Learning in the Vestibular System: 
Simulations of Vestibular Compensation 
Using Recurrent Back-Propagation 
Thomas J. Anastasio 
University of Illinois 
Beckman Institute 
405 N. Mathews Ave. 
Urbana, IL 61801 
Abstract 
Vestibular compensation is the process whereby normal functioning is 
rgained following destruction of one member of the pair of peripheral 
vestibular receptors. Compensation was simulated by lesioning , dynamic 
neural network model of the vestibulo-ocular rflex O/OR) and retraining it 
using recurrent back-propagation. The model reproduced the paneam of VOR 
neuron activity experimentally observed in compensated animals, but only if 
connections hertofor considered uninvolved were allowed to be plastic. 
Because the model incorporated nonlinear units, it was able to reconcile 
previously conflicting, linear analyses of experimental results on the dynamic 
properties of VOR neurons in normal and coted animals. 
1 VESTIBULAR COMPENSATION 
Vestibular compensation is one of the oldest and most well studied paradigms in motor 
learning. Although it is neurophysiologically well described, the ,cltive mechanisms 
underlying vestibular compensation, and its effects on the dynamics of vestibular 
responses, are still poorly understood. The purpose of this study is to gain insight into 
the compensatory process by simulating it as learning in a recurrent neural network 
model of the vestibulo-ocular reflex (VOR). 
603 
604 Anastasio 
The VOR stabilizes gaze by producing eye rotations that counterbalance head 
rotations. It is mediated by brainstem neurons in the vestibular nuclei (VN) that relay 
head velocity signals from vestibular sensory afferent neurons to the motoneurons of 
the eye muscles (Wilson and Melvill Jones 1979). The VOR circuitry also processes 
the canal signals, stretching out their time constants by four times before transmitting 
this signal to the motoneurons. This process of time constant lengthening is known as 
velocity storage (Raphan et al. 1979). 
The VOR is a bilaterally symmetric structure that operates in push-pull. The VN are 
linked bilaterally by inhibitory commissural connections. Removal of the vestibular 
receptors from one side (hemilabyrinthectomy) unbalances the system, resulting in 
continuous eye movement that occurs in the absence of head movement, a condition 
known as spontaneous nystagmus. Such a lesion also reduces VOR sensitivity (gain) 
and eliminates velocity storage. Compensatory restoration of VOR occurs in stages 
(Fetter and Zee 1988). It begins by quickly eliminating spontaneous nystagmus, and 
continues by increasing VOR gain. Curiously, velocity storage never recovers. 
2 NETWORK ARCHITECTURE 
The horizontal VOR is modeled as a three-layered neural network (Figure 1). All of 
the units are nonlinear, passing their weighted input sums through the sigmoidal 
squashing function. This function bounds unit respons between zero and one. Input 
units represent afferents from the left (/hc) and right (rhc) horizontal semicircular 
canal receptors. Output units correspond to motoneurons of the lateral (lr) and roedial 
(mr) rectus muscles of the left eye. Interneurons in the VN are represented by hidden 
units on the left (lvnl, lvn2) and right (rvnl, rvn2) sides of the model brainstem. Bias 
units stand for non-vestibular inputs, on the left (lb) and right (rb) sides. 
Network connectivity reflects the known anatomy of mammalian VOR (Wilson and 
Melvill Jones 1979). Vestibular commissures are modeled as recurrent connections 
between hidden units on opposite sides. All connection weights to the hidden units are 
plastic, but those to the outputs are initially fixed, because it is generally believed that 
synaptic plasticity occurs only at the VN level in vestibular compensation (Galiana et 
al. 1984). Fixed hidden-to-output weights have a crossed, reciprocal pattern. 
3 TRAINING THE NORMAL NETWORK 
The simulations began by training the network shown in Figure 1, with both vestibular 
inputs intact (normal network), to produce the VOR with velocity storage (Anastasio 
1991). The network was trained using recurrent back-propagation (William.q and 
Zipset 1989). The input and desired output sequences correspond to the canal afferent 
signals and motoneuron eye-velocity commands that would produce the VOR response 
to two impulse head rotational accelerations, one to the left and the other to the right. 
One input (rhc) and desired output (lr) sequence is shown in Figure 2A (dotted and 
dsshed, respectivley). Those for/hc and mr (not shown) are identical but inverted. 
The desired output responses are equal in amplitude to the inputs, producing VOR 
Learning in the Vestibular System 605 
Figure 1. Recurrent Neural Network Model of the Horizontal Vestibulo-Ocular 
Reflex O/OR). /hc, rhc: left and right horizontal semicircular c. anal mferents; lvnl, 
/vn2, rvnl, rvn2: vestibular nucleus neurons on left and right sides of model 
brainstem; It, mr: lateral and medial rectus muscles of left eye; lb, rb: left and right 
non-vestibular inputs. This and subsequent figures redrawn from Anastasio (in press). 
eye movements that would perfectly counterbalance head movements. The output 
respo decy more slowly than the input responses, reflecting velocity storage. 
Between head movements, both desired outputs have the same spontaneous firing rate 
of 0.50. With output spontaneous rates (SRs) balanced, no push-pull eye velocity 
command is given and, consequently, no VOR eye movement would be mde. 
The normal network learns the VOR transformation after about 4,000 training 
sequence presentations (passes). The network develops reciprocal connections from 
input to hidden units, as in the actual VOR (Wilson and Melvill Jones 1979). 
Inhibitory recurrent connections form an integrating (Ivnl, rvnl) and a non-integrating 
(lvn2, rvn2) pair of hidden units (Anastasio 1991). The rotegrating pair subserve 
storage in the network. They have strong mutual inhibition and exert net positive 
feedback on themeIves. The non-integrating pair have almost no mutual inhibition. 
606 Anastasio 
4 SIMULATING VESTIBULAR COMPENSATION 
After the normal network is constructed, with both inputs intact, vestibular 
compensation can be simulated by removing the input from one side and retraining 
with recurrent back-propagation. Left hemilabyrinthectomy produces deficits in the 
model that correspond to those observed experimentally. The responses of output unit 
lr acutely (i.e. immediately) following left input removal are shown in Figure 2A. 
The SR of lr (solid) is greatly increased above normal (dashed); that of mr (not shown) 
is decreased by the same amount. This output SR imbalance would re. suit in eye 
movement to the left in the absence of head movement (spontaneous nystagmus). The 
gain of the outputs is greatly decreased. This is due to removal of one half the 
network input, and to the SR imbalance forcing the output units into the low gain 
extremes of.the squashing function. Velocity storage is also eliminated by left input 
removal, due to events at the hidden unit level (see below). 
During retraining, the time course of simulated compensation is similar to that 
0 10 20 30 40 50 0 0 10 20 30 40 50 0 
NETWOHK CYOL$ NETWK CYOLE$ 
Figure 2. Simulated Compensation in the VOR Neural Network Model. Response of 
lr (solid) is shown at each stage of coml'nsation: A, acutely (i.e. immediately) 
following the lesion; B, after spontaneous nystagmus has been eliminated; C, after 
VOR gain has been largely restored; D, after full recovery of VOR. Desired response 
of lr (dashed) shown in all plots. Intact input from rhc (dotted) shown in A only. 
Learning in the Vestibular System 607 
observed experimentally (Fetter and Zee 1988). Spontaneous nystagmus is eliminated 
after 200 passes, as the SRs of the output units are brought back to their normal level 
(Figure 2B). Output unit gain is largely restored by 900 passes, but time constant 
remains close to that of the inputs (Figure 2C). At this stage, VOR gain would have 
increased substantially, but its time constant would remain low, indicating loss of 
velocity storage. This stage approximates the extent of experimeatally observed 
compensation (ibid.). Completely restoring the normal VOR, with full velocity 
storage, requires over seven times more retraining (Figure 2D). 
The responses of the hidden units during each stage of simulated compensation are 
shown in Figure 3A and 3C. Average hidden unit SR and gain are shown as dotted 
lines in Figure 3A and 3C, respectively. Acutely following left input removal (AC 
stage), the SRs of left (dashed) and right (solid) hidden units decrease and increase, 
respectively (Figure 3A). One left hidden unit (lvnl) is actually silenced. Hidden unit 
gain at AC stage is greatly reduced bilaterally (Figure 3C), as for the outputs. 
At the point where spontaneous nystagmus is eliminated (NE stage), hidden units SRs 
are balanced bilaterally, and none of the units are spontaneously silent (Figure 3A). 
When VOR gain is largely restored (GR stage, corresponding to experimentally 
observed compensation), the gains of the hidden units have substantially increased 
(Figure 3C). At GR stage, average hidden unit SR has also increased but the bilateral 
SR balance has been strictly maintained (Figure 3A). A comparison with experimental 
data (Yagi and Markham 1984; Newlands and Perachio 1990) reveals that the behavior 
of hidden units in the model does not correspond to that observed for real VN neurons 
in compensated animals. Rather than having bilateral SR balance, the average SR of 
VN neurons in compensated animals is lower on the lesion-side and higher on the 
intact-side. Moreover, many lesion-side VN neurons are permanently silenced. Also, 
rather than substantially recovering gain, the gains of VN neurons in compensated 
animals increase little from their low values acutely following the lesion. 
The network model adopts its particular (and unphysiological) solution to vestibular 
compensation because, with fixed connection weights to the outputs, compensation can 
be brought about only by changes in hidden unit behavior. Thus, output SRs will be 
balanced only if hidden SRs are balanced, and output gain will increase only if hidden 
gain increases. The discrepancy between model and actual VN neuron data suggests 
that compensation cannot rely solely on synaptic plasticity at the VN level. 
5 RELAXING CONSTRAINTS 
A better match between model and experimental VN neuron data can be achieved by 
rerunning the compensation simulation with modifiable weights at all allowed network 
connections (Figure 1). Bias-to-output and hidden-to-output synaptic weights, which 
were previously fixed, are now made plastic. These extra degrees of freedom give the 
adapting network greater flexibility in achieving compensation, and release it from a 
strict dependency upon the behavior of the hidden units. The time course of 
compensation in the all-weights-modifiable example is similar to the previous case 
(Figure 2), but each stage is reached after fewer passes. 
608 Anastasio 
A 
0.8 0.8 
0.6 0.6 
NM AC NE GR NM AC NE GR 
2  
Figure 3. Behavior of Hidden Units at Various Stages of Compe. nsation in the VOR 
Neural Network Model. Spontaneous rate (SR, A and B) and gain (C and D) are 
shown for networks with hidden layer weights only modifiable (A and C) or with all 
weights modifiable (B and D). Normal average SR (A and B) and gain (C and D) 
shown as dotted lines. NM, normal stage; AC, acutely following lesion; NE, after 
spontaneous nystagmus is eliminated; GR, after VOR gain is largely restored. 
The behavior of the hidden units in the all-weights simulation more closely matches 
that of actual VN neurons in compensated animals (Figure 3B and 3D). At NE stage, 
even though spontaneous nystagmus is eliminated, there remains a large bilateral 
imbalance in hidden unit SR, and one lesion-side hidden unit (Ivnl) is silenced (Figure 
3B). At GR stage, hidden unit gain has increased only modestly from the low acute 
level (Figure 3D), and the bilateral $R imbalance persists, with lvnl still essentially 
spontaneously silent (Figure 3B). This modeling result constitutes a testable 
prediction that synapfic plasticity is occurring at the motoneuron as well as at the VN 
level in vestibular compensation. 
6 NETWORK DYNANHCS 
In the all-weights simulation at GR stage, as well as in compeasated animals, some 
lesion-side VN neurons are silenced. Hidden unit Ivnl is silenced by its inhibitory 
commissural interaction with rvnl, which in the normal network allowed the pair to 
Learning in the Vestibular System 609 
form an integrating, recurrent loop. Silencing of lvnl breaks the commissural loop 
and consequently eliminates velocity storage in the network. VN neuron silencing 
could also account for the loss of velocity storage in the real, compensated VOR. 
Loss of velocity storage in the model, in response to step head rotational acceleration 
stimuli, is shown in Figure 4. The output step response that would be expected given 
the longer VOR time constant is shown for lr in Figure 4A (dashed). The response of 
mr (not shown) is identical but inverted. Instead of expressing the longer VOR time 
constant, the actual step response of lr in the all-weights compensated network at GR 
stage (Figure 4A, dotted) has a rise time constant that is equal to the canal time 
constant, indicating complete loss of velocity storage. This is due to the behavior of 
the hidden units. The step responses of the integrating pair of hidden units in the 
compensated network at GR stage are shown in Figure 4B (lvnl, lower dotted; rvnl, 
upper dotted). Velocity storage is eliminated because Ivnl is silenced, and this breaks 
the commissural loop that supports integration in the network. 
Paradoxically, in the normal network with all hidden units spontaneously active, the 
output step response rise time constant is also equal to that of the canal afferents, again 
indicating a loss of velocity storage. This is shown for lr from the normal network in 
Figure 4A (solid). The step responses of the hidden units in the normal network are 
shown in Figure 4B (lvnl, dashed; rvnl, solid). Unit lvnl, which is spontaneously 
active in the normal network, is quickly driven into cut-off by the step stimulus. This 
breaks the commissural loop and eliminates velocity storage, accounting for the short 
rise time constants of hidden and output units network wide. 
This result can explain some conflicting experimental findings concerning the 
A 
0. I I I I I 
0 10 2o 3o 4o 5o 
0.8 
0.6 
0.4 
02 
0 
60 o 
lO o 80 
NETWORK CYCLES 
NETWORK CYCLES 
Figure 4. Responses of Units to Step Head Rotational Acceleration Stimuli in VOR 
Neural Network Model. A, expected response of Ir with VOR time constant (dashed), 
and actual responses of lr in normal (solid) and all-weights compensated (dotted) 
networks. B, response of lvnl (dashed) and rvnl (solid) in normal network, and of 
lvnl (lower dotted) and rvnl (upper dotted) in all-weights compensated network. 
610 Anastasio 
dynamics of VN neurons in normal and compensated animals. Using sinusoidal 
stimuli, the time constants of VN neurons were found to be lower in compensated than 
in normal gerbils (Newlands and Perachio 1990). In contrast, using step stimuli, no 
difference in rise time constants were found for VN neurons in normal as compared to 
compensated cats (Yagi and Markham 1984). 
Rather than being a species difference, the disagreement may involve the type of 
stimulus used. Step accelerations are intense stimuli that can drive VN neurons to 
extreme levels. In response to a step in their off-directions, many VN neurons in 
normal cats were observed to cut-off (ibid.). As shown in Figure 4, this would 
disrupt commissural interactions and reduce velocity storage and VN neuron rise time 
constants, just as if these neurons were silenced as they are in com?osated animals. In 
fact, VN neuron rise time constants were observed to be low in both normal and 
compensated cats (ibid.). In contrast, sinusoidal stimuli at an intensity that does not 
cause widespread VN neuron cut-off would not be expected to disrupt velocity storage 
in normal animals. 
Acknowledgements 
This work was supported by a grant from the Whitaker Foundation. 
References 
Anastasio TJ (1991) Neural network models of velocity storage in the horizontal 
vestibulo-ocular reflex. Biol Cybem 64:187-196 
Anastasio TJ (in press) Simulating vestibular compensation using recurrent back- 
propagation. Biol Cybern 
Fetter M, Zee DS (1988) Recovery from unilateral labyrinthectomy in rhesus monkey. 
 Neurophysiol 59:370-393 
Galiana HL, Flohr H, Melvill Jones G (1984) A reevauation of intervestibular nuclear 
coupling: its role in vestibular compensation. J Neurophysiol 51:242-259 
Newlands SD, Perachio AA (1990) Common of horizontal canal related activity 
in the roedial vestibular nucleus following tmilateral labyrinth ablation in the 
decerebrate gerbil. I. type I neurons. Exp Brain Res 82:359-372 
Raphah Th, Matsuo V, Cohen B (1979) Velocity storage in the vestibulo-ocular reflex 
are (VOR). Exp Brain Res 35:229-248 
Williams RJ, Zipser D (1989) A learning algorithm for continually nmning fully 
recurrent neural networks. Neural Comp. 1:270-280 
Wilson VJ, Melvill Jones G (1979) Mammalian vestibular physiology. Plenum Press, 
New York 
Yagi T, Markham CH (1984) Neural correlates of compensation after 
hemilabyrinthectomy. Exp Neurol 84:98-108 
