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The Journal of Neuroscience, January 1, 1998, 18(1):399-410
A Model That Accounts for Activity in Primate Frontal Cortex
during a Delayed Matching-to-Sample Task
Sohie Lee
Moody1, 2,
Steven P.
Wise2,
Giuseppe
di Pellegrino2, and
David
Zipser1
1 Cognitive Science Department, University of
California, San Diego, La Jolla, California 92093-0515, and
2 Laboratory of Systems Neuroscience, National Institute of
Mental Health, Poolesville, Maryland 20837
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ABSTRACT |
A fully recurrent neural network model was optimized to perform a
spatial delayed matching-to-sample task (DMS). In DMS, a stimulus is
presented at a sample location, and a match is reported when a
subsequent stimulus appears at that location. Stimuli elsewhere are
ignored. Computationally, a DMS system could consist of memory and
comparison components. The model, although not constrained to do so,
worked by using two corresponding classes of neurons in the hidden
layer: storage and comparator units. Storage units form a dynamical
system with one fixed point attractor for each sample location.
Comparator units constitute a system receiving input from these storage
units as well as from current input stimuli. Both unit types were tuned
directionally. These two sources of information combine to create
unique patterns of activity that determine whether a match has
occurred. In networks with abundant hidden units, the storage and
comparator functions were distributed so that individual units took
part in both. We compared the model with single-neuron recordings from
premotor (PM) and prefrontal (PF) cortex. As shown previously, many PM
and PF neurons behaved like storage units. In addition, both regions
contain neurons that behave like the comparator units of the model and
appear to have dual functionality similar to that observed in the model units. No neuron in either area had properties identical to those of
the match output neuron of the model. However, four PF neurons and one
PM neuron resembled the output signal more closely than any of the
hidden units of the model.
Key words:
model; attractor; prefrontal; premotor; neural network; matching-to-sample; comparator
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INTRODUCTION |
Delayed matching-to-sample tasks
(DMS) have been important in studying the neural basis of short-term
memory. In spatial versions of these tasks, a stimulus is presented at
one location as a sample. Later, stimuli (termed
current stimuli) are presented at either the location of the
sample (matches) or at different locations (distractors). Matches are to be reported. DMS requires two
major functional components: (1) memory, buffered against distractors, to hold the sample; and (2) comparison of current and stored stimuli to
detect matches. From a computational viewpoint, these two functions can
be implemented using an attractor neural network, which has stable
points to store the sample value, and a filter to detect matches.
The first of the two functional components of a DMS network have been
studied in both theoretical work and neural modeling. Short-term
information storage can be accounted for by fixed point attractor
dynamics of neural activity in recurrently connected networks (Cowan,
1972 ; Zipser, 1991; Amit and Brunel, 1995; Zhang, 1996). Furthermore,
neuronal activity consistent with this mode of information storage has
been reported widely, e.g., in prefrontal (Fuster and Alexander, 1971),
supplementary motor (Tanji et al., 1980), premotor (Weinrich and Wise,
1982), primary motor (Evarts and Tanji, 1976), somatosensory (Zhou and
Fuster, 1996), posterior parietal (Crammond and Kalaska, 1989),
auditory (Vaadia et al., 1982), and visual (Mikami and Kubota, 1980)
cortex. Buffering of stored information against distractor events has
also been reported. It appears to occur in frontal cortex (di
Pellegrino and Wise, 1993a,b; Miller et al., 1996) but not in temporal
(Miller et al., 1996) or posterior parietal areas (Steinmetz et al.,
1994; Steinmetz and Constantinidis, 1995). Recent neuroimaging studies have yielded corresponding results in human subjects regarding storage
and buffering (Cohen et al., 1997; Courtney et al., 1997). However, the
second component of a DMS network, involving comparison and matching,
has not been addressed.
To investigate how the brain may implement both major components of a
DMS network, we trained a recurrent neural network to perform spatial
DMS. This approach, called neural systems identification, has been shown to generate realistic models (Zipser and Anderson, 1988). Analysis of the trained network revealed that the underlying computational solution indeed uses an attractor network to store sample
information, as well as a set of comparator neurons, the combined
action of which approximates a match filter. The implementation of the
model involved specific features that are not obvious consequences of
the basic computational mechanism, such as directional tuning of both
the attractor network and the comparator neurons, together with a
considerable degree of distributed function. When frontal cortex
activity was compared with the model, directionally tuned units
resembling comparator and attractor network neurons were found, along
with evidence for distributed function. These results suggest that a
computational solution similar to that in our model may be implemented
in a network that includes frontal cortex neurons.
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MATERIALS AND METHODS |
Modeling methods. The model described in this paper
was generated using a technique called neural systems identification
(NSI) (Zipser, 1992). As this technique was applied here, an initially randomly weighted, fully recurrent network of simple model neurons was
trained to emulate the input-output behavior conjectured to occur in
frontal cortex during the DMS task. Neural systems identification differs from most conventional modeling techniques in that the model is
generated from a general conjecture about the function of a brain
area, rather than being constructed from detailed knowledge or
hypotheses about the internal structure of that area. This approach has
the advantage that identification models often generate mechanisms that
otherwise would not be considered. Moreover, NSI spawns model neurons
with response properties closely resembling those of cortical neurons.
Identification models, in their current form, have the disadvantage
that they are limited in the amount of realistic detail they provide.
They generally give information only about the average activity of
component neurons.
Neural systems identification generates models by adjusting the
synaptic weights recurrently connecting the internal, or hidden, units
in the network so that they function to perform the desired input-output behavior. The process of evolving a set of synaptic weights that minimizes the error produced by the network is called optimization or "training." The results are typically independent of the exact optimization procedure used, because the set of possible final configurations of the model depends on the task rather than on
how the optimization was done. For the model described here we used a
gradient descent, error correction optimization algorithm for recurrent
networks, called back-propagation through time (Williams and Zipser,
1995). Because the functions of the hidden units develop during the
model generation process and are not specified at the beginning of
training, post hoc analysis of the mechanisms of the model
for solving the input output transform may yield insight into how
biological networks may solve similar problems.
The model network is shown in Figure 1.
It consists of a set of fully interconnected model neurons, simulated
with logistic functions. The model is implemented by the system of
nonlinear difference equations shown below:
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(1)
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where yj(t) are the
output values of all other model neurons at time t;
wij are the weight values connecting model
neuron i to model neuron j;
pk(t) are the external inputs at time
t; vik are the weights connecting
model neuron i to input line k; and
f(x) is the logistic function
f(x) = 1/(1 + e x).
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Figure 1.
Diagram of the recurrent network model. Each
large, sigmoid-containing
triangle represents a soma or a model unit, which receives external input and feedback from other network units. The activation of
a model unit is determined by performing a nonlinear operation on the
weighted sum of its inputs (see Eq. 1). Inputs are shown in the
bottom left corner and labeled x,
y, and gate, respectively. For clarity,
only five model units are shown here; actual network models contained
between 9 and 50 of these units. The black diamonds represent the wij; white
diamonds represent output unit weights. The three small,
sigmoid-containing triangles labeled match,
x, and y represent the output units. The
activation of an output unit is determined by a nonlinear operation on
the weighted sum of the hidden unit activity.
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In our model, there are three input lines: two for the (x,y)
coordinate of the stimulus and one called the "gate." The gate takes a value of 1 when new information is to be stored and is 0 otherwise, including when distractor and matching stimuli are applied
to the stimulus position inputs. These three inputs, then, provide the
information that must be available solve the DMS problem. Other input formats, e.g., retinotopic coordinates, could have been
chosen, but the exact format used here was chosen for simplicity. Whereas the information content and dimensionality of NSI model inputs
are critical, the precise format of inputs generally has only a second-order quantitative effect and does not change the major
functional properties of the model (Moody and Zipser, 1998; Sanger,
1994). The input lines connect to all model neurons except the output
units. The output of the network consists of a set of three units that
receive input from all of the hidden units but do not feed back to
them. In addition to the match output unit there are two additional
output units that indicate the coordinates of the stored stimulus
position. These output units acted as an external copy of the location
to be remembered, thereby facilitating the match process. The units
were found to be required for efficient training but were not necessary
for the basic properties of the hidden units or the overall performance
of the model.
To train the model, randomized sequences of stimulus positions and gate
signals were provided at appropriate times. The output was trained to
indicate when a match occurs, as well as the location of the previously
stored stimulus. Figure 2 provides
details of the training paradigm. Gate signals were separated by
intertrial intervals in which the stimulus position was set to zero,
i.e., at the center of the circle of stimuli positions. Models were generated by training networks for about 10 million network time steps.
On average, three distractors were shown before presentation of an
input that matched the stored information. The average total duration
from sample to match was 15 time steps. Starting from random weights,
networks of nine or more units always learned to do the task
correctly.
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Figure 2.
Schematic of training algorithm used for delayed
match-to-sample network. The row of
circles represents the input coordinate stimuli, and the
bottom line represents the output match response. The
top line represents the gate signal. There are eight
possible input coordinates, represented by the small
lines on the circles. A solid
circle indicates an input stimulus pattern; an outlined circle indicates a gated stimulus pattern. The output match
unit indicates when the current input matches the last gated input. The
output also carries a copy of the last gated location, which is not
shown. Each gated sample input is followed by a pseudorandom number of
distractors. The number of distractors, n, decreases exponentially as n increases and is determined as the
probability, p(n), that the number
of test patterns is n = k(n  1)(1 - k), where k was set to 0.35. In addition,
there was an interstimulus interval of either two or three
(0,0) inputs separating each new input stimuli.
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Neurophysiological methods. We compared the response
properties of hidden units in our model with those of frontal cortex neurons recorded in previously reported experiments (di Pellegrino and
Wise, 1993a,b). The experimental details can be found in the previous
reports but are briefly summarized here. A rhesus monkey was trained in
a manner roughly analogous to that of the model described above. In the
experimental condition used for the present analysis (termed the
"compatible condition" by di Pellegrino and Wise, 1993a,b), each
trial began with the monkey centering a two-joint manipulandum beneath
a light-emitting diode (LED) that was in the center of a circular array
of eight LEDs. The monkey fixated a central LED, and later, one of the
eight peripheral LEDs was illuminated for 500 msec as the sample
stimulus. After a delay of either 550 or 750 msec, a current stimulus
was presented for 100 msec. If it was one of the seven LEDs other than
the sample, no response was required, and any motor response terminated
the trial. If the current stimulus matched the location of the sample, then the monkey had to move the manipulandum to that location within
650 msec to report that a match had occurred. (This positional motor
response is analogous to the analog information contained in the
x and y output units of the network.) If
performed accurately, juice reinforcement was delivered; otherwise the
trial terminated. The present analysis focuses on 68 neurons recorded
from the dorsal premotor cortex (PM), a part of the frontal cortex
thought to be involved in visually guided movement. In addition, 37 neurons from part of the prefrontal cortex (PF) were also analyzed.
Analytical methods. To quantify the degree and depth of
direction tuning, we developed four indices, computed for a given unit
across all eight directions. Similar types of indices have been used in
the past, often based on fitting the data to a cosine function
(Georgopoulos et al., 1982, 1988). However, inspection of the
neurophysiological data indicated that regression to a cosine function
would not yield many good fits. Accordingly, we developed indices that
did not depend on sinusoidal directional tuning. A selectivity index
(si), depth-of-tuning index
(di), activity level index
(ai), and modulation index
(mi) are defined as follows:
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(2)
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(3)
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(4)
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(5)
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where k is the number of directions;
 event denotes the activity level during a
given event period (such as sample, delay, or match) for a given
cell across eight directions; and imin and imax are, respectively, the minimum and maximum
responses of the ith neuron across the
eight different directions.
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RESULTS |
Mechanism of the model
To determine the mechanism of the model, several analytical
approaches were used, based on the following properties of the model
neurons: (1) the activity pattern within a simulated trial; (2) the
steady-state activity pattern during delay period; (3) the consequences
of single-unit lesions; and (4) the synaptic weight connections.
An important parameter in NSI models is the number of hidden units
used. We found significant differences between the behavior of hidden
units in minimal versus larger models. The hidden units in minimal size
networks were of relatively "pure" functional types, with each unit
devoted to one of the main information-processing components of the
task. In larger models, only a fraction of the units were of pure
functional types. Most units seemed to be participating in several of
the necessary information-processing components, with varying degrees
of participation in each. This distinction between minimal and larger
networks allowed us to use the operational mechanisms of minimal
networks, which were fairly transparent, to gain insight into the
potential mechanism of more complex networks, which were more difficult
to analyze. It also allowed us to gain further insight into the
neurophysiological data, because the biological units more closely
resembled the hidden units in large networks than in minimal ones.
At the start of a typical simulated behavioral trial, the center
coordinate (0,0) was gated into the model network,
corresponding to the starting position in a reaching task. After an
intertrial interval, a stimulus location was gated in. This was
followed by zero to three distractor stimuli and finally by the match
stimulus. Analysis of the data from these simulations revealed two
distinct kinds of hidden units: storage and comparator units.
Storage units maintain a sustained level of activation that is
determined by the last input loaded simultaneously with a gate pulse. A
new gate pulse is needed to cause a change in the activity of a storage
unit (see Fig. 4). Storage units are directionally tuned and quite
insensitive to postgate events, such as distractors and matches (Figs.
3, 4).
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Figure 3.
Typical temporal behavior of a the storage unit of
a model, shown as unit activity plotted as a function of time. At
t = 5, a sample stimulus pattern is gated in, and
at t = 17, the same stimulus is presented again.
Both events are marked with arrows, and dotted
vertical lines demarcate the delay period. The top plot shows the sustained response for a subset of input
patterns (sample stimuli at locations 8 and 1-3); the bottom
plot shows the sustained response for the remaining inputs
(sample stimuli at locations 4-7). In this and most subsequent
figures, model unit activity levels are normalized to the range
[0.0-1.0].
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Figure 4.
Temporal behavior of a storage unit across
multiple gated sample input patterns. Each arrow along
the x-axis indicates gating in of a new sample pattern.
At t = 6 and 25 a "preferred" sample location was gated in; at t = 17 a
nonpreferred sample location was presented.
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Comparator units receive input from both the current stimulus and the
stored sample. They can respond to distractors as well as to match
stimuli, and their responses are directionally tuned to the location of
the current input stimulus. In the majority of comparator units,
amplitudes of response to current stimuli are modulated by the value
held by the storage units. This modulation includes both potentiation
and suppression. An example of how a comparator unit responds to
all current stimuli for various stored samples is shown in Figure
5. Note that the response is directionally tuned, and that the shape and peak of the tuning curve
remain fixed for different stored samples. It is the magnitude of the
tuning curve that is dependent on the current stored sample. This
relatively fixed shape of the tuning curve for current stimuli allows
us to incorporate both the current stimulus and the stored sample by
describing the output of a comparator unit as approximately their
product. Thus, the output of the network can be represented, to a first
approximation, as:
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(6)
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where mjk is the output of the match unit,
wi is the weight connecting the ith
comparator unit to the output, and
aijaik is the product of
the response to the jth current stimulus and the
kth stored sample of the ith comparator unit.
This equation has the general form of a match filter that signals a
match when the sum mjk exceeds a preset
threshold (Oppenheim et al., 1996). In the network model, this
threshold is implemented by the sigmoidal activation function of the
output unit, thereby enabling the network output to detect the eight
match conditions of the 64 possible combinations of current stimulus
and stored sample. A strong indication that the output match unit uses
the responses of comparator units to make its decision can be seen in
the large magnitude of the weights that connect them to the match
output unit. The analog of Figure 5, using experimental data, is shown
in Figure 12. It is quite noisy but suggests that a similar
computational mechanism may be used by the brain. It is interesting
that no units were found in the recurrent layer that carry the match
decision signal. No true match units were found in the cortical areas
studied either, as will be discussed later.
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Figure 5.
Model comparator unit for three different stored
values. The response to current stimuli, matches, and distractors at
locations 1-8 when the sample has previously appeared at location 3 is
shown in the top plot. The middle and
bottom plots show the response to current stimuli at the
same locations for sample stimulus locations 7 and 4, respectively.
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When the number of hidden units is increased from the minimum needed, a
significant difference appears in the properties of many of the hidden
units. There are still some relatively pure functional types, but most
hidden units in larger networks are of complex, mixed types. These
mixed types have activity profiles that seem to combine storage and
comparison functions to various degrees. Analysis of the operations of
the model, by examining the effects of removing single units from the
network, demonstrate that these composite functional units play an
essential role in the DMS task.
Additional information about the model was obtained by studying its
steady states. All instances of the model settled to steady states;
that is, the set of model neurons evolved to a state that was
changeless over time. The steady states were found by gating in a
stimulus and then returning the input lines to zero until the activity
of all units became fixed over time. The effect of stored information
on the steady-state values of all the units in a minimal size network
is shown in Figure 6. This instance of
the model has two storage units (labeled S), six comparator units (labeled C), and one unit that is directionally tuned
to gate events but is not modulated by stored value. The two storage units are directionally tuned to the stored information, but one has
eight distinct values over direction, and the other has just two
values, high and low. Within the set of six storage-modulated comparator units, all but one of the steady-state tuning curves are
approximately unimodal. Note that the steady-state tuning curves for
the six tuned comparator units are all different. These differences
play a central role in enabling the comparator units to provide unique
information about all combinations of input and stored information.
This information is then used by the match output unit for recognizing
matching stimuli.
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Figure 6.
Steady-state values of the network, for a minimal
network, shown as activation profiles of the nine model neurons across
eight input patterns. The activation shown is after the network has settled to a steady state. C, Comparator cell;
S, storage unit. Note how one unit (bottom left
corner) does not distinguish among the different input
patterns.
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The stable states of our model are fixed point attractors. Fixed point
attractors have the property that if the system is given a small
perturbation from its steady state it will return to that state. The
region of state space from which the system will evolve to a specified
attractor is called a basin of attraction. In our model, the remembered
stimuli are stored in basins of attraction. There are eight attractors,
one for each of the eight possible stimuli in the training set. It is
often hard to visualize basins of attraction, because they are in a
space with the same number of dimensions as the number of units in the
network. However, the attractor structure of our model networks is
relatively simple and could be visualized in the two-dimensional space
that contains the eight input stimuli. To plot the basins of
attraction, we systematically gated in a square grid of 57 × 57 (3249) points covering the two-dimensional input space and including
the eight training stimuli locations. To maximize the number of
attractors found, all model neurons were set to randomly chosen values
before presentation of a new grid location. After gating in a new
location, the input lines were held at zero until the network settled
to a stable state. Two stable states were considered the same if each
model neuron in one stable state had the same activity level as the
corresponding neuron in the second stable state. This procedure produced only eight stable states for all 3249 points (Fig.
7). Figure 7, A and
B, shows these eight stable states for a nine unit and a 50 unit network model. Each of the eight stimuli locations on which the
network was trained was surrounded by a large basin of attraction.
These eight basins of attraction accounted for all of the input space,
and there were no other attractors in the network.
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Figure 7.
Spatial extent of the basins of attraction for
model networks and the effects of lesions on attractor basins.
A, Minimal, nine-unit network. B,
Fifty-unit network. C, Nine-unit network with a lesioned
comparator unit. D, Nine-unit network with a lesioned storage unit. Steady network state activation is plotted as a function
of the location of the gated-in (x,y) coordinate sample stimulus across a matrix of 57 × 57 (x and
y ranged from [0.2:1.2], with a step of 0.025). The
network settled for 25 activation sweeps after each gated coordinate
position. The various colors serve to distinguish one
attractor basin from another; there is no correlation between hue and
relative distances among attractor basins. The small white
circles indicate the eight training target locations. Note
that, because of storage unit activity, the basins of attraction remain
stable with a comparator lesion (compare A,
C). Note the serious disruption of several basins of
attraction with a storage unit lesion (compare A,
D), including one large basin that now subsumes three of
the eight locations in the sample stimulus training set.
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The robustness of the attractors was examined by studying the effect of
initial network starting position on the resulting attractors. The
initial state of the network refers to the collective set of initial
activity level of each model neuron. The overall structure of these
attractor basins was not affected by the initial state of the network;
only the basin boundaries were affected. If the network always started
from the same initial state, a smooth border evolved between basins
(Fig. 8 right), whereas if the
network started from a randomly selected initial state each time, then a noisy boundary resulted (Fig. 8, left). Thus, the general
structure of the attractor basins are robust, which implies that the
stored information will be buffered against noise and irrelevant neural activity.
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Figure 8.
Higher-resolution map of a boundary between two
basins of attraction. These plots show an x range of
[0.670-0.794], a y range of [0.540-0.664], and a
step size of 0.002 (vs 0.025 in Fig. 7). Left, Each
hidden unit was initialized with a different random value.
Right, Each hidden unit was initialized with the same
value.
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The differential roles of the storage and comparator units can be
analyzed further by examining the effect of removing them selectively.
Removing a comparator unit from a minimal network has very little
effect on the spatial pattern of the basins of attraction (Fig.
7C). Nonetheless, the matching process is disturbed, and
there are several matching errors (data not shown). Removing a storage
unit (Fig. 7D), on the other hand, substantially disrupts the spatial structure of the attractor basins. The values of the attractors are changed, their numbers are reduced, and several targets
end up in the same basins of attraction.
The spatial patterns of attractor basins are similar in small and large
networks (Fig. 7A,B). However, there are some differences. First, larger networks degrade more gracefully with lesioned storage units. Second, the boundaries between basins of attraction are more
sensitive to starting state in the larger networks.
Comparison of model and empirical data
In the analysis of networks of relatively large size, two tests
were required to show the function of the different types of hidden
units: first, examination of the activation properties during the time
course of a trial as a function of the stored and current input
stimulus; and, second, the effect on the basins of attraction when the
unit was deleted from the network. Because we are unable to perform the
second of these tests on the experimental data, we are limited to the
statement that a neuron is consistent with some particular functional
type.
For the PM population, 68 neurons were included in the final data set.
Only cells with unimodal directional tuning and increases in activity
were included. Twenty-four of those 68 neurons had activity patterns
that resembled, by qualitative assessment, the pure functional types
found in the minimal model. Of these, there were seven storage units
and 17 comparator units. The remainder showed either complex activity
patterns that appeared to include elements of both functions or, in a
few cases, were of types that did not appear in the model. For the PF
population, 37 neurons were included using the same criteria. Of those,
two resembled storage units, and five resembled comparator units. The
remainder were of mixed or different types.
Storage units
The storage units in our model network have several
characteristics: they are set to stimulus-specific levels of activity by the first stimulus in a trial, sustain this activity with little disruption despite the presentation of distractors, and are
directionally tuned to the location of the initial, gated stimulus.
Figure 9 shows the activity of a typical
neuron with sustained activity. Illustrated are the periods before and
after samples, distractors, and matches. The PM neuron shown in Figure
9 has the three characteristic response features of the storage units
of the model. It is set to stimulus-specific levels of activity by the
first stimulus in a trial (Fig. 9, left column); it sustains
this activity with little disruption through the presentation of
distractors (Fig. 9, middle column); and it is directionally
tuned to the location of the initial, gated stimulus (Fig.
10). Unlike the storage units in the
model, the activity of the cell diminishes soon after the match
stimulus presentation (Fig. 9, right column). This
characteristic is typical of neurons with delay period activity in a
wide range of experiments (Zipser, 1991), and it can be reproduced in
the model by gating in a stimulus representing the center location at
the end of a trial (Fig. 4). The shutoff indicates that, in addition to
some general source of input gating that loads new information into the
system, there is also an information source, not addressed by our
model, that indicates when the task is complete and information need no
longer be maintained. The storage-like units in PF had similar
characteristics.
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Figure 9.
A storage unit from PM. Average neuronal
activity for stimuli at each of the eight locations in the training set
(rows 1-8). Left column, Activity
aligned on the onset of the sample stimulus. Middle
column, Activity aligned on the onset of a distractor stimulus. Right column, activity aligned on the onset of a match
stimulus. Each trace is an average across a variable
number of trials, plotted to the same scale (activity scale is in
impulses per second). Top row, Average for each
column.
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Figure 10.
Tuning curve for PM cell illustrated in Figure 9.
Activity and SE/SD for activity during the delay period (for the 750 msec period immediately preceding match stimulus onset) across stimulus location.
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Comparator units
Comparator units in the model have two critical properties that
can be compared with PM and PF neurons. They have a directionally tuned
response to stimuli presented during any stage of a trial, and their
responses are modulated by the value currently stored in memory. In the
model, the first of these properties results from comparator units
receiving afferent information about the current input. The second
property stems from storage unit input to comparator units. In the
cortex, both PM and PF contain neurons that exhibit these two
properties. The responses of a PM neuron to each of the eight input
stimuli, whether that stimulus is a sample (Fig.
11, left column), a
distractor (Fig. 11, middle column), or a match (Fig. 11,
right column), gives a rough idea of the directional tuning
of the cell. As with the comparator units of the model (Fig. 5), this
neuron shows directional tuning to current stimuli, as well as
responses that are modulated by stored values (Fig. 12). In PF cells, the directionally
tuned response to the sample stimulus presentation tends to be similar
to that of a current stimulus presentation. In contrast, the
directional preferences of PM cells are more complex (see di Pellegrino
and Wise, 1993b). In model neurons, the sample tuning curve is often
quite similar to the current input tuning curve; however, there are
many instances in larger networks in which the two curves are
dissimilar.
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Figure 12.
Tuning curves for PM cell illustrated in Figure
11. As in Figure 5 from the model, each plot shows the response to
stimuli at one of the eight locations in the training set after a
sample at one location. Top, middle, bottom, Sample
stimulus at locations 1, 5, and 4, respectively.
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Match output units
There were no match units in the recurrent layer of the model. The
two principal characteristics of the match output unit, as expressed in
the present terminology, are that it is "untuned" for direction;
i.e., it reports a match regardless of the spatial location of the
match stimulus, and it does not show activity at any other period
during a "trial." By those criteria, there were no match units
found in either PM or PF. Taken literally, this finding suggests that
the actual decision that a match has occurred takes place in a
different brain area, although all the relevant information is present
in PM. However, closer examination of the data revealed a small number
of units, four in PF and one in PM, with properties that resembled the
match output neuron in the model more closely than did any of the
hidden units of the model.
This characteristic of frontal cortex activity was explored further by
examining the correlation between the depth and selectivity of
directional tuning. We calculated si,
di, ai, and
mi for each model neuron (Eqs. 2-5) in both
larger and minimal networks, as well as for PM and PF neurons, selected
as described above. Figure 13
illustrates large and small values for the directional selectivity index and the depth-of-tuning index, si and
di, respectively. si measures the extent to which activity in all
nonpreferred directions deviates the maximal activity, and
di measures the greatest proportional reduction
from maximal activity. We found that PM, PF, and model data all show a
significant, positive correlation between the depth
(di) and selectivity
(si) of directional tuning that is similar in certain details (Fig. 14).
For activity after match presentation in larger networks,
r2 = 0.877 (n = 50); in
PM neurons, r2 = 0.744 (n = 68); and in PF neurons, r2 = 0.753 (n = 37). Neither the independent correlations of PM and the model nor those of PF and the model significantly differ (two-tailed test,  = 0.01) (Myers and Well, 1991).
View larger version (13K):
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Figure 13.
Schematic of tuning properties described by the
directional selectivity (si) and
depth-of-tuning (di) indices (see
Eqs. 2, 3).
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View larger version (12K):
[in this window]
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Figure 14.
Directional selectivity index versus
depth-of-tuning index for PM neurons, PF neurons, and model neurons.
The diameter of each data point is proportional to the
normalized activity modulation (mi)
after the match stimulus event. Because of the unusually large
modulation of activity for one PF neuron (>200 impulses/sec), the rest
of the PF population appears to have minimal modulation. However, this
is merely a result of normalization to the maximum value.
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There is an apparent difference between the model and neuronal
distributions as the origin is approached (Fig. 14). More model units
have very low depth-of-tuning as well as very low directional selectivity indices. For all of those model units, it was found that
the level of modulation, mi, was also
very low, as was their activity during the delay period and after the
match event. The very low activity levels (<6% of maximal activity)
of these hidden units and the small weights linking these units to the
network output suggest that these units contribute little, if any, to the operation of the model. Frontal cortex neurons with such low levels
of activity and modulation are unlikely to be sampled with current
neurophysiological sampling methods. Four PF cells and 1 PM cell with
low di and si values were
sampled (Fig. 14). However, unlike the hidden units of the model, these
frontal cortex neurons have high modulation
(mi) levels (>44% of maximal
modulation), with a moderate, rather than low, activity during the
delay period. One of the PF neurons showed the maximal activity, which
was a postmatch modulation of >200 impulses/sec, one of the highest levels of activity ever reported for frontal cortex. Thus, these four
PF and one PM neurons resemble the match output cell of the model more
closely than any of the hidden units of the model in having low
directional tuning but high activity modulation after the match event.
Some of these neurons also differ from the match output neuron in
having significant activity after the sample stimulus, as well as the
match stimulus.
| |
DISCUSSION |
Contribution of model
The model described here augments previous DMS models in several
important ways. First, it incorporates the matching function in the
same network as short-term information storage. Although active storage
has been modeled (Lukashin, 1990; Zipser, 1991; Zhang, 1996), it has
not previously been combined with matching in a single model. Second,
the present model also allows for distractors and can distinguish
repeats from true matches. Third, the model can be generalized readily
to other short-term memory tasks, such as nonspatial DMS, nonmatching,
and paired associate tasks. For example, the dimension and format of
the input can be altered to represent the desired stimulus as
xheight , xwidth , and
xcolor for object x in a nonspatial
DMS task.
We found that in models with a small number of hidden units, these
units, to a first approximation, could be characterized as storage or
comparator units. Recall, however, that the minimal network described
above contains two storage units and six comparator units (Fig. 6).
This suggests that comparator units are involved in storage, because
two storage units cannot collectively represent eight different sample
locations, and moreover, because some storage attractor basins are
still intact after a storage unit lesion. Thus, although minimal-sized
models produce predominantly storage or comparator units, these two
unit types interact to support each other functionally. By contrast,
networks with relatively large numbers of units tended to have what
appear to be multifunction units. In this regard, the behavior of
hidden units in large networks more closely resembles that of frontal
cortex neurons. The role played by these multifunction units in the
model is difficult to determine, as has proven to be the case for
frontal cortex neurons. In the present analysis, we have examined the
properties of frontal cortex neurons mainly in comparison with the
properties of large networks. We focused on the properties of storage
units, comparator units, and the match output unit, which signals the decision of the network.
Storage units
Short-term active memory of the kind used in DMS must be buffered
against distractor inputs. In the lateral intraparietal area and in
areas 7a, IT, and V4, delay activity appears to carry information only
about the immediately preceding stimulus (Mountcastle et al., 1987;
Miller et al., 1993; Steinmetz and Constantinidis, 1995). In those
sensory cortical areas activity is usually "reset" by distractor
stimuli (Miller et al., 1996), presumably reflecting the displacement
of sample information. In contrast, PF and PM neurons exhibit much
less, if any, resetting by intervening distractors (di Pellegrino and
Wise, 1993a; Miller et al., 1996). The buffering of stored information
across distractors reinforces the conjecture that the loading of new
information into active short-term memory requires some kind of
specific gate or load signal. This signal appears to be necessary for
shifting the units to a new attractor. For units in which memory is
reset to a new value for each new stimulus, such a load signal would
not be required. For those units, the afferent stimulus could shift the
network to a new attractor. The source of the load signals for
short-term memory is not known. One possibility is what has been termed
anticipatory or precue activity: a directionally nonselective signal
that precedes a temporally predictable event (Mauritz and Wise, 1986;
Vaadia et al., 1988). In most tasks, the sample in a DMS task is
predictable in this sense. In principle, this signal can provide
information about the control of the sequence of computations that
generate continuous cognition. The same reasoning also applies to the
signals that turn off sustained activity at the end of a trial.
In the model, the function of the storage units in maintaining
information about the location of the sample is unambiguous. However,
in animal behavior, the situation is not always as clear. During
periods when animals must remember a stimulus location, they may also
reorient selective spatial attention to the same location and/or, under
certain circumstances, maintain an intention to make a movement, either
oculomotor or skeletomotor, to that location. It is also possible that
animals could use overt movements for self-cueing, for example, if an
animal looks in the direction of the sample stimulus or adopts a
posture that could encode the same information. Eye position and
electromyograpic measurements seem to exclude overt motor strategies
for the matching task (di Pellegrino and Wise, 1993a), but covert
actions cannot be ruled out. For the present purpose, these
distinctions are not particularly pertinent. Whatever the strategy of
the animal for retaining information about the sample stimulus, the
requirements of the DMS network remain much the same: location-specific
sustained neural activity and comparison between this stored
information and current stimuli.
We did not examine the dynamics of cortical discharge rates in detail.
It has been noted that neuronal activity in a delay period has many
patterns, including, in frontal cortex, a buildup of delay period
activity over time (Quintana and Fuster, 1993; Miller et al., 1996).
Although the model, in its current form, cannot account for such
augmentation in discharge rate, a minor modification that enhances the
effect of the previous network activation is likely to produce such an
effect.
Comparator units
The model network functions by virtue of the combinations of
inputs from current stimuli and storage units onto comparator units.
This conclusion is supported by three lines of evidence: the properties
of comparator unit activity, the synaptic weights that these neurons
have on the match output neuron, and the effects of selective removal
of comparator neurons from a trained model. Comparator unit activity
reflects both the location of the sample stimulus (as provided by the
storage units) and the location of the current stimulus. It appears
that a unique combination of storage and current stimulus inputs to
each comparator unit is used by the network to identify match events.
This conclusion is supported further by the fact that the largest
synaptic weights on the match output neuron of the model arise from the
comparator cells as well as from the observation that removal of
comparators from the network causes many "reporting" errors without
changing the basins of attraction.
Of course, it is impossible to perform the latter two analyses on
the frontal cortex neurons. No one knows the weight of its neurons on
output elements, and there is no method for ablating comparator units
selectively in the frontal cortex. However, we can examine the activity
patterns and levels of PF and PM neurons in the context of the behavior
of hidden units in both minimal and relatively large networks. A large
class of PF and PM neurons has the properties predicted by the model
for comparator units. Comparator cells are characterized by receiving
input regarding the stored stimulus, as well as the current stimulus.
In terms of our neuronal activity indices (Eqs. 4, 5), this corresponds to moderate but nonzero delay period activity
(delay) and moderate postmatch
stimulus modulation (mi). PM, PF, and the
model all contain populations of comparator cells by these
criteria.
Match output units
There were no true match units, i.e., units that became active
only when a match occurred and did so equally for all match-stimulus locations, in PM, PF, or the hidden layer of the model. This negative finding is of importance, because it indicates that hidden units of the
model probably do not make the match decision. In this context, we
examined the behavior of the PF and PM neurons in our sample closely.
The finding of four PF neurons and one PM neuron that had virtually
untuned, but substantial, activity modulation after the match event
suggests a larger role of frontal cortex neurons in the match decision
than envisioned for the hidden units in the model.
Neural systems identification and top-down engineering
Top-down engineering concepts are useful in combined modeling and
neurophysiological studies, especially as a source of conjectures concerning how a network may be solving a complex input-output mapping. As outlined in the introductory remarks, an optimal top-down solution to the DMS task could consist of an attractor network to store
the stimuli and a match filter to detect matches. In the NSI model, the
storage units implement the attractor network, and the comparator units
implement the match filter. Thus, the NSI model did implement both of
the proposed mechanisms, although it was not constrained to do so.
Furthermore, the model network acquired the property of buffering of
the relevant information, without individual elements exclusively
devoted to this function, and lacked "pure" match units. These
properties accord with the experimental results, although in an
explicitly engineered system, components might have been designed with
those properties. It is of interest that, among the many potential
designs for a DMS network, the NSI model and perhaps the cortical
network adopt the optimized architecture proposed in the top-down
engineering solution described above.
| |
FOOTNOTES |
Received May 13, 1997; revised Oct. 10, 1997; accepted Oct 15, 1997.
Correspondence should be addressed to Dr. Sohie L. Moody, Laboratory of
Systems Neuroscience, National Institute of Mental Health, P.O. Box
608, Poolesville MD 20837.
| |
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Top
Abstract
Introduction
