{"title": "Learning in the Vestibular System: Simulations of Vestibular Compensation Using Recurrent Back-Propagation", "book": "Advances in Neural Information Processing Systems", "page_first": 603, "page_last": 610, "abstract": null, "full_text": "Learning in the Vestibular System: \n\nSimulations of Vestibular Compensation \n\nUsing Recurrent Back-Propagation \n\nThomas J.  Anastasio \nUniversity of Dlinois \n\nBeckman Institute \n\n405 N.  Mathews Ave. \n\nUrbana, II... 61801 \n\nAbstract \n\nVestibular  compensation  is  the  process  whereby  normal  functioning  is \nregained  following  destruction  of  one  member  of  the  pair  of  peripheral \nvestibular  receptors.  Compensation  was  simulated  by  lesioning  a  dynamic \nneural  network  model  of the  vestibulo~ular reflex  (VOR)  and  retraining  it \nusing  recurrent back-propagation.  The model reproduced the pattern of VOR \nneuron activity  experimentally observed  in compensated animals,  but only  if \nconnections  heretofore  considered  uninvolved  were  allowed  to  be  plastic. \nBecause  the  model  incorporated  nonlinear  units,  it  was  able  to  reconcile \npreviously conflicting, linear analyses of experimental  results on the dynamic \nproperties of VOR neurons in normal and compensated animals. \n\n1 VESTIBULAR COMPENSATION \n\nVestibular compensation is one of the oldest and most well studied paradigms in motor \nlearning.  Although it is neurophysiologically well described, the adaptive mechanisms \nunderlying  vestibular  compensation,  and  its  effects  on  the  dynamics  of vestibular \nresponses,  are still poorly understood.  The purpose of this study  is to gain insight into \nthe  compensatory  process  by  simulating  it  as  learning  in  a  recurrent  neural  network \nmodel of the vestibulo-ocular reflex (VOR). \n\n603 \n\n\f604 \n\nAnastasio \n\nThe  VOR  stabilizes  gaze  by  producing  eye  rotations  that  counterbalance  bead \nrotations.  It is mediated by brainstem neurons in the vestibular nuclei  (VN) that  relay \nhead  velocity  signals  from  vestibular  sensory  afferent  neurons  to  the  motoneurons  of \nthe  eye  muscles  (Wilson  and  Melvill  Jones  1979).  The  VOR  circuitry  also  processes \nthe  canal  signals,  stretching  out their time constants  by  four  times  before  transmitting \nthis  signal  to  the motoneurons.  This process of time constant lengthening is known as \nvelocity storage (Raphan et al.  1979). \n\nThe  VOR  is  a bilaterally  symmetric structure  that  operates  in  push-pull.  The VN  are \nlinked  bilaterally  by  inhibitory  commissural  connections.  Removal  of the  vestibular \nreceptors  from  one  side  (hemilabyrinthectomy)  unbalances  the  system,  resulting  in \ncontinuous  eye  movement  that  occurs  in  the  absence  of head  movement,  a  condition \nknown as  spontaneous  nystagmus.  Such  a lesion  also  reduces  VOR  sensitivity  (gain) \nand  eliminates  velocity  storage.  Compensatory  restoration  of VOR  occurs  in  stages \n(Fetter and  Zee  1988).  It begins by  quickly  eliminating  spontaneous  nystagmus,  and \ncontinues by increasing VOR gain.  Curiously, velocity storage never recovers. \n\n2 NETWORK ARCHITECTURE \n\nThe horizontal  VOR is  modeled  as  a three-layered  neural  network  (Figure  1).  All  of \nthe  units  are  nonlinear,  passing  their  weighted  input  sums  through  the  sigmoidal \nsquashing function.  This function bounds unit responses between zero and one.  Input \nunits  represent  afferents  from  the  left  (lhc)  and  right  (mc)  horizontal  semicircular \ncanal  receptors.  Output units correspond to  motoneurons of the lateral  (lr) and medial \n(mr)  rectus muscles of the left eye.  Interneurons in the VN  are  represented by hidden \nunits on the left (lvnl, Ivn2)  and  right (rvnl, rvn2)  sides of the model brainstem.  Bias \nunits stand for non-vestibular inputs, on the left (lb) and right (rb) sides. \n\nNetwork  connectivity  reflects  the  known  anatomy  of mammalian  VOR  (Wilson  and \nMelvill  Jones  1979).  Vestibular  commissures  are  modeled  as  recurrent  connections \nbetween hidden units on opposite sides.  All connection weights to the hidden units are \nplastic,  but those to the outputs are initially fixed,  because it is generally  believed that \nsynaptic plasticity  occurs  only  at  the  VN  level  in  vestibular compensation  (Galiana et \nal.  1984).  Fixed hidden-to-output weights have a crossed,  reciprocal pattern. \n\n3 TRAINING THE NORMAL NETWORK \n\nThe simulations began by training the network shown in Figure I, with both vestibular \ninputs  intact (normal  network),  to produce  the  VOR  with  velocity  storage  (Anastasio \n1991).  The  network  was  trained  using  recurrent  back-propagation  (Williams  and \nZipser 1989).  The input and desired output sequences correspond to  the canal afferent \nsignals and  motoneuron eye-velocity commands that would produce the VOR response \nto  two impulse head rotational  accelerations,  one to  the left and the other to  the  right. \nOne input (rhc)  and  desired  output  (lr)  sequence  is  shown  in  Figure  2A  (dotted  and \ndashed,  respectivley).  Those  for  /hc  and  mr (not  shown)  are identical  but  inverted. \nThe desired  output  responses are equal  in amplitude to  the inputs,  producing VOR \n\n\fLearning in  the Vestibular System \n\n605 \n\nFigure  1.  Recurrent  Neural  Network  Model  of  the  Horizontal  Vestibulo-Ocular \nReflex  (VOR). \n/he,  The:  left  and  right  horizontal  semicircular  canal  afferents;  lm1, \nlm2,  rvnl,  rvn2:  vestibular  nucleus  neurons  on  left  and  right  sides  of  model \nbrainstem;  lr,  mr:  lateral  and  medial  rectus  muscles  of left  eye;  lb,  rb:  left  and  right \nnon-vestibular inputs.  This and subsequent figures redrawn from Anastasio (in press). \n\neye  movements  that  would  perfectly  counterbalance  head  movements.  The  output \nresponses  decay  more  slowly  than  the  input  responses.  reflecting  velocity  storage. \nBetween head  movements.  both desired outputs have the same spontaneous  firing  rate \nof 0.50.  With  output  spontaneous  rates  (SRs)  balanced.  no  push-pull  eye  velocity \ncommand is given and. consequently, no VOR eye movement would be made. \n\nThe  normal  network  learns  the  VOR  transformation  after  about  4.000  training \nsequence  presentations  (passes).  The  network  develops  reciprocal  connections  from \ninput  to  hidden  units.  as  in  the  actual  VOR  (Wilson  and  Melvill  Jones  1979). \nInhibitory recurrent connections form an integrating (lvnl. rvnl) and a non-integrating \n(1m2.  rvn2)  pair  of hidden  units  (Anastasio  1991). \nThe  integrating  pair  subserve \nstorage  in  the  network.  They  have  strong  mutual  inhibition  and  exert  net  positive \nfeedback on themselves.  The non-integrating pair have almost no mutual  inhibition. \n\n\f606 \n\nAnastasio \n\n4 SIMULATING VESTmULAR COMPENSATION \n\ninputs \n\nAfter  the  normal  network  is  constructed,  with  both \nintact,  vestibular \ncompensation  can  be  simulated  by  removing  the  input  from  one  side  and  retraining \nwith  recurrent  back-propagation.  Left  hemilabyrinthectomy  produces  deficits  in  the \nmodel  that correspond to those observed experimentally.  The responses of output unit \nIr acutely  (i.e.  immediately)  following  left  input  removal  are  shown  in  Figure  2A. \nThe SR of Ir (solid) is greatly increased above normal  (dashed);  that of mr (not shown) \nis  decreased  by  the  same  amount.  This  output  SR  imbalance  would  result  in  eye \nmovement to  the left in the absence  of head  movement  (spontaneous nystagmus).  The \ngain  of the  outputs  is  greatly  decreased.  This  is  due  to  removal  of one  haJf  the \nnetwork  input,  and  to  the  SR  imbalance  forcing  the  output  units  into  the  low  gain \nextremes  of \u00b7the  squashing  function.  Velocity  storage  is  also  eliminated  by  left  input \nremoval, due to events at the hidden unit level (see below). \n\nDuring  retraining,  the  time  course  of  simulated  compensation  is  similar  to  that \n\n0.75 \n\nen w \n(J)o.65 \nZ \n2 \n(J)o.55 \nw a: \nt::0.45 \n2 \n::> \n\n1'\\1 \n\nr'~ \n\n0.65 \n\nA \n\n0.55 \n\n.V \".,-\n\nI \nI \n1/ \nV \n\n0.45 \n\nt \n, \\  '  ... \n\no PASSES \n\nB \n\n\" , \\ , \n\n200 PASSES \n\nQ.35 0 \nQ.65 \n\nen w \n(J) \n~o.55 \n(J) \nw \na:Q.45 \nt:: \n2 \n::> \n\nQ.350 \n\n10 \n\n20 \n\n3l  \u00abl \n\n50 \n\ntil \nC \n\nQ.35 \n\nQ.65 \n\n0 \n\n10 \n\n20 \n\n30 \n\n40 \n\n!II \n\ntil \nD \n\n.... \n\n--\n\n0.55 \n\n0.45 \n\n900 PASSES \n\n6,700 PASSES \n\n20 \n\n10 \n50 \nNETWORK CYCLES \n\n3l \n\n40 \n\nQ.35 \n\n0 \n\ntil \n\n20 \n\n10 \n50 \nNElWORK CYCLES \n\n30 \n\n40 \n\ntil \n\nFigure 2.  Simulated Compensation in  the  VOR  Neural  Network Model.  Response of \nIr  (solid)  is  shown  at  each  stage  of  compensation:  A,  acutely  (i.e.  immediately) \nfollowing  the  lesion;  B,  after  spontaneous  nystagmus  has  been  eliminated;  C,  after \nVOR gain  has  been largely  restored;  D,  after full  recovery of VOR.  Desired  response \nof lr (dashed) shown in all plots.  Intact input from  rhe (dotted) shown in  A only. \n\n\fLearning in  the Vestibular System \n\n607 \n\nobserved experimentally (Fetter and  Zee  1988).  Spontaneous nystagmus  is  eliminated \nafter 200  passes,  as  the  SRs of the output units are brought back  to  their normal  level \n(Figure  2B).  Output  unit  gain  is  largely  restored  by  900  passes,  but  time  constant \nremains  close to  that  of the inputs (Figure 2C).  At  this  stage.  VOR  gain would have \nincreased  substantially.  but  its  time  constant  would  remain  low.  indicating  loss  of \nvelocity  storage.  This  stage  approximates  the  extent  of  experimentally  observed \ncompensation  (ibid.).  Completely  restoring  the  normal  VOR.  with  full  velocity \nstorage. requires over seven times more retraining (Figure 2D). \n\nThe responses  of the  hidden  units  during  each  stage  of simulated  compensation  are \nshown  in  Figure  3A and  3C.  Average  hidden  unit  SR  and  gain  are  shown  as  dotted \nlines  in  Figure  3A  and  3C,  respectively.  Acutely  following  left  input  removal  (AC \nstage).  the  SRs  of left  (dashed)  and  right  (solid)  hidden  units  decrease  and  increase. \nrespectively (Figure 3A).  One left hidden unit (lvnl)  is actually silenced.  Hidden unit \ngain at AC stage is greatly reduced bilaterally (Figure 3C). as  for the outputs. \n\nAt the point where spontaneous nystagmus  is  eliminated  (NE stage).  hidden units SRs \nare  balanced  bilaterally.  and  none  of the  units  are  spontaneously  silent  (Figure  3A). \nWhen  VOR  gain  is  largely  restored  (GR  stage.  corresponding  to  experimentally \nobserved  compensation),  the  gains  of the  hidden  units  have  substantially  increased \n(Figure 3C).  At GR stage.  average hidden unit SR  has also  increased  but the  bilateral \nSR balance has been strictly maintained (Figure 3A).  A comparison with experimental \ndata (Yagi and Markham 1984;  Newlands and Perachio  1990) reveals that the behavior \nof hidden units in the model does not correspond to  that  observed for real  VN neurons \nin compensated  animals.  Rather  than  having  bilateral  SR  balance.  the  average  SR  of \nVN  neurons  in  compensated  animals  is  lower  on  the  lesion-side  and  higher  on  the \nintact-side.  Moreover,  many  lesion-side VN  neurons are permanently silenced.  Also. \nrather  than  substantially  recovering  gain.  the  gains  of VN  neurons  in  compensated \nanimals increase little from their low values acutely following the lesion. \n\nThe network  model  adopts  its  particular  (and  unphysiological)  solution  to  vestibular \ncompensation because. with fixed connection weights to the outputs.  compensation can \nbe  brought about only  by changes in  hidden  unit behavior.  Thus.  output  SRs  will  be \nbalanced only if hidden SRs are balanced.  and output gain will  increase only  if hidden \ngain increases.  The discrepancy  between  model  and  actual  VN  neuron data  suggests \nthat compensation cannot rely solely on synaptic plasticity at the VN level. \n\n5 RELAXING CONSTRAINTS \n\nA better  match  between  model  and  experimental  VN  neuron  data  can  be  achieved  by \nrerunning  the compensation simulation with modifiable weights at all  allowed network \nconnections  (Figure  1).  Bias-to-output  and  hidden-to-output  synaptic  weights.  which \nwere previously  fixed,  are now made plastic.  These extra degrees of freedom give the \nadapting  network  greater  flexibility  in  achieving  compensation.  and  release  it  from  a \nstrict  dependency  upon  the  behavior  of  the  hidden  units.  The  time  course  of \ncompensation  in  the  all-weights-modifiable  example  is  similar  to  the  previous  case \n(Figure 2).  but each stage is reached after fewer passes. \n\n\f608 \n\nAnastasio \n\nW \n\n, \n~ 0.8 \n\n().4 \n\nUJ \n~ 0.6 \n0 \nW \nZ \n~ \nZ  02 \n~ (/J \n\n~M \n\nA \n\n, \n\n0.8 \n\n0.6 \n\n0.4 \n02  .....  , \n\n.....  , \n\n.....  ~ \n\nNE \n\nGR  ~M \n\nAC \n\nNE \n\n,/ \n\n\" \nAC \n\n3 \n\n2 \n\n1 \n\n3 \n\n2 \n\n1 \n\n---\nGR \nD \n\nAC \n\nNE \n\nGR  ~M \n\nAC \n\nNE \n\nGR \n\nFigure 3.  Behavior of Hidden  Units  at  Various  Stages  of Compensation  in  the  VOR \nNeural  Network  Model.  Spontaneous  rate  (SR,  A  and  B)  and  gain  (C  and  D)  are \nshown  for  networks  with  hidden  layer weights  only  modifiable (A and  C)  or with  all \nweights  modifiable  (B  and  D).  Normal  average  SR  (A  and  B)  and  gain  (C  and  D) \nshown  as  dotted  lines.  NM.  normal  stage;  AC,  acutely  following  lesion;  NE.  after \nspontaneous nystagmus is eliminated; GR. after VOR gain is largely restored. \n\nThe behavior  of the  hidden  units in the  all-weights  simulation  more closely  matches \nthat of actual  VN  neurons in compensated animals (Figure 3B and 3D).  At NE stage. \neven  though  spontaneous  nystagmus  is  eliminated.  there  remains  a  large  bilateral \nimbalance in hidden unit SR. and one lesion-side hidden unit (lvn}) is silenced (Figure \n3B).  At  GR  stage.  hidden  unit  gain  has  increased  only  modestly  from  the  low  acute \nlevel  (Figure  3D).  and  the  bilateral  SR  imbalance  persists.  with  Ivnl  still  essentially \nspontaneously  silent  (Figure  3B). \nThis  modeling  result  constitutes  a  testable \nprediction that synaptic plasticity  is occurring  at the  motoneuron as well  as  at the  VN \nlevel in vestibular compensation. \n\n6 NETWORK DYNAMICS \n\nIn  the  all-weights  simulation  at  GR  stage.  as  well  as  in  compensated  animals,  some \nlesion-side  VN  neurons  are  silenced.  Hidden  unit  lvnl  is  silenced  by  its  inhibitory \ncommissural  interaction  with  rvnl,  which  in  the  normal  network  allowed  the  pair  to \n\n\fLearning in the Vestibular System \n\n609 \n\nform  an  integrating,  recurrent  loop.  Silencing  of 1m}  breaks  the  commissural  loop \nand  consequently  eliminates  velocity  storage  in  the  network.  VN  neuron  silencing \ncould also account for the loss of velocity storage  in the real,  compensated VOR. \n\nLoss of velocity storage in the model,  in response to  step  head  rotational  acceleration \nstimuli,  is shown in  Figure 4.  The output step  response that  would be expected given \nthe longer VOR time constant is shown  for  lr in Figure 4A (dashed).  The response of \nmr  (not  shown)  is  identical  but  inverted.  Instead  of expressing  the  longer  VOR  time \nconstant,  the actual  step  response of lr  in  the all-weights  compensated network at  GR \nstage  (Figure  4A,  dotted)  has  a  rise  time  constant  that  is  equal  to  the  canal  time \nconstant,  indicating complete loss  of velocity  storage.  This is due  to  the  behavior of \nthe  hidden  units.  The  step  responses  of the  integrating  pair  of hidden  units  in  the \ncompensated network at GR stage are shown  in Figure 4B  (lml,  lower dotted;  rvnl, \nupper dotted).  Velocity storage is eliminated because lvnl  is silenced,  and  this  breaks \nthe commissural loop that supports integration in the network. \n\nParadoxically,  in  the normal  network  with all  hidden  units  spontaneously  active,  the \noutput step response rise time constant is also equal to that of the canal afferents,  again \nindicating a loss of velocity  storage.  This is shown for  lr from the normal  network in \nFigure 4A  (solid).  The  step  responses  of the hidden units  in  the normal  network  are \nshown  in  Figure  4B  (lvnl,  dashed;  rvnl,  solid).  Unit  lml,  which  is  spontaneously \nactive in  the normal  network,  is  quickly driven into cut-off by  the step  stimulus.  This \nbreaks the commissural loop  and eliminates  velocity  storage,  accounting  for  the short \nrise time constants of hidden and output units network wide. \n\nThis  result  can  explain  some  conflicting  experimental  findings  concerning \n\nthe \n\nA \n\n0.8 \n\n0.8 \n\nr \n\nl.  ,,-\nrl \n\nI \n\n1---' \n\nffi  0.65 \nUl \nZ \n~ \n0.55 m \na: \nt:  OAS \nZ \n:J \n\nl \n\n0.35  ______ ....L.._...10-___  ........ _\"\"\"\" \n..0  SJ  8) \n\n10  3)  al \n\no \n\nB \n\n, \n~ \n~ \n;---\n'\" \n\nI \nI \n40 \n\n50  8) \n\n0.4 \n\n10-1 \n\nl--{ \n\n0.2 \n\n\\ \n\\ \n\n10  Zl \n\n31 \n\no \no \n\nNElWORK CYCLES \n\nNETWORK CYCLES \n\nFigure 4.  Responses  of Units  to  Step  Head  Rotational  Acceleration  Stimuli  in  VOR \nNeural Network Model.  A,  expected response of lr with VOR time constant (dashed), \nand  actual  responses  of  lr  in  normal  (solid)  and  all-weights  compensated  (dotted) \nnetworks.  B,  response  of lml  (dashed)  and  rvnl  (solid)  in  normal  network,  and  of \nlvnl (lower dotted) and rvnl (upper dotted) in all-weights compensated network. \n\n\f610 \n\nAnastasio \n\ndynamics  of  VN  neurons  in  normal  and  compensated  animals.  Using  sinusoidal \nstimuli,  the time constants of VN neurons were found  to be lower in  compensated than \nIn  contrast,  using  step  stimuli,  no \nin  normal  gerbils (Newlands  and  Perachio  1990). \ndifference in rise time constants were found  for  VN neurons in DOrmal  as compared  to \ncompensated cats (Yagi and Markham 1984). \n\nRather  than  being  a  species  difference,  the  disagreement  may  involve  the  type  of \nstimulus  used.  Step  accelerations  are  intense  stimuli  that  can  drive  VN  neurons  to \nIn  response  to  a  step  in  their  off-directions,  many  VN  neurons  in \nextreme  levels. \nnormal  cats  were  observed  to  cut-off  (ibid.).  As  shown  in  Figure  4,  this  would \ndisrupt commissural  interactions and  reduce velocity  storage and  VN  neuron  rise time \nconstants, just as if these neurons were silenced as they  are in compensated animals.  In \nfact,  VN  neuron  rise  time  constants  were  observed  to  be  low  in  both  normal  and \ncompensated  cats (ibid.).  In contrast,  sinusoidal  stimuli  at  an  intensity  that does  not \ncause widespread VN neuron cut-off would not be expected to disrupt velocity storage \nin normal animals. \n\nAcknowledgements \n\nThis work was supported  by a grant from the Whitaker Foundation. \n\nReferences \n\nAnastasio  TJ  (1991)  Neural  network  models  of  velocity  storage  m  the  horizontal \nvestibulo-ocular reflex.  Bioi Cybem 64: 187-196 \n\nAnastasio  TJ  (in  press)  Simulating  vestibular  compensation  using  recurrent  back(cid:173)\npropagation.  Bioi  Cybem \n\nFetter M, Zee DS (1988) Recovery from unilatera1labyrinthectomy in rhesus monkey. \nI  Neurophysiol 59:370-393 \n\nGaliana HL,  Flohr H, Melvill Iones G (1984) A reevauation of intervestibular nuclear \ncoupling:  its role in vestibular compensation. J  Neurophysiol 51:242-259 \n\nNewlands  SD,  Perachio AA (1990)  Compensation of horizontal  canal  related  activity \nin  the  medial  vestibular  nucleus  following  unilateral  labyrinth  ablation  in  the \ndecerebrate gerbil. I. type I neurons.  Exp Brain Res 82:359-372 \n\nRaphan Th, Matsuo V, Cohen B (1979) Velocity storage in  the  vestibulo-ocular reflex \narc (VOR).  Exp Brain Res 35:229-248 \n\nWilliams  RJ,  Zipser  D  (1989)  A  learning  algorithm  for  continually  running  fully \nrecurrent neural networks.  Neural Comp 1:270-280 \n\nWilson VI,  Melvill Jones G  (1979) Mammalian vestibular physiology.  Plenum Press, \nNew York \n\nYagi  T,  Markham  CH \nhemilabyrinthectomy.  Exp Neurol 84:98-108 \n\n(1984)  Neural  correlates  of  compensation  after \n\n\f", "award": [], "sourceid": 474, "authors": [{"given_name": "Thomas", "family_name": "Anastasio", "institution": null}]}