{"title": "A Neural Net Model for Adaptive Control of Saccadic Accuracy by Primate Cerebellum and Brainstem", "book": "Advances in Neural Information Processing Systems", "page_first": 595, "page_last": 602, "abstract": null, "full_text": "A  Neural  Net  Model  for  Adaptive  Control  of \nSaccadic  Accuracy  by  Primate  Cerebellum  and \n\nBrainstem \n\nPaul  Deana,  John  E.  W.  Mayhew  and  Pat  Langdon \n\nDepartment of Psychology a and Artificial Intelligence \n\nVision Research Unit, University of Sheffield, \n\nSheffield S10 2TN, England. \n\nAbstract \n\nAccurate saccades require interaction between brainstem circuitry and the \ncerebeJJum.  A model of this interaction is described, based on Kawato's \nprinciple  of  feedback-error-Iearning. \nIn  the  model  a  part  of  the \nbrainstem  (the superior colliculus) acts as a simple feedback controJJer \nwith no knowledge of initial eye position, and provides an error signal \nfor the cerebeJJum to correct for eye-muscle nonIinearities.  This teaches \nthe cerebeJJum,  modelled as a CMAC, to adjust appropriately the gain \non the brainstem burst-generator's internal feedback loop and so alter the \nsize of burst sent to  the  motoneurons.  With  direction-only errors  the \nsystem rapidly learns to make accurate horizontal eye movements from \nany  starting position, and  adapts realistically to  subsequent simulated \neye-muscle weakening or displacement of the saccadic target. \n\n1  INTRODUCTION \n\nThe use of artificial neural nets (ANNs) to control robot movement offers advantages in \nsituations  where  the  relevant analytic  solutions  are  unknown,  or  where  unforeseeable \nchanges, perhaps as  a result of damage or wear, are likely to occur.  It is also a mode of \ncontrol  with  considerable similarities  to  those  used  in  biological  systems.  It may thus \nprove possible to  use ideas derived from  studies of ANNs  in  robots  to  help  understand \nhow  the  brain  produces  movements.  This  paper  describes  an  attempt  to  do  this  for \n595 \nsaccadic eye movements. \n\n\f596 \n\nDean, Mayhew,  and Langdon \n\nThe  structure  of the  human  retina,  with  its  small  foveal  area  of high  acuity,  requires \nextensive use of eye-movements  to  inspect  regions of interest.  To  minimise  the  time \nduring  which  the retinal  image is blurred, these saccadic refixation movements are  very \nrapid - too rapid for visual feedback to be used in  acquiring the target (Carpenter 1988). \nThe saccadic control system must therefore know in advance the size of control signal to \nbe sent to the eye muscles.  This is a function of both target displacement from  the fovea \nand  initial  eye-position.  The  latter  is  important  because  the  eye-muscles  and  orbital \ntissues are elastic, so that more force is required to move the eye away from  the straight(cid:173)\nahead position than towards it (Collins  1975). \n\nSimilar rapid movements may be required of robot cameras.  Here too the desired control \nsignal  is  usually  a  function  of both  target  displacement  and  initial  camera  positions. \nExperiments with a simulated four degree-of-freedom  stereo camera rig have shown that \nappropriate ANN architectures can learn this kind of function reasonably efficiently (Dean \net al.  1991),  provided  the  nets  are  given  accurate  error  information.  However,  this \ninfonnation is only available if the relevant equations have been solved;  how can ANNs \nbe used in situations where this is not the case? \n\nA  possible solution  to  this kind of problem  (derived in part from  analysis of biological \nmotor control systems) has been suggested by Kawato (1990), and was implemented for \nthe simulated stereo camera rig (Fig 1). Two controllers are arranged in \n\nCamera \nPositions \n\nFirst Saccade (1) \n\n'Thrget \n\nCoordinates \n\n(1) \n\n(2) \n\nSecond \n\n(corrective) \nSaccade (2) \n\nAdaptive \n\nFeedforward \n\nController (ANN) \n\nCommand No.1 \nChange in camera \n\nposition \n\nERROR \n\n(1) \n\nSimple \nFeedback \nController \n\nI-..... --~ ... \n\n(2) \nCommand No.2 \nChange in camera \n\nposition \n\nFig 1:  Control architecture for robot saccades \n\nparallel.  Target coordinates, together with information about camera positions, are passed \nto  an  adaptive  feedforward  controller in  the  form  of an  ANN,  which  then  moves  the \ncameras.  If the  movement is  inaccurate,  the  new  target coordinates  are passed  to  the \nsecond controller.  This knows nothing of initial camera position, but issues a corrective \nmovement command that is simply proportional to target displacement.  In the absence of \nthe adaptive controller it can be used to home in on the target with a series of saccades: \n\n\fAdaptive Control of Saccadic Accuracy by  Primate Cerebellum and Brainstem \n\n597 \n\nthough each individual saccade is ballistic, the sequence is generated by visual feedback, \nhence  the  tenn  simple  feedback  controller.  When  the  adaptive  controller is  present, \nhowever, the output of the simple feedback controller can be used not only to generate a \ncorrective saccade but also as a motor error signal (Fig  1).  Although this error signal is \nnot accurate,  its imperfections become less important as the ANN learns and so takes on \nmore responsibility for  the movement (for proof of convergence see Kawato  1990). The \narchitecture is robust in that it learns on-line, does not require mathematical knowledge, \nand still functions to some extent when the adaptive controller is untrained or damaged. \n\nThese qualities are also important for control of saccades in biological systems, and it is \ntherefore of interest that there are similarities between the architecture shown in Fig 1 and \nthe structure of the primate saccadic system (Fig 2).  The cerebellum is widely (though \n\nCerebellar Structures \n\nI \n\nNPH \n\nI \nI \n\nMouyFibm \n\nMouy \nFibre \n\nPosterior \nVermis \n\n~ \n\n..... \n\nClimbing \nFibre \n\nl  NRTP  J  Inferior \n\nOlive \n\nFastigial \nNucleus \n\nNPH = nucleus prepositus hypoglossi \n\nNKfP= nucleus reticularis tegmenti \n\npontis \n\n(  Retina  ) \n\nf-' \n\nSuperior \nCollic:ulus \n\nPontine \n\nReticular  r---\n\nFormation \n\nOculomotor \n\nNuc:lei \n\nEye Muscles \n\nBrainstem Structures \n\nFig 2:  Schematic diagram of major components of primate saccadic control system \n\nnot  universally)  regarded  as  an  adaptive  controller, and  when the relevant part of it is \ndamaged the remaining brainstem structures function like the simple feedback controller \nof Fig  1.  Saccades can  still  be made, but (i)  they are  not accurate;  (ii)  the degree of \ninaccuracy depends on initial eye position;  (iii) multiple saccades are required to home in \non the target; and (iv) the system never recovers (eg Ritchie 1976;  Optic an and Robinson \n1980). \n\nThese similarities suggest that it is  worth exploring the idea  that  the brains tern  teaches \nthe cerebellum to make accurate saccades (cf Grossberg and Kuperstein  1986), just as the \nsimple feedback controller teaches the adaptive controller in  the Kawato architecture.  A \nmodel of the primate system  was  therefore constructed, using 'off-the-shelf components \nwired together in accordance with known  anatomy and physiology, and its performance \nassessed under a variety of conditions. \n\n\f598 \n\nDean, Mayhew,  and Langdon \n\n2  STRUCTURE  OF  MODEL \n\nThe overall  structure of the model is  shown in  Fig 3.  It has three  main  components:  a \nsimple feedback controller, a burst generator,  and a CMAC.  The simple feedback \n\nEye \nPosition \n\n----------, \nCMAC \n\nI \nI \nI \nI \nI~--,.~~ \nI \nL __  E~~~~J \n\nCrude \n\nCommand \n\n(copy) \n\nViaNJ(['P \n\nr,------.. \nI \n\nFeedback \nController \n\n'IlIrget \n\nError \n\nVia \nolivt \n\nFlxed \ngain \n\n...... II-.J ........ - ,  \nI \nI \n\nIntegrator \n(ftsettable) \n\nI I I \n\nI \n\nPLANT \n\nFigure 3:  Main components of the model.  The corresponding biological structures are \nshown in italics and dotted lines. \n\ncontroller sends a signal proportional to  target displacement from  the fovea  to the burst \ngenerator.  The  function  of  the  burst  generator  is  to  translate  this  signal  into  an \nappropriate command for the eye muscles, and it is based here on the model of Robinson \nIts  output  is  a  rapid  burst  of neural \n(Robinson  1975;  van  Gisbergen  et  at.  1981). \nimpulses, the frequency of which is esentially a velocity command.  A crucial feature of \nRobinson's  model  is  an  internal  feedback  loop,  in  which  the output of the  generator is \nintegrated and compared with the input command.  The saccade tenninates when the two \nare equal.  This  system  ensures  that the generator gives  the  output  matching  the  input \ncommand in  the face of disturbances that might alter burst frequency and hence saccade \nvelocity. \n\nThe simple feedback controller sends to the CMAC (Albus  1981) a copy of its command \nto the burst generator.  The CMAC (Cerebellar Model Arithmetic Computer) is a neural \nnet  model  of  the  cerebellum  incoporating  theories  of  cerebellar  function  proposed \nindependently  by  Marr  (1969)  and  Albus  (1971).  Its  function  is  to  learn  a  mapping \nbetween  a  multidimensional  input and  a single-valued output,  using  a  form  of lookup \ntable with local interpolation. The entries in  the lookup table are modified using the delta \nrule, by an error signal which is either the difference between desired and actual output or \nsome estimate of that difference.  CMACs  have been  used successfully in  a  number of \n\n\fAdaptive Control of Saccadic Accuracy by Primate Cerebellum and Brainstem \n\n599 \n\napplications  concerning prediction or control  (eg Miller et aI.  1987;  Honnel  1990).  In \nthe present case the function  to be learnt is  that relating desired  saccade amplitude and \ninitial eye position (inputs) to gain adjustment in the internal  feedback loop of the burst \ngenerator (output). \n\nThe correspondences between the model structure and the anatomy and physiology of the \nprimate saccadic system are as follows. \n(1) The simple feedback controller represents the superior colliculus. \n(2) The burst generator corresponds to groups of neurons located in the brainstem. \n(3) The CMAC models a particular region of cerebellar cortex, the posterior vennis. \n(4) The pathway conveying a copy of the feedback controller's crude command corresponds \nto the  projection  from  the superior colliculus  to the nucleus reticularis  tegmenti pontis, \nwhich in tum sendes a mossy fibre projection to the posterior vennis. \nSpace  precludes  detailed  evaluation  of the  substantial  evidence  supporting  the  above \ncorrespondences (see eg Wurtz and Goldberg 1989).  The remaining two connections have \na less secure basis. \n(5)  The idea that the cerebellum adjusts saccadic accuracy by altering feedback gains in \nthe  burst  generator  is  based  on  stimulation  evidence  (Keller  1989);  details  of  the \nprojection, including its anatomy, are not known. \n(6)  The  error  pathway  from  feedback  controller  to  CMAC  is  represented  by  the \nanatomically identified projection from  superior colliculus to inferior olive, and thence via \nclimbing  fibres  to  the  posterior vermis.  There is considerable debate  concerning  the \nfunctional  role  of climbing  fibres,  and  in  the  case of the  tecto-olivary  projection  the \nrelevant physiological evidence appears to be lacking. \n\n3  PERFORMANCE  OF  MODEL \n\nThe system  shown in Fig 3 was trained to  make horizontal movements only. The size of \nburst ~I (arbitrary units) required to produce an accurate rightward saccade ~9 deg was \ncalculated  from  Van  Gisbergen  and  Van  Opstal's  (1989)  analysis  of  the  nonlinear \nrelationship between eye position and muscle position as \n\n~I =  a  [~92 +  ~9 (b  + 29)] \n\n(1) \n\nwhere 9 is initial eye-position (measured in deg from  extreme leftward eye-position) and a \nand  b  are  constants.  In  the  absence  of the CMAC,  the  feedback  controller  and  burst \ngenerator produce a burst of size \n\n~I  =  x.  (c/d) \n\n(2) \n\nwhere x is  the rightward  horizontal displacement of the target, c is  the gain constant of \nthe feedback controller, and d a constant related to the fixed gain of the internal feedback \nloop of the burst generator. The kinematics of the eye are such that x (measured in deg of \nvisual  angle)  is equal  to ~9.  The constants were chosen so that  the perfonnance of the \nsystem without the CMAC resembled that of the primate saccadic system after cerebellar \ndamage (fig 4A), namely position-dependent overshoot (eg Ritchie 1976; Optican and \n\n\f600 \n\nDean,  Mayhew,  and Langdon \n\nA \n\n(No cerebellum) \n\n5.0 \n\nB \n\n(Infant) \n\n5.0 \n\nC \n\n('fralned) \n\n4.5  1 RiKhhrardsaccade  -.1  4 . 5 \n\n5.0 \n\n4.5 \n\n4.0 \n\n3.5 \n\n3 . 0 \n\nl \n\ni = --; = ~ < \n\n2.5 \n\n2.0 \n\n4.0 \n\n3 . 5 \n\n3.0 \n\n2 . 5 \n\n2.0 \n\nS Iat1mg pooin\"\" \n\n(deg.  righr) \n\n- -0 - - -40 \n\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 \n-20 \n_0  \n. - - . - - +20 \n\n4.0 \n\n3.5 \n\n3 . 0 \n\n2.5 \n\n2 . 0 \n\n1.5 \n\n1.0 \n\n0 . 5 \n\n0.0 \n\n20 \n\n40 \n\n'0 \n\n10 \n\n100 \n\n20 \n\n40 \n\n'0 \n\n10 \n\n100 \n\nsaccade amplitude (deg.) \n\n~ \u2022\u2022\u2022 _. u aIhn \u2022\u2022 \u2022 -- aCOlrate 0_-\n\novershoot t \n\nundlhoot \n\no. o+-O\"\"-T~-r--\"'-O\"\"-T----' \n100 \n\n'0 \n\n20 \n\n40 \n\n10 \n\nFig 4.  Performance of model under different conditions before and after training \n\nRobinson 1980).  When the CMAC is present, the size of burst changes to \n\n~I  =  x.  [c/(g  +  d)] \n\n(3) \n\nwhere  g  is  the  output of the  CMAC.  This  was  initialised  to  a  value  that  produced  a \ndegree of saccadic  undershoot (Fig  4b)  characteristic  of initial  performance in  human \ninfants (eg Aslin  1987). \n\nTraining data were generated as 50,000 pairs of random numbers representing the initial \nposition of the eye and the location of the target respectively.  Each pair had to satisfy the \nconstraints  that  (i)  both  lay  within  the  oculomotor  range  (45  deg  on  either  side  of \nmidline) and (ii)  the target lay to the right of the starting position.  For the test data the \nstarting position  varied  from  40 deg  left to  30 deg  right in  10  degree steps.  For each \nstarting position there was a series of targets, starting at 5 deg to the right of the start and \nincreasing in 5 degree steps  up to 40 dcg to the right of midline (a subset of the test data \nwas used in Fig 4).  The main measure of performance was the absolute gain error (ie the \nthe difference between the actual gain and 1.0, always taken as positive) averaged ovcr the \ntest set. \n\nThe configuration of the CMAC was examined in pilot experiments. The CMAC coarse(cid:173)\ncodes its inputs,  so that for a given resolution r, an input span of s can be represented as \nset of m measurement grids each dividing the input span into n compartments,  where sIr \n=  m.n.  Combinations  of m  and  n  were examined,  using  perfect error  feedback.  A \nreasonable compromise between learning speed and asymptotic accuracy was achieved by \nusing  10 coarse-coding grids each with  lOxlO resolution (for the two input dimensions). \ngiving a total of 1000 memory cells. \n\n\fAdaptive Control of Saccadic Accuracy by Primate Cerebellum and Brainstem \n\n601 \n\nThe main part of the study investigated first the effects of degrading  the quality of the \nerror feedback  on  learning.  The main  conclusion  was  that efficient learning could  be \nobtained  if the  CMAC  were  told  only the  direction  of the  error,  ie  overshoot  versus \nundershoot. This infonnation was used to increase by a small fixed amount the weights in \nthe activated cells (thereby producing increased gain in  the internal feedback loop) when \nthe  saccade  was  too  large,  and  to  decreasing  them  similarly  when  it  was  too  small. \nAppropriate choice of learning rate gave a realistic overall error of 5% (Fig 4c) after about \n2000 trials.  Direct comparison  with  learning  rates of human  infants,  who  take  several \nmonths to achieve accuracy, is confounded by such factors  as the maturation of the retina \n(Aslin  1987). \n\nLearning parameters  were then kept constant, and  the model  tested  with  simulations of \ntwo different conditions that produce saccadic plasticity in adult humans.  One involved \nthe  effects of weakening  the rightward  pulling eye muscle  in  one eye.  In  people,  the \nweakened eye can be trained  by covering  the  nonnal eye with a  patch, an  effect which \nexperiments with  monkeys  indicate depends on the cerebellum  (Optic an  and  Robinson \n1980).  For the model  eye-weakening  was  simulated  by  increasing  the  constant  a  in \nequation  (1) such that the trained system gave an  average gain of about 0.5.  Retraining \nrequired  about 400-500  trials.  Testing  the previously  normal  eye (ie  with  the  original \nvalue of a)  showed that it now overshot, as  is also the case in patients and experimental \nanimals.  Again  normal  performance was  restored  after 400-500  trials.  These learning \nrates compare favourably with those observed in experimental animals. \n\nFinally, the second simulation of adult saccadic plasticity concerned the effects of moving \nthe target during a saccade.  If the target is moved in  the opposite direction to its original \ndisplacement the saccade will  overshoot, but after a few  trials adaptation occurs and  the \nsaccade becomes 'accurate' once more.  Simulation of the procedure used by Deubel et al. \n(1986) gave system adaptation rates similar to those observed experimentally in people. \n\n4  CONCLUSIONS \n\nThese results indicate that the model can account in general terms for the acquisition and \nmaintenance of saccadic accuracy in primates (at least in one dimension).  In addition  to \nits  general  biologically  attractive  properties,  the  model's  structure  is  consistent  with \ncurrent anatomical and physiological knowledge, and offers testable predictions about the \nfunctions  of the  hitherto  mysterious  projections  from  superior  colliculus  to  posterior \nIf these  predictions  are  supported  by  experimental  evidence,  it  would  be \nvennis. \nappropriate to  extend the model  to incorporate greater physiological detail, for example \nconcerning the precise location(s) of cerebellar plasticity. \n\nAcknowledgements \n\nThis work was supported by the Joint Council Initiative in  Cognitive Science. \n\n\f602 \n\nDean,  Mayhew.  and Langdon \n\nReferences \n\nAlbus, J.A. (1971)  A theory of cerebellar function.  Math. Biosci.  10:  25-61. \nAlbus, J.A. (1981)  Brains, Behavior and Robotics.  BYTE books (McGraw-Hill), \n\nPeterborough New Hampshire. \n\nAslin, R.N. (1987)  Motor aspects of visual development in infancy.  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(1989)  The Neurobiology of Saccadic Eye Movements. \n\nElsevier Science Publishers, North Holland. \n\n\f", "award": [], "sourceid": 549, "authors": [{"given_name": "Paul", "family_name": "Dean", "institution": null}, {"given_name": "John", "family_name": "Mayhew", "institution": null}, {"given_name": "Pat", "family_name": "Langdon", "institution": null}]}