Division of Biology, California Institute of Technology, Pasadena,
California 91125
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INTRODUCTION |
The lateral intraparietal cortex
(LIP) is involved in programming saccadic eye movements
(Andersen and Gnadt 1989
; Lynch et al.
1977). Many LIP neurons exhibit sustained responses to
remembered visual or auditory targets (Mazzoni et al.
1996a). During delayed-saccade tasks in which the monkey
withheld a saccade to a remembered target for a short period of time,
the response of LIP neurons triggered by the target was sustained until
the saccade was initiated (Andersen et al. 1990a,b;
Gnadt and Andersen 1988). Moreover, neurons could maintain the memory for the saccade even if the monkey was presented with new stimuli during the withholding period. Negatively correlated memory responses have also been observed in LIP, and such responses occurred when the remembered saccade was opposite the neuron's preferred saccadic direction (Barash et al. 1991a,b).
Memory activity was further characterized with the
delayed-double-saccade experiments (Mazzoni et al.
1996b) in which the monkey was trained to memorize two
consecutively flashed targets and to plan two saccades to the targets
in the order that the targets were presented. During the delayed
period, many LIP neurons whose preferred directions were in the
direction of the first saccade fired continuously until the execution
of the saccade. These neurons thus held the correct memory for the
first saccade regardless of the flash of the second target. Neurons
coding for the second saccade started to fire only after the first
saccade was executed. The results indicated that memory activities for
the majority of LIP neurons encode the next planned saccade. On the
other hand, a small percentage of LIP neurons encode the memory of
target locations instead. The sustained responses in all kinds of
delayed-saccade tasks have a common feature: neurons begin to encode a
new saccadic movement only after the current motor plan is disengaged.
We call this the "single-purpose" feature.
Short-term memory activity has been observed in a number of cortical
areas (Funahashi et al. 1989; Gnadt and Andersen
1988; Goldman-Rakic 1995; Kalaska and
Grammond 1995; Quintana and Fuster 1992).
Several computational studies have proposed that recurrent connections
might be the mechanism for this activity (Cowan 1972; Dehaene and Changeux 1989; Fuster 1995;
Zipser 1991). The purpose of this report was to study
the mechanisms of saccadic-related memory activities in area LIP.
Especially, we were interested in how the single-purpose feature was
related to programming delayed double saccades. Based on experimental
tasks, we used recurrent neural networks to simulate the memory
features of LIP neurons. We first studied the mechanisms of memory
saccades and then examined an extended model for planning
double-saccades. Preliminary results of this report have been presented
in abstract form (Xing et al. 1995).
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METHODS |
The model is a three-layered neural network, with a similar
structure to that of Zipser and Andersen model (1988).
The diagram of this model is shown in Fig.
1. The model was not designed to resemble
the complex anatomy of area LIP. It is the typical classic neural
network that can be trained to carry out the required sensorimotor transformations. The input layer, like area LIP, has access to visual
and auditory target locations as well as eye position in the orbit. The
output layer is a topographic map of eye motor errors. The middle
layer, or the hidden layer, is a recurrent network with every unit
receiving activities from all other hidden units. Every unit in the
input layer is connected to each of the hidden units, which are in turn
connected to all the output units. The weights of connections vary
between 
1 and +1. They are initially set to small random values
between 0.1 and 0.1. The weights are adjusted to encode the motor
errors of visual or auditory targets at the output map.
The input layer consists of a visual map in retinal coordinates, an
auditory map in head-centered coordinates, and eye-position units. The
visual map uses 8 × 8 units to model a 40° to 40° retinal
space. Each of the units has a Gaussian receptive field (RF) with a
1/e width of 15°. The centers of the RFs were equally spaced over the 8 × 8 grid with 10° spacing. These units encode target locations with their activation values between 0 and 1. The
auditory input is modeled using an auditory map of an 8 × 8 array
of units, similar to the visual one. The only difference between the
two input maps is that the auditory units encode target locations in
head-centered coordinates and the visual units encode target locations
in eye-centered coordinates. Eye positions is coded by four sets of
eight units representing horizontal and vertical eye coordinates with
positive and negative slopes. The activation of the units, with various
intercepts and slopes, is thus an increasing function of eye positions.
The middle layer, also called the hidden layer, typically has 30 units
in the simulations presented in this report. Each hidden unit receives
inputs from all three input channels. In addition, each hidden unit
receives recurrent projections from all other hidden units. The
activation of a hidden unit is calculated by first summing all inputs
and then calculating the output as a sigmoidal function of the total
input. At a given simulated time step, the activation of a hidden unit
can be expressed as the following: output activation = 1/[1 + exp(net)] where net = sum of weighted inputs + bias.
The inputs here include the activities of the visual, auditory, and
eye-position units at the current time step and the activities of other
hidden units at the previous time step. The sigmoid function is chosen
as the activation function because it resembles the operation performed
by actual neurons that sum inputs, have a threshold, and saturate at
high levels of activity. In the middle region of its dynamic range, the
sigmoid approximates a linear function.
The output layer is an eye-centered map encoding eye motor errors (ME)
of saccades. An 8 × 8 array of output units is used to represent
MEs topographically. Each of the units covers a 10° space of MEs with
a Gaussian 1/e width of 15°. The activation of the output
units, like the hidden units, is a sigmoidal function of the sum of the
weighted inputs from the hidden units. We use E to represent the
initial eye position, V for the locations of visual targets in
retinal coordinates, and A for the locations of auditory targets
in head-centered coordinates. For simple saccades, ME = V for
visual targets and ME = A E for auditory
targets. For double saccades, we use E0 to represent the initial
eye position, V1 for the location of the first visual target in
retinal coordinates, and A1 for the location of the first auditory
target in head-centered coordinates. E1 represents the eye
position after the first saccade. V2 and A2 indicate the
second visual and auditory targets, respectively. The desired ME output
for the first saccade is ME = V1 for visual targets or
ME = A1 E0 for auditory targets. The ME for the
second saccade is ME = A2 E1 or ME = V2 + E0 E1.
Training process
We use an algorithm "backpropagation-through-time" to train
the network. This algorithm gradually optimizes connection weights to
produce the desired output in a recurrent neural network (Munro et al. 1994; Werbos 1990; Williams and
Zipser 1995). We use this algorithm simply to train the network
to perform the required sensorimotor transformations with no intention
to claim that the algorithm is similar to the learning mechanisms in
the brain.
The backpropagation algorithm uses supervised learning. It first
computes an error signal, which is the difference of the desired output
(the teacher signal) and the actual output. This error signal is then
used to update connection weights. The amount of weight change depends
on the error signal, the activities of the two connected units, and an
arbitrary learning rate. In our implementation of the algorithm, the
desired activity Aexp for each output
unit k is determined by the expected ME of a saccadic target. The actual output Ao of an
output unit is computed for a given target location, eye position and
the initial weights. The error signal 
k for
an output unit k is
A connection weight Who from a
hidden unit to an output unit is updated according to
where Ah is the activity of the
hidden unit. The learning rate n in our simulations is 0.05.
A connection weight Wih from an input
unit to a hidden unit is updated according to
where Ai is the activity of the
input unit and k is the error signal of an
output unit k.
A recurrent connection weight Whh from
a hidden unit i to another hidden unit j is
updated according to
where
Ahi(t 1) is the activity of the hidden unit i at the previous
time step and
Ahj(t) is
the activity of the hidden unit j at the present time step.
In a recurrent network, the output of the network accounts for both the
current inputs and the activities at earlier times. We run the network
in 13 discrete time steps for each training cycle. To compare with
experimental recordings, one time step can be viewed as a duration of
100 ms. The time lag of the recurrent connection is one time step. The
input of a visual or auditory target location lasts for one time step
while an eye-position signal sustains until a saccade is made. The
teacher signal, which is the expected ME in the output layer, appears
several steps after the onset of a target simulation and lasts for one
time step. This signal mimics the command to make a saccade. The
weights of the feedforward connections and recurrent connections are
updated at the time of this saccade command. Note that we did not
simulate the shut-off of the neuronal activity after a saccade is made (i.e., the postsaccadic suppression). Therefore the recurrent activity
in the network may sustain indefinitely unless it is turned off by
other mechanisms, as detailed later in the extended double-saccade
model. Since different training patterns are employed for models of
single- and double-memory saccades, details about the training patterns
will be described in each section as needed.
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RESULTS |
Model of memory saccades
MODEL TRAINED WITH SINGLE MEMORY SACCADES.
We first trained the model to perform single memory
saccades. Twenty-five target locations across the input space and 25 eye positions were chosen as training samples. For each training cycle, a visual or an auditory target at a chosen location was presented at
the first time step. A saccadic target was simulated as a dot stimulus
with the amplitude of 1. The saccade was made randomly between the
fifth to ninth time steps. The model was trained to encode the ME of a
saccade at the time step when the saccade was made. The paradigm is
illustrated in Fig. 2A. After
approximately 3,000 training cycles, the network learned to produce and
memorize saccadic MEs correctly to any input pairs of target location
and eye position. The performance of the trained network was evaluated by comparing the expected ME for a given target location and eye position with the produced ME at the output layer. We tested 100 random
input pairs of eye position and target location for the trained
network. The standard deviation of the actual ME outputs from the
expected MEs was 2.62°. Figure 2B shows one example of the
model output. For simplification, only eight units (which include the
one with the maximum response) along one dimension (1-D) of the
two-dimensional (2-D) output map are shown. The vertical axis is the
1-D ME and the horizontal axis indicates time steps. The gray level of
squares is proportional to the responses of the output units. The
horizontal bar indicates the gravity center of the responses. "T"
indicates the expected ME of the target. Figure 2B shows
that the model produces the correct output and the activity sustains
throughout the delay period.
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Fig. 2.
The training pattern and the performance of the simple memory-saccade
model. A: the typical training pattern. Eye movement is
indicated with the lines and the short bar indicates the timing of the
target. B: the 1-dimensional (1-D) ME output
(y axis) through time (x axis). Each
square indicates 1 output unit, with the gray level of the square
representing the responsiveness. The short bars indicate the averaged
response center of the 1-D output. The black dot indicates the time of
the presentation (x axis) and the expected ME of the
target. C: the 1-D output when a stimulus is presented
during the delay period. The output is shifted by the stimulus.
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One important feature of LIP neurons is that the memory activity
sustains even when new stimuli are presented during the memory period.
A stimulus that appears at a different location from the target during
the delay period is called an irrelevant stimulus. The memory activity
of LIP neurons is resistant to irrelevant stimuli (Mazzoni et
al. 1996b). However, the preceding trained network
failed to produce this feature. When a new stimulus was presented
during the delay period, the output pattern of the network shifted away
from the expected ME, as shown in Fig. 2C. The final motor
command for the saccade was thus incorrect. Correspondingly, the memory
activity of hidden units was disturbed with the presentation of the
irrelevant stimulus. Therefore although this network can perform simple
memory saccades, it is insufficient to model the memory properties of
LIP neurons.
The network also failed to produce the inhibitory activity observed in
many LIP neurons. By examining the weights of the recurrent connections, we found that connections between units with similar preferred saccade directions (PD) became stronger with the progress of
training. Strong excitatory connections mostly occurred between units
with similar PD at the end of the training. The responses to targets
were sustained through the circulation of the activity using these
connections. On the other hand, inhibitory connections were rarely
observed in the network.
MEMORY-SACCADE MODEL TRAINED WITH THE SINGLE-PURPOSE FEATURE.
Training and network performance. We retrained the
same model in Fig. 1 by applying the single-purpose feature to the
training procedure as a constraint. Figure
3A shows a typical training pattern. The target was flashed for one time step as before. In addition to the target, an irrelevant stimulus was presented at a
random location during the delay period. The irrelevant stimulus was a
dot stimulus lasting for one time step. The network was required to
yield the correct ME of the saccade to the target. Thus the activation
of the irrelevant stimulus was to be ignored. At the time of the
saccade command, the difference between the expected ME and the actual
output was computed for each output unit; the weights of connections
were adjusted accordingly.
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Fig. 3.
The training pattern and the performance of the model with the
memory-saccade feature. A: the training pattern. The
timing of the target and the irrelevant stimulus are indicated with
short bars and the eye movements are indicated with lines.
B: the 1-D output of the model after training,
illustrated in the same way as in Fig. 2. *, the presentation of the
irrelevant stimulus. Compared to Fig. 2C, the stimulus
did not shift the output center.
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In the beginning of training, the output of the network was shifted by
the presentation of the irrelevant stimulus. Gradually, the effect of
the irrelevant stimulus became less. Eventually, after 4,000-5,000
training cycles, the network learned to hold the correct ME memory of
the first target at the end of the delay period, irrespective of the
presentation of the irrelevant stimuli at any location and any time
during the delay period. Figure 3B shows an example of such
a response. The standard deviation of the actual output from the
expected output is 2.91°.
Through training the hidden units acquired localized RFs for both
visual and auditory inputs. The visual and auditory responses to
targets were modulated by eye position. The map of this modulation over
different eye positions is called a "gain field" (Zipser and
Andersen 1988). Most hidden units were also tuned to saccadic movement directions. These properties are similar to those observed in
LIP neurons and to those obtained from a similar model without recurrent connections (Xing et al. 1994). In this
report, we are more interested in the sustained response patterns of
the hidden units.
Figure 4 shows two typical response
patterns of a hidden unit. The left panel
indicates the RF of the unit as well as the locations of the targets
and irrelevant stimuli. The right panel shows the responses
through 13 time steps. The timing of inputs and the expected saccades
is indicated at the top of the figure. In Fig. 4A, the
target falls onto the unit's RF, and the saccade is in the unit's
preferred direction. The unit responds to the target and activity
sustains throughout the delay period. Notice that the brief
presentation of the irrelevant stimulus during the delay period does
not affect the memory activity. In Fig. 4B, the target is
opposite to the preferred saccadic direction, while the irrelevant
stimulus falls in the center of the RF. The unit does not respond to
the target. It has a brief response to the irrelevant stimulus, but the
response is immediately suppressed. Some units do not respond to the
irrelevant stimuli at all. This kind of activity is often observed in
double-saccade experiments in which neurons have little or no response
to the brief flash of the second target during the delay period.
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Fig. 4.
Typical response patterns of a hidden unit in the memory-saccade model.
Left: spatial arrangement of the tasks. The receptive
field (RF) of the unit is indicated with the dashed area. The star
symbol indicates the irrelevant stimulus (IS), and the target (T) is
represented with the black dot. The arrow line shows the saccade.
Right: each graph shows the response of the hidden unit
through time. The height of the bars corresponds to the responsiveness.
A: the sensory and memory activity to a target in the
unit's RF. B: the brief response to an irrelevant
stimulus in the RF.
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Through the use of various test patterns, we find that there are
different types of hidden units. A small portion of the hidden units
only have sensory responses but no sustained activity during the delay
period
the units respond to a target, and the responses die away soon
after the target disappears. Detailed examination of these units
reveals that the weights of inward recurrent connections to them are
very weak. These units are merely the result of the random process of
training. The majority of the hidden units exhibit different types of
response patterns, depending on the tasks. A unit may have sensory
responses and memory activity to a saccadic target presented in its RF
as shown in Fig. 4A. Alternatively, if the stimulus in the
RF is an irrelevant stimulus, the unit may only show a weak, brief
responses or no response at all (Fig. 4B). More importantly,
the irrelevant stimulus does not shift the firing activity away from
the response evoked by the first stimulus. When the target is in a
unit's preferred direction but does not fall in the center of the RF,
the unit has a weak response to the flash of the target but its
elevated activity is sustained during the delay period. This memory
activity is due to the excitatory inputs from other units with similar
PDs (as will be explained in the next section). These response patterns
are exactly what were found in LIP neurons in memory-saccade
experiments (Mazzoni et al. 1996b).
Structure of the recurrent network.
To understand the underlying mechanisms of saccadic memory activity, we
examined the connectivity developed in the recurrent network. Figure
5A shows the weights of
recurrent connections between the hidden units. The weights are plotted
against the difference of preferred directions of the connected units
with each dot for one connection. Compared to the recurrent
connectivity in the model trained without the single-purpose
constraint, strong inhibitory connections were developed between the
units with dissimilar PDs in addition to the excitatory connections
between the units with similar PDs. The distribution of all connection
weights is relatively continuous, varying between 1 and +1. Figure
5B summarizes the data in Fig. 5A. The units with
similar PDs have the strongest excitatory connections, and the
excitatory connections become weaker as the PD difference increases.
With the PDs further apart, the connections between the units become
inhibitory. The strongest inhibitory connections occur to units with
opposite PDs.
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Fig. 5.
The weights of recurrent connections. A: the weight of
recurrent connections (y axis) are plotted against the
difference of the preferred directions of the 2 connected hidden units.
Each dot is for 1 connection. B: the diagram of the
push-pull mechanism. Shaded circles represent hidden units and lines
represent recurrent connections.
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We therefore propose a recurrent model for memory activity: lateral
excitation pulls responses together from units with similar PDs to
maintain the activity over a period of time, while lateral inhibition
pushes away any response in units with dissimilar PDs so that their
responses do not disturb the ongoing memory activity. Such a push-pull
structure could be the basic architecture for the single-purpose
feature of memory activity in area LIP. Recurrent excitation may invoke
a set of neurons with similar PDs to maintain the memory activity. Once
this neuron population is engaged, those neurons with dissimilar PDs
are suppressed due to the inhibition. Thus when a new stimulus is
presented at a different location, the neurons tuned to that direction
are inhibited. Even if some of these neurons may respond weakly, as
shown in Fig. 4B, the activity is immediately suppressed by
the existing cooperative activity of the first population. Therefore
the push-pull structure can lock the ongoing activity to prevent it
from being disturbed. Only after the remembered saccade is made and the
cooperative activity is turned off, can the network perform a new task.
Notice that the inhibition is a training result of ignoring irrelevant
stimuli, i.e., a result of the single-purpose feature. The weights of
feedforward and recurrent connections were adjusted such that the
hidden unit activity evoked by the one-time-step presentation of the
dot stimulus was not strong enough to override the inhibition. Since
the ability of the network to resist irrelevant stimuli depends on the
training stimuli used, a strong sustained irrelevant stimulus or
simultaneously presented multiple stimuli could override the recurrent
activity of the network trained here. Similarly, a strong sustained
inhibitory input to the hidden layer could override the recurrent
activity maintained by excitatory recurrent connections. This allows
the network to be reset quickly.
Model of double saccades
LIP neurons participate in planning sequential eye movements. This
has been typically studied with double-saccade experiments. In this
section, we first summarize the neurophysiological data and then extend
the memory-saccade model to make a sequence of two saccades.
PHYSIOLOGICAL RESULTS TO BE MODELED.
The delayed double-saccade tasks by Mazzoni et al.
(1996b) were designed to test whether LIP neurons encoded
sensory locations or motor plans of saccades in sequential eye
movements. The monkeys were required to memorize two targets briefly
flashed in succession during a delay period and to make a sequence of
two saccades to the two targets after the fixation light went off. The
memory activities during the delay period (before the 1st saccade) and during the intersaccadic interval (after the 1st saccade and before the
2nd saccade) were examined. Extracellular recordings showed that during
the delay period, many neurons whose movement fields were in the
direction of the first saccade fired continuously until the first
saccade was made, whereas neurons coding for the direction of the
second saccade started to fire only after the first saccade was
performed. Figure 6 shows the responses
of a typical LIP neuron in different double-saccade tasks. The
left panel shows the two saccades made toward the two
remembered targets. The dashed curve indicates the neuron's RF. This
neuron preferred saccades in the down-left direction. The saccadic
targets are indicated with black dots and labeled as T1 and T2.
Responses of the neuron are shown in the right panel. The
delay period is labeled as M1. The horizontal and vertical eye
positions are plotted under the responses. The first deflection in
these eye traces corresponds to the first saccade and the second
deflection corresponds to the second saccade. In Fig. 6A,
both targets fall in the RF, and only the first saccade is in the
neuron's PD. The neuron fires during the delay period. The sustained
activity goes off after the first saccade is made. In Fig.
6B, the first target is outside the RF and the second target
falls in the RF. The second saccade is in the neuron's PD. The neuron
has a brief response following the flash of the second target, and this
activity does not sustain during the delay period. After the first
saccade is completed, the neuron begins to fire and the activity
sustains until the monkey makes the second saccade. Thus the activity
is related to the second saccade. In Fig. 6C, no targets
fall in RF, but the second saccade is in the neuron's PD. The neuron
has no response to the flash of either target. However, it fires during
the intersaccadic interval and thus codes for the second saccade.
Therefore this neuron encodes a preferred impending movement regardless
of target locations. As shown in Fig. 6C, the activity does
not even depend on sensory stimulations. Seventy-seven percent of LIP
neurons recorded encode the impending saccade. It is concluded that the memory activity of the majority of LIP neurons encodes the next planned
saccade. On the other hand, 16% of neurons encode target locations
instead. These neurons begin to fire after the flash of the second
target, which falls in their RFs, and the activity lasts through the
delay period and the intersaccadic interval. These neurons may
participate in programming subsequent saccades because information
about the second target needs to be held until the first saccade is
performed. The remaining neurons, approximately 7%, were difficult to
classify into one or the other of the two categories.
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Fig. 6.
Activity of a lateral intraparietal cortex (LIP) neuron coding for
motor intention. The responses of a typical cell encoding impending ME
in 3 double-saccade tasks. Each panel has a plot that includes, from
top to bottom, the spike rasters for each
trial, the time histogram of the firing rate, and the horizontal and
vertical eye positions (30°/division) (abscissa: 100 ms/division).
The vertical dotted lines and the thick horizontal lines
below each panel show the onset and offset of the visual
stimuli. The deflections in the eye traces correspond to the first and
the second saccades in sequence. The diagrams to the
left of each panel show the spatial arrangement of the
1st and 2nd target (T1 and T2, respectively), the 1st and 2nd saccades
(arrows), and the neuron's RF. This figure is modified from
Mazzoni et al. (1996b).
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From a large amount of experimental data, we generalized three basic
features about LIP neurons in double-saccade tasks. Feature 1: Single purposeThe sustained activity for the first saccade is
only minimally transiently affected by the brief presentation of the
second target. Feature 2: Postsaccadic suppressionThe sustained activity is sharply turned off after the saccade is performed. This turning off is also seen in simple memory saccades. Feature 3: Memory bufferA separate population of neurons
hold information about the second target. This population should
project to those LIP neurons which, in turn, project to other
motor/premotor areas.
MODEL.
Based on the preceding experimental observations, we extended the
memory-saccade model to simulate double-saccade tasks. Figure 7 is a diagram of the extended model.
Besides the recurrent network in the original memory-saccade model,
called recurrent net I (RN-I) here, the extended model has an
additional recurrent net in the hidden layer (RN-II). This population
of units also receive visual, auditory and eye-position inputs. Its
output projects to the primary hidden net (RN-I). Every RN-II unit
projects to all RN-I units. Like RN-I units, RN-II units are fully
interconnected. The postsaccadic suppression is also built into the
model. It artificially resets the activity of RN-I units to the initial
state after the first saccade is made. The push-pull structure of the
RN-I network is capable of carrying out feature 1, the
single-purpose feature; postsaccadic suppression serves feature
2, i.e., turning off the memory activity in RN-I after a saccade
is made; and the RN-II network serves the memory buffer for
feature 3. This model is expected to produce the following
response patterns: RN-I units encode the first saccade, and the
activity is sustained while a brief presentation of the second target
does not affect the on-going activity in RN-I due to the push-pull
mechanism; information about the second target and the initial eye
position is maintained in RN-II; the postsaccadic suppression turns off
RN-I activity after the first saccade is made; and after the first
saccade is performed, RN-I combines the new eye-position information
with the input from RN-II and produces a new ME for the second saccade.
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Fig. 7.
The diagram of the extended model for double saccades. The recurrent
net-II (RN-II) and the postsaccadic suppression are added to the simple
memory-saccade model shown in Fig. 1.
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The RN-II network acts as a memory buffer for the second target. In a
delayed double-saccade task, different populations of neurons must be
involved to hold the information about each target and thus a memory
buffer is necessary. This memory buffer could correspond to the 16% of
LIP neurons coding for target locations (Mazzoni et al.
1996), or it may come from some brain areas outside area LIP,
such as area 7a or the frontal lobe. We do not specify which of the two
possibilities correspond to the RN-II network since there is currently
not sufficient experimental evidence to make this determination. The
RN-II network loads the target that is retained in a memory buffer,
i.e., the input lines of the RN-II network are open only after the
onset of the second target.
An important control structure of the model is the postsaccadic
suppression, which turns off the activity of RN-I units after the
saccade is made. Such a turning-off action is necessary for neurons to
encode a new saccade. During single-memory-saccade and double-saccade
tasks, sharp turning-off of LIP neuronal activity is often observed
right before or after the saccade. One possible source of such
suppression is the efferency copy of the eye movement command. However,
in a change-plan experiment (Bracewell et al. 1996),
where the monkey was required to prepare a saccade to a new target
during the fixation period, the memory activity of LIP neurons for the
previous planned saccade was turned off sharply even though no eye
movement was made. Thus eye movement information could not be the only
source for the suppression. A high-level signal that changes the
memorized saccadic plan may terminate the activity of the neurons. The
suppression thus could be due to strong inhibitory inputs from other
high-order cortical areas, such as the frontal eye field (FEF). Many
neurons in the FEF exhibit postsaccadic activities (Bruce and
Goldberg 1985; Goldberg and Bruce 1990).
Given that the FEF has feedback connections to area LIP, it is possible
that those FEF neurons send a damping signal to LIP to provide the
postsaccadic suppression. The generation of such inhibitory inputs is
beyond the scope of the model. We mimicked this postsaccadic
suppression by simply resetting the network artificially.
TRAINING PROCEDURE.
In each training cycle, two targets (T1 and T2), either visual or
auditory, are randomly selected for position and modality and presented
to the network for a duration of one time step. With E0 representing
the initial eye position, V1 for the location of the first visual
target in retinal coordinates, and A1 for the location of the auditory
target in head-centered coordinates, the desired ME output at the end
of the delay period is ME = V1 for visual targets or ME = A1 E0 for auditory targets. After the first saccade is made,
the eye is moved to the new position E1. The desired output at the time
of the second saccade is ME = V2 + E0 E1 or ME = A2 E1. Here V2 and A2 indicate the second visual and auditory targets.
Figure 8A illustrates the
training protocol. Target T1 is flashed at the beginning of a training
cycle and T2 is flashed at a randomly selected later time step. The two
saccade commands, labeled as S1 and S2, are made for the two targets,
separated by two time steps in the intersaccadic interval. The length
of this interval is arbitrary, simply mimicking the approximately 100- to 200-ms time lag between two consecutive saccades in double-saccade tasks. The initial eye-position signal E0 lasts until the time of S1;
the new eye-position signal E1 starts after S1. The RN-I network is
open all the time except for the reset at the time of S1. The RN-II
network begins to open only after the onset of target T2. The error
signals for learning are computed at the time of S1 and S2. The
connection weights are adjusted accordingly.
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Fig. 8.
Training pattern and the performance of the double-saccade model.
A: the training pattern includes 2 targets, T1 and T2,
and 2 saccades, S1 and S2. The time lag between S1 and S2 is the
intersaccadic interval. B: the 1-D motor error output of
the model illustrated in the same way as in Fig. 2. The timing of T1
and T2 and S1 and S2 are indicated on the top.
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Figure 8B shows an example of the model performance at the
output layer after training. After the training is completed, the connections are fixed. Like in the training period, the network is run
for 13 time steps for a given combination of the two target locations
and the initial eye position. The ME outputs of the network are plotted
along the vertical axis. The two black dots indicate the expected MEs
of the two saccades. The output of the model encodes the first saccadic
ME before the first saccade is made, and then encodes the second
saccade. Thus the model produced two saccade commands in sequence. The
push-pull structure assures that the model carries out multiple saccade
plans sequentially.
RESPONSES OF THE HIDDEN UNITS.
After training, most hidden units in RN-I and RN-II developed localized
RFs for both visual and auditory inputs. When eye position was centered
in the orbit, the visual and auditory RFs of a given unit were usually
aligned. The RFs were very large; some of them even occupied up to half
of the input space. The responses of the hidden units to visual or
auditory targets were gain modulated by initial eye position. Later we
will discuss how these gain fields are essential for coordinate transformations.
As in the single-memory-saccade model, most hidden units in the
double-saccade model exhibit sustained memory activity to visual and
auditory targets. Here we show the typical response patterns of the
hidden units to visual targets to make direct comparisons with the
experimental data in Fig. 6. Figure 9
illustrates five response patterns of two typical hidden units. Figure
9, A-C, shows the responses of a unit in the RN-I network;
Fig. 9, D and E, shows the responses of a unit in
the RN-II network. The left panel shows the spatial
arrangements of the saccades. The RFs of the units are outlined with
the dashed areas. The initial eye positions are indicated with + symbols. The two targets are labeled as T1 and T2, and the two saccades
are labeled as S1 and S2. The responses of the units are shown on the
right panel with the height of the vertical bars
proportional to the responsiveness. The targets are flashed
sequentially on the first and fourth steps and the model produces the
first saccade (S1) at the 10th time step and the second saccade (S2) at
the 13th time step, as indicated (top right).
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Fig. 9.
Typical responses of 2 hidden units in the double-saccade model. The
timing of targets and saccades are shown on the top of
the figure. Left: the spatial arrangements, with the
dashed area for the RFs, T1 and T2 for the 2 targets, and S1, S2 for
the 2 saccades. Right: the response patterns.
A-C: responses of a RN-I unit in 3 double-saccade
tasks. D and E: the responses of a RN-II
unit in 2 tasks.
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The double-saccade arrangements in Fig. 9, A-C, are the
same as those in Fig. 6, A-C. In Fig. 9A, S1 is
in the unit's preferred direction. The unit responds to the target and
the activity sustains until the postsaccadic suppression turns it off
at the time of S1. In Fig. 9B, only T2 falls in the RF and
S2 is in the unit's preferred direction. The unit has a brief response
when T2 is presented, and this activity is suppressed by other hidden
units that encode S1 during the delay period. This unit begins to fire after S1. In Fig. 9C, no targets fall in the RF, but S2 is
in the unit's preferred direction. The unit still fires during the intersaccadic interval, coding for S2. Like the neuron shown in Fig. 6,
the sustained responses of this model unit code the upcoming saccade.
The result of Fig. 9C is intriguing in that a unit can be
activated without a target in its RF.
Notice that the neuronal responses shown in Fig. 6 exhibited complex
dynamic patterns. For example, the activity in Fig. 6A had a
dip between the offset of the second target and the onset of the
saccade. This dip might correspond either to the second target or to
the saccade onset. The activities in Fig. 6, B and C, also had similar dips. The model responses in Fig. 9,
A-C, did not capture these dynamic response patterns. The
model units updated their activities at a time step of 100 ms while
neurons updated their activities at an order of 1 ms. To capture those neuronal dynamics requires a network with realistic model neurons and
stochastic processing.
Figure 9, D and E, shows the responses of a
typical unit in the RN-II network. The unit begins to respond after the
onset of T2 in its RF, and the activity is sustained. The locations of
target T2 in Fig. 9, D and E, are the same, but
the initial eye positions in the two graphs are different. The unit
responds to T2 in both cases. However, the responses are strongly
modulated by the eye position. The responsiveness in Fig. 9E
is weaker than that in Fig. 9D as the eye position moves in
the opposite direction to the unit's RF from Fig. 9, D to
E. The information about the eye position is thus combined
with the target's retinal location through this modulation. Therefore
the information about head-centered representation is implicitly
carried in the activity of a set of RN-II units.
COORDINATE TRANSFORMATIONS.
One traditional question about double-saccade tasks is how the motor
vector for the second saccade is computed, given that eye position at
the time of the second saccade is different from the time when the
visual target was flashed. How are the spatial transformations required
for double-saccades carried out? To answer this question, we examined
how eye-position information is utilized by the hidden units in the model.
We first examined the hidden units in the RN-II network. The RF
of a unit was first measured at the central eye position. Next, for
8 × 8 eye positions, the responses to a target presented in the
RF were measured. Results showed that the responses of most hidden
units were modulated by eye position. The 2-D plot of responses against
different eye positions is called gain field (GF) as reported by
Andersen et al. (1985). The GFs of RN-II units monotonically increase in particular directions. Figure
10, A and B,
shows the RF and the GF of a typical unit. In Fig. 10A, the gray levels of the small squares correspond to the responses of the
unit to the target presented at different locations of the input map
while the eye position is pointed at the central fixation. In Fig.
10B, the sizes of the squares indicate the responses to a
target presented in the center of the RF for different eye positions. Notice that the unit's RF and its GF are in the same direction. This
is typical for the majority of the RN-II units. Figure 10C shows the direction differences of the GF and the RF for every RN-II
unit. Most units have an aligned RF-GF structure. The two units whose
RF-GF direction differences are close to 180° have weak responses.
Therefore they have little contribution to the network. A group of
units with the aligned RF-GF structure is well suited for the
transformation from eye- to head-centered coordinates since this
transformation requires addition of eye position and retinal position.
Previously we have demonstrated that a population of units with aligned
RF-GF contains an implicit representation of target locations in
head-centered coordinates (Xing et al. 1994;
Zipser and Andersen 1988).
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Fig. 10.
RF and GF of a RN-II unit. A: the visual RF of a typical
hidden unit measured at the central eye position. The gray level of the
dashed squares is proportional to the evoked response in the hidden
unit. B: the spatial gain field (GF) of the unit. The
GFs are the responsiveness of the unit to a target within its RF
plotted against an 8 × 8 grid of eye positions spaced by 10°.
The gray level and the size of small squares in the graphs correspond
to the activation of the unit. C: the RF-GF direction
differences for every hidden unit in the RN-II network. The direction
of a RF was calculated as the vector direction from the center of the
input map to the center of the RF. The difference between tuning
direction of a GF and the RF direction was computed for every hidden
unit and shown in the figure. Hidden units are listed along the
horizontal axis; the vertical axis indicates the corresponding absolute
value of direction difference. Most hidden units have direction
differences close to 0°, i.e., the aligned RF-GF structure.
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Next we examined RFs and GFs of the units in the RN-I network. After
training, most RN-I units developed RFs for visual and auditory inputs
and monotonic GFs for eye position. Figure
11, A and B,
shows the RF and GF of a typical RN-I unit. Unlike the one in Fig. 10,
this RF and GF of the unit are in opposite directions. Figure
11C shows the RF-GF direction differences for all the RN-I units. The result indicates that most RN-I units have an opposite RF-GF
structure. The opposite RF-GF structure is well suited to carry out the
transformation from head-centered coordinates to eye-centered
coordinates. This transformation requires subtraction of eye position
from a head-centered target location. The opposite signs for changes of
eye position and head-centered location, due to the opposite RF-GF
structure, meet the requirement of the subtractive operation
(Xing et al. 1994). This operation is required for
computing the ME of the second saccade from a distributed head-centered
representation in the RN-II network.
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Fig. 11.
RF and GF of a RN-I unit. The illustrations are the same as in Fig. 10.
A: the RF of a typical RN-I unit. B: the
GF. C: the direction differences. Notice that most RN-I
units have GF and RF in the opposite direction.
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We further found that the visual and auditory RFs (VRFs and ARFs) of
RN-I units differed in two aspects: 1) although the VRF and
ARF of a given unit usually aligned roughly, the VRF was smaller than
the ARF. Most ARFs were planar and spread toward the edges of the
auditory input map. 2) The GFs for ARFs were much stronger (with steeper slopes) than those for the VRFs. Further examining the
connection weights we found that the weights to the RN-I units from the
visual inputs were on the average stronger than the weights from the
auditory inputs and the RN-II inputs. With the sigmoidal integration
between the signals of eye position and target location, the stronger
connection weights to visual inputs resulted in a weak effect of eye
position on the visual responses. Due to this weak gain modulation, no
coordinate transformation occurred to visual inputs of single visual
saccades or the first visual saccade in a double-saccade task. This
resulted in one of the model functions: ME = V1.
The results of Figs. 10 and 11 show that the majority of RN-I units
have an opposite RF-GF structure and the majority of RN-II units have
an aligned RF-GF structure. This segregation of RF-GF types is
associated with the output function of the double-saccade model. The
output layer in the present model is a single map of eye MEs. Hence the
only task for the hidden layer is to compute MEs. There might be other
types of coordinate transformations occurring in area LIP as well. The
double-saccade model here may only reflect a part of the more
complicated LIP functional structures for different sensorimotor
integrations. When we modified this model by having multiple output
maps in different coordinates, for example, a ME map and a
head-centered spatial map, the distribution of RF-GF types in the
hidden layer changed; the units in both RN-I and RN-II networks
exhibited aligned, opposite, and intermediate RF-GF structures
(Andersen et al. 1997).
The results in the preceding text outline the coordinate frames used by
the hidden units to encode saccadic targets in double-saccade tasks. We
further looked into the coordinates of RN-I and RN-II network. For
RN-II units, the tuning curves to target retinal locations were plotted
for different initial eye positions. A diagram showing how the tuning
curves are computed is shown in Fig.
12A. The and - - -
represent retinotopic frames at the two eye positions E and E'; the
trajectories indicate the saccades to eight target locations. The
retinal target locations in the two eye-position frames are identical.
If a unit encodes saccadic targets in retinal coordinates, the
retinotopic tuning curves for different eye positions should align with
each other. In contrast, if the unit encodes targets in motor
coordinates, the tuning curves should shift with eye position. Figure
12B shows the retinotopic tuning curves for a typical RN-II
unit. In Fig. 12B, the vertical axis represents the
responses and the horizontal axis indicates retinal locations. The and - - - are for the two eye positions. Although the responsiveness
for a given retinal location is modulated by eye position, the two
tuning curves align well with each other. Therefore RN-II units encode
inputs of saccadic targets in retinal coordinates. These units may
correspond to the small portion of LIP neurons that encode the memory
of target locations (Mazzoni et al. 1996b).
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Fig. 12.
Tuning curves of a typical RN-II unit. A: the method for
computing retinal location tuning curves for different eye positions.
and - - -, retinotopic frames at the 2 eye positions, E and E'.
For each eye position, the arrays indicate the saccades to 8 retinal
locations. The retinal locations are identical for the 2 eye positions.
B: the tuning curves of a typical RN-II unit. The
responsiveness of the unit (the vertical axis) is plotted against
target retinal locations (the horizontal axis). and - - -, the two
initial eye positions, respectively. The 2 tuning curves align well
with each other.
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Next we investigated the coordinates of the RN-I network. Figure
13A shows the diagram for
computing tuning curves of RN-I units. The x and
y axes are in head-centered coordinates. The target
positions of the first saccade are indicated by 
, i.e., the initial
eye positions of the second saccade. The trajectories represent the
second saccades. In one test, the second saccades are made outward to
eight targets, as indicated with . In the other test, the second
saccades are made inward from a different set of initial eye positions
to the same sets of targets as in the first test. Thus the target
locations are the same for the two tests although the directions of the
second saccades toward a given target are different in the two tests.
The tuning curves of RN-I units are plotted for each test. Figure
13B shows the tuning curves for a typical RN-I unit. The
responsiveness of the unit is plotted against the retinal location of
the second saccadic targets; the and - - - are for the two tests.
The results show that the two tuning curves do not align in retinotopic
coordinates. In Fig. 13C, the same set of data in Fig.
13B is plotted against eye MEs. The two ME tuning curves
align well with each other. Therefore RN-I units encode saccadic
targets in motor coordinates. These units may correspond to the
majority of LIP neurons that encode MEs of saccades (Mazzoni et
al. 1996b).
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Fig. 13.
Tuning curves of a typical RN-I unit. A: the diagram for
computing tuning curves in double-saccade tests. ,
retinal locations of the 1st target, i.e., the initial eye positions of
the 2nd saccade. The arrays represent the 2nd saccades. , saccades to
8 target locations in 1 test; - - -, the saccades that are in the
opposite direction but end at the same locations as in the 1st test.
B: the tuning curves for a typical RN-I unit. The
responsiveness of the unit is plotted against the retinal location of
the 2nd saccadic targets; and - - -, for the 2 tests,
respectively. The 2 tuning curves do not align on the retinotopic
space. C: the same set of data as in Fig.
13B is plotted against saccadic motor errors (the
horizontal axis). The 2 motor error tuning curves align well with each
other. Thus the unit encodes saccades in motor coordinates.
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Theoretically, eye-position modulation with the aligned RF-GF structure
yields a head-centered representation of target locations in the
distributed activity of RN-II units. This head-centered representation
is fed into the RN-I network after the first saccade. With the opposite
RF-GF structure in the RN-I network, the new eye-position information
is subtracted from the head-centered representation to yield a ME of
the second saccade. Hence RN-I units encode saccadic targets in motor
coordinates. Therefore the model carries out coordinate transformations
required for double saccades in the following steps: the RN-I network
transforms target locations into the representation of MEs through the
opposite RF-GF structure (for auditory targets), and the RN-II network provide the RN-I network with a head-centered representation of the
second target through the aligned RF-GF structure. Thus the RN-I
network encodes motor plans of saccades, while the RN-II network
represents head-centered information implicitly through distributed
coding of RN-II units.
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DISCUSSION |
The mechanisms for programming memory saccades and sequential
saccades remain unclear to neurophysiologists. A number of
computational models of saccade generation have been proposed.
Dominey and Arbib (1992) proposed a cortical-subcortical
model of the control of saccadic eye movement and suggested that the
parietal cortex may dynamically remap the target locations in saccade
ME maps to program double saccades. The network model developed by
Droulez and Berthoz (1991) showed that target position
could be memorized in a sensory map and updated with eye-movement
signals. Krommenhoek et al. (1993) trained a neural
network to compute MEs using information about eye position. These
computational approaches yield valuable insights into memory saccades.
On the other hand, the frameworks in these models did not correspond
well to known neurophysiological data. Given that LIP neurons can
withhold their saccade-related activity and participate in programming
double saccades, the network model in this report studied the memory
activity in area LIP for saccadic eye movements. With the
implementation of the single-purpose rule in the training process, the
network developed lateral excitation-inhibition (the push-pull
structure) that was essential to memory and sequential saccades. The
simulated neurons in our model exhibited properties similar to those
recorded in area LIP. After training to make double saccades, the model
carried out the coordinate transformations required to program double
saccades by the means of gain modulations. In our model, one group of
neurons maintain the sensory memory of saccadic targets, while the
other group of neurons encode the motor plan of an impending saccade.
Thus coding the motor commands of double saccades is achieved by
different neuronal populations rather than by dynamically remapping the
same neuronal population.
One prediction of the model is that neurons corresponding to the memory
buffer RN-II respond to the second target but not the first one.
Mazzoni et al. (1996b) found that 16% of LIP neurons encoded the location of the second target in a memory-saccade task.
These cells were referred as the "sensory memory" cells. It would
be interesting to test experimentally whether these cells encode only
the second target or any visual stimuli within their RFs. Furthermore
the model predicts that the responses of RN-II neurons are gain
modulated by the initial eye position. Due to the push-pull structure,
the activity of RN-II neurons is not affected by the new eye position.
This remains to be tested experimentally.
Push-pull structure
Examining data from various kinds of delayed-saccade experiments,
we found a common feature in the response patterns of LIP neuronsonce
a neuron is engaged in a saccade command, its activity is maintained
irrespective of further stimuli; the neuron starts to respond to
another stimulus only after the saccade being encoded is completed or
the intention of the saccade is dismissed by some high level command.
We called this feature single-purpose. This feature is essential for
the behaviors of a motor system. The eyes can never make saccades
simultaneously to two different spots.
The single-purpose feature is used as a constraint for the training
process of our networks. This constraint results in the push-pull
structure, i.e., excitatory connections between units with similar
preferred saccadic directions and inhibitory connections between units
with dissimilar preferred directions. Such an excitation-inhibition structure is the neuronal basis for the single-purpose feature. In the
extended model of the double-saccade system, the push-pull structure
allows the model to program two saccadic commands sequentially, rather
than mixing the two commands into one. Therefore the
excitation-inhibition connections ensure that LIP encodes the next
planned saccade.
Ideally, a push-pull structure suppresses any irrelevant stimuli that
differ from the target location. However, through simulation we found
that responses to stimuli close to the target were often sustained
rather than suppressed. The minimal distance for an irrelevant stimulus
to be suppressed varied from unit to unit but was roughly in an order
of about 10°. Within this distance, the output memory activity
represented a ME that was a weighted average between the irrelevant
stimulus and the target. The function of the connection weights in Fig.
5A reflected this inaccuracy: Excitatory connections could
occur to PDs that are 10-20° apart. Several reasons contribute to
this inaccuracy: the tuning of the hidden units is broad; the limited
number of the hidden units prevents precise excitatory connections; and
the training samples of the stimulus locations are often more than
10° apart. We expect that using a large set of hidden units and finer
spaced training stimuli, or an attention mechanism, would improve the
accuracy of the push-pull structure.
A number of neural network studies have used a push-pull structure as a
memory-storage mechanism (Grossberg and Levine 1975; Seung 1996; Zhang 1995).
Typically, adjacent units in these networks excite each other while
distant units inhibit each other. Such an arrangement could prevent
recurrent activities from spreading to the whole network. Thus a
push-pull mechanism also enforces the stability of a recurrent network.
Salinas and Abbott (1996) recently proposed another
functional role of the push-pull structure in the parietal cortex. They
found that neurons in a recurrently connected network with push-pull
connections could perform a product operation on additive synaptic
inputs. The resulting multiplicative gain modulation is important for
coordinate transformations in the parietal cortex. In our model, the
push-pull structure emerged as the result of the single-purpose
feature. Moreover, the excitation and inhibition were organized
according to the preferred directions of the units, rather than the
geometric positions. Goldman-Rakic (1995) observed a
similar lateral inhibition structure in the opponent memory field of
neurons in the frontal cortex. Schlag et al. (1998)
found that, in the FEF, cells that encoded similar eye movements
mutually excited each other while silencing those that would produce
conflicting eye movements. Since the single-purpose feature might be
common for cortical areas involved in motor planning, it is likely that
the push-pull structure is a principle applicable to these cortical areas.
An analogy to the single-purpose feature is the winner-take-all
mechanism. The latter has been widely applied to the models of visual
search processes (Braddick 1997; Ferrera and
Lisberger 1995; Lee et al. 1999). In a visual
search task, a target is searched among a number of distractors. A
winner-take-all mechanism allows the neurons representing the target
and the distractors to compete against one another. Attention serves to
bias the outcome of this competition toward the direction of the
selected target. As a result, the neuronal response to the target
remains and the response to the distractors is suppressed.
Salzman and Newsome (1994) also proposed that a
winner-take-all mechanism existed in the motion cortex (area MT and
MST). When more than one motion cue was presented, monkeys chose the
direction encoded by the largest signal in the representation of motion
direction. Braddick (1997) suggested that local motion
detectors use winner-take-all interactions in global motion analysis.
The single-purpose feature and the winner-take-all mechanism are
similar in that both generate only one single output representation. The latter evokes neuronal competition based on the context of stimuli
and enhances the response to the target stimulus through attention.
Such a mechanism is not suitable for area LIP because LIP neurons are
generally insensitive to stimulus context and thus do not support a
competition process. The target to be represented in LIP is chosen by
motor intention and is not the result of an attention-biased
competition. The winner-take-all mechanism handles spatial conflicts in
visual selection. The single-purpose feature assures no conflicts in a
temporal sequence of motor plans. Neurophysiological data support our
assumption that a single-purpose feature exists in area LIP. It would
be interesting to test this assumption further by recording the
responses of LIP neurons to a target and many distractors presented simultaneously.
Coordinate transformations
A traditional question about planning double saccades is how the
motor command of the second saccade is computed. Two hypotheses have
been proposed. One hypothesis is head-centered coding (Robinson 1975; Sparks and Mays 1983): the absolute target
location in head-centered coordinates is computed and stored, and then
the new eye position after the first saccade is subtracted. With this
hypothesis, one would expect to find neurons that encode visual targets
explicitly in head-centered coordinates. However, physiological studies
have largely failed to find such neurons. Most LIP neurons have retinal RFs with their responses modulated by eye position. The other hypothesis is retinotopic coding, also called vector subtraction (Bruce and Goldberg 1985; Scudder 1988):
the retinal location of the target is stored and then the change of eye
position is subtracted. This hypothesis requires neurons that
explicitly encode the change of eye position.
The simulation results of this report suggest a third possibility:
instead of computing explicit head-centered target locations or the
change of eye position, LIP neurons utilize eye position with the use
of GFs to carry out coordinate transformation through the distributed
activity of many neurons. In the double-saccade model, information
about the second target location is combined with the current
eye-position signal through aligned RF-GF gain modulation to form a
distributed head-centered representation. After the first saccade, the
new eye position comes in and is combined with the head-centered
representation through the opposite RF-GF structure so that the ME of
the second saccade is computed. This model does not require individual
neurons to encode target locations in explicit head-centered
coordinates. The presence of GFs could account for the computation of
double saccades. Moreover, the experimental results by Li et al.
(1995) suggested that a distributed head-centered
representation of targets might be maintained in LIP for programming
sequences of eye movements. Using reversible lesions of LIP, Li et al.
found that the monkeys depended on the new eye position more than the
retinal vectors to make the second saccade. Thus this model fits
current data well.
Theoretically, coordinate transformations suggested by the first two
hypotheses above can be carried out by shift circuits. Quaia et
al. (1998) proposed a shift circuit to simulate RF remapping in
LIP, in which the FEF neurons shifted the RFs of the LIP neurons. However, the large RFs and the distributed coding feature of parietal neurons make it difficult for a precise shift circuit to work. The
modeling results in this report show that the gain modulation is
essential to carry out the coordinate transformations in area LIP.
Using this strategy, neurons may remain in retinotopic coordinates for
visual stimuli. With eye-position modulation, the distributed activity
of these neurons can represent the stimuli in other coordinates. Varying RF-GF structures carries out different kinds of
transformations. Hence the gain modulation along with distributed
coding is an efficient way to achieve sensorimotor transformations
without using complex shift circuits. Other theoretic studies also
revealed the importance of GF properties in coordinate transformations. Goodman and Andersen (1990) analytically demonstrated
that an aligned GF and RF relationship was required for transformations from oculocentric to craniocentric coordinates. A similar mechanism of
eye-position modulation in the saccadic system was studied by
Krommenhoek et al. (1993, 1996). They developed a neural
network in which retinal signals and an efference copy of eye position could be remapped to a ME map in two steps: distributed coding of
head-centered target position at one level and of ME in eye-centered coordinates at another stage.
RF remapping versus ME coding
Experimental data demonstrate that the memory activity of LIP
neurons encodes saccadic eye movements (Snyder et al.
1997). Furthermore it has been shown that LIP neurons
encode motor intention, irrespective of the actual execution of the
planned movements (Bracewell et al. 1996; Snyder
et al. 1997). The simulated LIP neurons in our models indeed
encode the impending saccade. On the other hand, Duhamel et al.
(1992) proposed that LIP neurons encoded sensory stimuli
instead of saccades. In their experiment, as illustrated in Fig.
14A, the monkey was required
to make a saccade to a remembered target, and this saccade would bring
a stimulus onto the RF of the LIP neuron being recorded. It was found
that the neuron responded to the stimulus outside it
TOP
ABSTRACT
INTRODUCTION
