time-step of integration, 7 
is the gain and  is the bias. The continuous framework is preferable to a discrete 
event-based one in that it allows for a plausible way to scale events appropriately 
to the exact temporal specifications of the task (i.e., the duration of stimuli and 
the delay between cue and probe). In addition, the continuous character of the 
simulation naturally provides a framework for inferring the reaction times in the 
various conditions. 
146 Todd S. Braver, Jonathan D. Cohen, David Servan-Schreiber 
4 Simulations of Behavioral Performance 
We used a continuous recurrent generalization of backpropagation (Pearlmutter, 
1989) to train the network to perform the CPT-AX. All of the connection weights 
were developed entirely by the training procedure, with the constraint that that all 
self and between layer weights were forced to be positive and all within layer weights 
were forced to be negative. Training consisted of repeated presentation of each of 
the 8 conditions in the task (A-X,A-Y,B-X,B-Y, at both long and short delays), with 
the presentation frequency of each condition matching that of the behavioral task. 
Weights were updated after the presentation of each trial, biases (fl) were fixed at 
-2.5, and dt was set at 0.1. The network was trained deterministically; completion 
of training occurred when network accuracy reached 100% for each condition. 
Following training, weights were fixed. Errors and reaction time distributions were 
then simulated by adding zero-mean Gaussian noise to the net input of each unit 
at every time step during trial presentation. A trial consisted of the presentation 
of the cue stimulus, a delay period and then the probe stimulus. As mentioned 
above, the duration of these events was appropriately scaled to match the temporal 
parameters of the task (e.g., 300 msec. duration for cue and probe presentation, 
750 msec. for short delays, 5000 msec. for long delays). A time constant (r) of 50 
msec. was used for simulation in the network. This scaling factor provided sufficient 
temporal resolution to capture the relationship between the two task delays while 
still permitting a tractable way of simulating the events. 
Responses were determined by noting which output unit reached a threshold value 
first following presentation of the probe stimulus. Response latency was determined 
by calculating the number of time steps taken by the model to reach threshold 
multiplied by the time constant r. To facilitate comparisons with the experimental 
reaction times, a constant k was added to all values produced. This parameter might 
correspond to the time required to execute a motor response. The value of k was 
determined by a least mean squares fit to the data. 1000 trials of each condition 
were run in order to obtain a reliable estimate of performance under stochastic 
conditions. The standard deviation of the noise distribution (r) and the threshold 
(T) of the response units were adjusted to produce the best fit to the subject data. 
Figure 1 compares the results of the simulation against the behavioral data. 
As can be seen in the figure, the model provides a good fit to the behavioral data 
in both the pattern of accuracy and reaction times. The model not only matches 
the qualitative pattern of errors and reaction times but produces very similar quan- 
titative results as well. The match between model and experimental results is par- 
ticularly striking when it is considered that there are a total of 24 data points that 
this model is fitting, with only 4 free parameters (a,T,r,k). The model's ability to 
successfully account for the pattern of behavioral performance provides convincing 
evidence that it captures the essential principles of processing in the task. We can 
then feel confident in not only examining normal processing, but also in extending 
the model to explore the effects of specific disturbances to processing in PFC. 
5 Behavioral Effects of Neuromodulation in PFC 
In a previous meeting of this conference a simulation of a simpler version of the CPT 
was discussed (Servan-Schreiber, Printz, & Cohen, 1990). In this simulation the 
A Computational Model of Prefrontal Cortex Function 147 
100 
90 
80 
70 
60 
Accuracy (Short Delay) 
I L I I 
AX AY BX BY 
Accuracy (Long Delay) 
I I I I 
I I I I 
AX AY BX BY 
MODEL (Normal Gain) 
--- MODEL (Reduced Gain) 
 DATA (Controls) 
Figure 3: Comparision of of model performance with normal and reduced gain. The graph illustrates the effect 
of reducing gain in the memory layer on task performance. In the baseline network q=l, in the reduced-gain 
network 3'=0.8. 
effects of system-wide changes in catecholaminergic tone were captured by changing 
the gain (7) parameter of network units. Changes in gain are thought correspond to 
the action of modulatory neurotransmitters in modifying the responsivity of neurons 
to input signals (Servan-Schreiber et al., 1990; Cohen & Servan-Schreiber, 1992). 
The current simulation of the CPT offers the opportunity to explore the effects 
of neuromodulation on the information processing functions specific to PFC. The 
transmitter dopamine is known to modulate activity in PFC, and manipulations 
to prefrontal dopamine have been shown to have effects on both memory-related 
neuronal activity and behavioral performance (Sawaguchi & Goldman-Rakic, 1991). 
Furthermore, it has been hypothesized that reductions of the neuromodulatory ef- 
fects of dopamine in PFC are responsible for some of the information processing 
deficits seen in schizophrenia. To simulate the behavior of schizophrenic subjects, 
we therefore reduce the gain (7) of units in the memory module of the network. 
With reduced gain in the memory module, there are striking changes in the model's 
performance of the task. As can be seen in Figure 3, in the short delay conditions 
the performance of the reduced-gain model is relatively similar to that of control 
subjects (and the intact model). However, at long delays, the reduced-gain model 
produces a qualitatively different pattern of performance. In this condition, the 
model has a high B-X error rate but a low A-Y error rate, a pattern which is opposite 
to that seen in the control subjects. This double dissociation in performance is a 
robust effect of the reduced-gain simulation (i.e., it seems relatively uninftuenced 
by other parameter adjustments). 
Thus, the model makes clear-cut predictions which are both novel and highly 
testable. Specifically, the model predicts that: 1) Differences in performance be- 
148 Todd S. Braver, Jonathan D. Cohen, David Servan-Schreiber 
tween control and schizophrenic subjects will be most apparent at long delays; 2) 
Schizophrenics will perform significantly worse than control subjects on B-X trials 
at long delays; 3) Schizophrenics will perform significantly better than control sub- 
jects on A-Y trials at long delays. This last prediction is especially interesting given 
the fact that tasks in which schizophrenics show superior performance relative to 
controls are relatively rare in experimental research. 
Furthermore, the model not only makes predictions regarding schizophrenic behav- 
ioral performance, but also offers explanations as to their mechanisms. Analyses of 
the trajectories of activation states in the memory module reveals that both of the 
dissociations in performance are due to failures in maintaining representations of 
the context set tip by the cue stimulus. Reducing gain in the memory module blurs 
the distinction between signal and noise, and causes the context representations to 
decay over time. As a result, in the long delay trials, there is a higher probability 
that the model will show both failtires of inhibition (more B-X errors) and memory 
(less A-Y errors). 
6 Conclusions 
The results of this paper show how a computational analysis of the temporal dynam- 
ics of PFC information processing can aid in understanding both normal and dis- 
turbed behavior. We have developed a behavioral task which simultaneously probes 
both the inhibitory and active memory functions of PFC. We have used this task in 
combination with a computational model to explore the effects of neuromodulatory 
dysfunction, making specific predictions regarding schizophrenic performance in the 
CPT-AX. Confirmation of these predictions now await further testing. 
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