A Neural Net Model for Adaptive Control of 
Saccadic Accuracy by Primate Cerebellum and 
Brainstem 
Paul Dean a, John E. W. Mayhew and Pat Langdon 
Department of Psychology a and Artificial Intelligence 
Vision Research Unit, University of Sheffield, 
Sheffield S 10 2TN, England. 
Abstract 
Accurate saccades require interaction between brainstem circuitry and the 
cerebellum. A model of this interaction is described, based on Kawato's 
principle of feedback-error-learning. In the model a part of the 
brainstem (the superior colliculus) acts as a simple feedback controller 
with no knowledge of initial eye position, and provides an error signal 
for the cerebellum to correct for eye-muscle nonlinearities. This teaches 
the cerebellum, modelled as a CMAC, to adjust appropriately the gain 
on the brainstem burst-generator's internal feedback loop and so alter the 
size of burst sent to the motoneurons. With direction-only errors the 
system rapidly learns to make accurate horizontal eye movements from 
any starting position, and adapts realistically to subsequent simulated 
eye-muscle weakening or displacement of the saccadic target. 
1 INTRODUCTION 
The use of artificial neural nets (ANNs) to control robot movement offers advantages in 
situations where the relevant analytic solutions are unknown, or where unforeseeable 
changes, perhaps as a result of damage or wear, are likely to occur. It is also a mode of 
control with considerable similarities to those used in biological systems. It may thus 
prove possible to use ideas derived from studies of ANNs in robots to help understand 
how the brain produces movements. This paper describes an attempt to do this for 
saccadic eye movements. 595 
596 Dean, Mayhew, and Langdon 
The structure of the human retina, with its small foveal area of high acuity, requires 
extensive use of eye-movements to inspect regions of interest. To minimise the time 
during which the retinal image is blurred, these saccadic refixation movements are very 
rapid - too rapid for visual feedback to be used in acquiring the target (Carpenter 1988). 
The saccadic control system must therefore know in advance the size of control signal to 
be sent to the eye muscles. This is a function of both target displacement from the fovea 
and initial eye-position. The latter is important because the eye-muscles and orbital 
tissues are elastic, so that more force is required to move the eye away from the straight- 
ahead position than towards it (Collins 1975). 
Similar rapid movements may be required of robot cameras. Here too the desired control 
signal is usually a function of both target displacement and initial camera positions. 
Experiments with a simulated four degree-of-freedom stereo camera rig have shown that 
appropriate ANN architectures can learn this kind of function reasonably efficiently (Dean 
et al. 1991), provided the nets are given accurate error information. However, this 
information is only available if the relevant equations have been solved; how can ANNs 
be used in situations where this is not the case? 
A possible solution to this kind of problem (derived in part from analysis of biological 
motor control systems) has been suggested by Kawato (1990), and was implemented for 
the simulated stereo camera rig (Fig 1). Two controllers are arranged in 
Camera) - Adaptive 
Positions Feedforward 
Controller (ANN)  Command No. 1 
Change in camera 
First Saccade (1) RRO position 
E 
, 1 (1) 
( Target  /(2) Simple I I , (2)  
oordinat Feedback ] ' 
Controller I Command No.2 
Second Change in camera 
(corrective) position 
Saccade (2) 
Fig 1: Control architecture for robot saccades 
parallel. Target coordinates, together with information about camera positions, are passed 
to an adaptive feedforward controller in the form of an ANN, which then moves the 
cameras. If the movement is inaccurate, the new target coordinates are passed to the 
second controller. This knows nothing of initial camera position, but issues a corrective 
movement command that is simply proportional to target displacement. In the absence of 
the adaptive controller it can be used to home in on the target with a series of saccades: 
Adaptive Control of Saccadic Accuracy by Primate Cerebellum and Brainstem 597 
though each individual saccade is ballistic, the sequence is generated by visual feedback, 
hence the term simple feedback controller. When the adaptive controller is present, 
however, the output of the simple feedback controller can be used not only to generate a 
corrective saccade but also as a motor error signal (Fig 1). Although this error signal is 
not accurate, its imperfections become less important as the ANN learns and so takes on 
more responsibility for the movement (for proof of convergence see Kawato 1990). The 
architecture is robust in that it learns on-line, does not require mathematical knowledge, 
and still functions to some extent when the adaptive controller is untrained or damaged. 
These qualities are also important for control of saccades in biological systems, and it is 
therefore of interest that there are similarities between the architecture shown in Fig 1 and 
the structure of the primate saccadic system (Fig 2). The cerebellum is widely (though 
NPH 
Cerebellar Structures 
Mossy Fibre 
Posterior 
ermis 
CUmbg 
NPH = nucleus prepositus hypoglossi 
NRTP = nucleus reticularis tegm enti 
pontis 
NRTP 
Inferior Fastigial 
Olive Nucleus 
Superior Pontine Oculomotor 
Colliculus Reticular Nuclei 
Formation 
Brainstem Structures 
Fig 2: Schematic diagram of major components of primate saccadic control system 
not universally) regarded as an adaptive controller, and when the relevant part of it is 
damaged the remaining brainstem structures function like the simple feedback controller 
of Fig 1. Saccarles can still be made, but (i) they are not accurate; (ii) the degree of 
inaccuracy depends on initial eye position; (iii) multiple saccades are required to home in 
on the target; and (iv) the system never recovers (eg Ritchie 1976; Optican and Robinson 
1980). 
These similarities suggest that it is worth exploring the idea that the brainstem teaches 
the cerebellum to make accurate saccades (cf Grossberg and Kuperstein 1986), just as the 
simple feedback controller teaches the adaptive controller in the Kawato architecture. A 
model of the primate system was therefore constructed, using 'off-the-shelf' components 
wired together in accordance with known anatomy and physiology, and its performance 
assessed under a variety of conditions. 
598 
Dean, Mayhew, and Langdon 
2 STRUCTURE OF MODEL 
The overall structure of the model is shown in Fig 3. It has three main components: a 
simple feedback controller, a burst generator, and a CMAC. The simple feedback 
Eye 
Position 
Crude 
Command 
(copy) 
Via NRTP 
l CMAC 
I 
Error 
Via 
olive 
Cerebellum 
Feedback 
Controller 
I 
! Superior ! Crude 
. _ c._ott_ic.__l Command 
Variable Integrator [ 
gain (resettable) l 
I 
I I 
I 
I Burst I 
Generator Accurate ! 
+ Command[ 
(burst) I 
I I 
PLANT 
Figure 3: Main components of the model. The corresponding biological structures are 
shown in italics and dotted lines. 
controller sends a signal proportional to target displacement from the fovea to the burst 
generator. The function of the burst generator is to translate this signal into an 
appropriate command for the eye muscles, and it is based here on the model of Robinson 
(Robinson 1975; van Gisbergen et al. 1981). Its output is a rapid burst of neural 
impulses, the frequency of which is esentially a velocity command. A crucial feature of 
Robinson's model is an internal feedback loop, in which the output of the generator is 
integrated and compared with the input command. The saccade terminates when the two 
are equal. This system ensures that the generator gives the output matching the input 
command in the face of disturbances that might alter burst frequency and hence saccade 
velocity. 
The simple feedback controller sends to the CMAC (Albus 1981) a copy of its command 
to the burst generator. The CMAC (Cerebellar Model Arithmetic Computer) is a neural 
net model of the cerebellum incoporating theories of cerebellar function proposed 
independently by Mart (1969) and Albus (1971). Its function is to learn a mapping 
between a multidimensional input and a single-valued output, using a form of lookup 
table with local interpolation. The entries in the lookup table are modified using the delta 
rule, by an error signal which is either the difference between desired and actual output or 
some estimate of that difference. CMACs have been used successfully in a number of 
Adaptive Control of Saccadic Accuracy by Primate Cerebellum and Brainstem 599 
applications concerning prediction or control (eg Miller et al. 1987; Hormel 1990). In 
the present case the function to be learnt is that relating desired saccade amplitude and 
initial eye position (inputs) to gain adjustment in the internal feedback loop of the burst 
generator (output). 
The correspondences between the model structure and the anatomy and physiology of the 
primate saccadic system are as follows. 
(1) The simple feedback controller represents the superior colliculus. 
(2) The burst generator corresponds to groups of neurons located in the brainstem. 
(3) The CMAC models a particular region of cerebellar cortex, the posterior vermis. 
(4) The pathway conveying a copy of the feedback controllet's crude command corresponds 
to the projection from the superior colliculus to the nucleus reticularis tegmenti pontis, 
which in turn sendes a mossy fibre projection to the posterior vermis. 
Space precludes detailed evaluation of the substantial evidence supporting the above 
correspondences (see eg Wurtz and Goldberg 1989). The remaining two connections have 
a less secure basis. 
(5) The idea that the cerebellum adjusts saccadic accuracy by altering feedback gains in 
the burst generator is based on stimulation evidence (Keller 1989); details of the 
projection, including its anatomy, are not known. 
(6) The error pathway from feedback controller to CMAC is represented by the 
anatomically identified projection from superior colliculus to inferior olive, and thence via 
climbing fibres to the posterior vermis. There is considerable debate concerning the 
functional role of climbing fibres, and in the case of the tecto-olivary projection the 
relevant physiological evidence appears to be lacking. 
3 PERFORMANCE OF MODEL 
The system shown in Fig 3 was trained to make horizontal movements only. The size of 
burst AI (arbitrary units) required to produce an accurate rightward saccade A0 deg was 
calculated from Van Gisbergen and Van Opstal's (1989) analysis of the nonlinear 
relationship between eye position and muscle position as 
AI = a [A0 2 + A0 (b + 20)] 
where 0 is initial eye-position (measured in deg from extreme leftward eye-position) and a 
and b are constants. In the absence of the CMAC, the feedback controller and burst 
generator produce a burst of size 
AI = x. (c/d) (2) 
where x is the rightward horizontal displacement of the target, c is the gain constant of 
the feedback controller, and d a constant related to the fixed gain of the internal feedback 
loop of the burst generator. The kinematics of the eye are such that x (measured in deg of 
visual angle) is equal to A0. The constants were chosen so that the performance of the 
system without the CMAC resembled that of the primate saccadic system after cerebellar 
damage (fig 4A), namely position-dependent overshoot (eg Ritchie 1976; Optican and 
600 Dean, Mayhew, and Langdon 
5.0- 
A 
(No cerebellum) 
5.0' 
B 
(Infant) 
5.0' 
c 
(Trained) 
4.5' 
:.$, 
2.0' 
..5' 
1.0' 
0.5' 
0.0 
4.5' 
3.5' 
3.0' 
2.5' 
0.5' 
0.0 
I Rightward saecade 
$ ttring ixition 
.... 4. ..... 20 
-I 
2.5 
2.0 
  , - , -  - , 
2 40 60 80 
overshoot 
 .......  _ _-. accutate ._ . 
undershoot 
saccade amplitude (deg.) 
Fig 4. Performance of model under different conditions before and after training 
Robinson 1980). When the CMAC is present, the size of burst changes to 
aI = x. [c/(g + d)] (3) 
where g is the output of the CMAC. This was initialised to a value that produced a 
degree of saccadic undershoot (Fig 4b) characteristic of initial performance in human 
infants (eg Aslin 1987). 
Training data were generated as 50,000 pairs of random numbers representing the initial 
position of the eye and the location of the target respectively. Each pair had to satisfy the 
constraints that (i) both lay within the oculomotor range (45 deg on either side of 
midline) and (ii) the target lay to the right of the starting position. For the test data the 
starting position varied from 40 deg left to 30 deg right in 10 degree steps. For each 
starting position there was a series of targets, starting at 5 deg to the right of the start and 
increasing in 5 degree steps up to 40 deg to the right of midline (a subset of the test data 
was used in Fig 4). The main measure of performance was the absolute gain error (ie the 
the difference between the actual gain and 1.0, always taken as positive) averaged over the 
test set. 
The configuration of the CMAC was examined in pilot experiments. The CMAC coarse- 
codes its inputs, so that for a given resolution r, an input span of s can be represented as 
set of m measurement grids each dividing the input span into n compartments, where s/r 
= m.n. Combinations of m and n were examined, using perfect error feedback. A 
reasonable compromise between learning speed and asymptotic accuracy was achieved by 
using 10 coarse-coding grids each with 10x10 resolution (for the two input dimensions), 
giving a total of 1000 memory cells. 
Adaptive Control of Saccadic Accuracy by Primate Cerebellum and Brainstem 601 
The main part of the study investigated first the effects of degrading the quality of the 
error feedback on learning. The main conclusion was that efficient learning could be 
obtained if the CMAC were told only the direction of the error, ie overshoot versus 
undershoot. This information was used to increase by a small fixed amount the weights in 
the activated cells (thereby producing increased gain in the internal feedback loop) when 
the saccade was too large, and to decreasing them similarly when it was too small. 
Appropriate choice of learning rate gave a realistic overall error of 5% (Fig 4c) after about 
2000 trials. Direct comparison with learning rates of human infants, who take several 
months to achieve accuracy, is confounded by such factors as the maturation of the retina 
(Aslin 1987). 
Learning parameters were then kept constant, and the model tested with simulations of 
two different conditions that produce saccadic plasticity in adult humans. One involved 
the effects of weakening the rightward pulling eye muscle in one eye. In people, the 
weakened eye can be trained by covering the normal eye with a patch, an effect which 
experiments with monkeys indicate depends on the cerebellum (Optican and Robinson 
1980). For the model eye-weakening was simulated by increasing the constant a in 
equation (1) such that the trained system gave an average gain of about 0.5. Retraining 
required about 400-500 trials. Testing the previously normal eye (ie with the original 
value of a) showed that it now overshot, as is also the case in patients and experimental 
animals. Again normal performance was restored after 400-500 trials. These learning 
rates compare favourably with those observed in experimental animals. 
Finally, the second simulation of adult saccadic plasticity concerned the effects of moving 
the target during a saccade. If the target is moved in the opposite direction to its original 
displacement the saccade will overshoot, but after a few trials adaptation occurs and the 
saccade becomes 'accurate' once more. Simulation of the procedure used by Deubel et al. 
(1986) gave system adaptation rates similar to those observed experimentally in people. 
4 CONCLUSIONS 
These results indicate that the model can account in general terms for the acquisition and 
maintenance of saccadic accuracy in primates (at least in one dimension). In addition to 
its general biologically attractive properties, the model's structure is consistent with 
current anatomical and physiological knowledge, and offers testable predictions about the 
functions of the hitherto mysterious projections from superior colliculus to posterior 
vermis. If these predictions are supported by experimental evidence, it would be 
appropriate to extend the model to incorporate greater physiological detail, for example 
concerning the precise location(s) of cerebellar plasticity. 
Acknowledgements 
This work was supported by the Joint Council Initiative in Cognitive Science. 
602 Dean, Mayhew, and Langdon 
References 
Albus, J.A. (1971) A theory of cerebellar function. Math. Biosci. 10: 25-61. 
Albus, J.A. (1981) Brains, Behavior and Robotics. BYTE books (McGraw-Hill), 
Peterborough New Hampshire. 
Aslin, R.N. (1987) Motor aspects of visual development in infancy. In: Handbook of 
Infant Perception, eds. P. Salapatek and L. Cohen. Academic Press, New York, pp.43- 
113. 
Collins, C.C. (1975) The human oculomotor control system. In: Basic Mechanisms of 
Ocular Motility and their Clinical Implications, eds. G. Lennerstrand and P. Bach-y- 
Rim. Pergamon Press, Oxford, pp. 145-180. 
Dean, P., Mayhew, J.E.W., Thacker, T. and Langdon, P. (1991) Saccade control in a 
simulated robot camera-head system: neural net architectures for efficient learning of 
inverse kinematics. Biol. Cybern. 66: 27-36. 
Deubel, H., Wolf, W. and Hauske, G. (1986) Adaptive gain control of saccadic eye 
movements. Human Neurobiol. 5: 245-253. 
Grossberg, S. and Kuperstein, M. (1986) Neural Dynamics of Adaptive Sensory-Motor 
Control: Ballistic Eye Movements. Elsevier, Amsterdam. 
Hormel, M. (1990) A self-organising associative memory system for control 
applications. In: Advances in Neural Information Processing Systems 2, ed. D.S. 
Touretzky. Morgan Kaufman, San Mateo, California, pp. 332-339. 
Kawato, M. (1990) Feedback-error-learning neural network for supervised motor learning. 
In Advanced Neural Computers, ed. R. Eckmiller. Elsevier, Amsterdam, pp.365-372. 
Keller, E.L. (1989) The cerebellum. In: The Neurobiology of Saccadic Eye 
Movements, eds. Wurtz, R.H. and Goldberg, M.E. Elsevier Science Publishers, North 
Holland, pp. 391-411. 
Mart, D. (1969) A theory of cerebellar cortex. J. Physiol. 202: 437-470. 
Miller, W.T. III, Glanz, F.H. and Gordon Kraft, L. III (1987) Application of a general 
learning algorithm to the control of robotic manipulators. Int. J. Robotics Res. 6: 84- 
98. 
Optican, L.M. and Robinson, D.A. (1980) Cerebellar-dependent adaptive control of 
primate saccadic system. J. Neurophysiol. 44: 1058-1076. 
Ritchie, L. (1976) Effects of cerebellar lesions on saccadic eye movements. J. 
Neurophysiol. 39: 1246-1256. 
Robinson, D.A. (1975) Oculomotor control signals. In: Basic Mechanisms of Ocular 
Motility and their Clinical Implications, eds. Lennerstrand, G. and Bach-y-Rita, P. 
Pergamon Press, Oxford, pp. 337-374. 
Van Gisbergen, J.A.M., Robinson, D.A. and Gielen, S. (1981) A quantitative analysis 
of generation of saccadic eye movements by burst neurons. J. Neurophysiol. 45: 417- 
442. 
Van Gisbcrgen, J.A.M. and van Opstal, A.J. (1989) Models. In: The Neurobiology of 
Saccadic Eye Movements, eds. Wurtz, R.H. and Goldberg, M.E. Elsevier Science 
Publishers, North Holland, pp. 69-101. 
Wurtz, R.H. and Goldberg, M.E. (1989) The Neurobiology of Saccadic Eye Movements. 
Elsevier Science Publishers, North Holland. 
