{"title": "Interference in Learning Internal Models of Inverse Dynamics in Humans", "book": "Advances in Neural Information Processing Systems", "page_first": 1117, "page_last": 1124, "abstract": null, "full_text": "Interference in Learning Internal \n\nModels of Inverse Dynamics in Humans \n\nReza Shadmehr; Tom Brashers-Krug, and Ferdinando Mussa-lvaldit \n\nDept. of Brain and Cognitive Sciences \n\nM.  I. T., Cambridge, MA  02139 \n\nreza@bme.jhu.edu,  tbk@ai.mit.edu, sandro@parker.physio.nwu.edu \n\nAbstract \n\nExperiments were  performed  to  reveal  some of the  computational \nproperties  of the  human  motor  memory  system.  We  show  that \nas  humans  practice  reaching  movements while  interacting  with  a \nnovel  mechanical environment, they learn an  internal model of the \ninverse dynamics of that environment.  Subjects show recall of this \nmodel  at testing  sessions  24  hours  after  the  initial practice.  The \nrepresentation  of the internal model in  memory is  such  that there \nis  interference  when  there  is  an  attempt  to  learn  a  new  inverse \ndynamics  map  immediately after  an  anticorrelated  mapping  was \nlearned.  We  suggest  that  this  interference  is  an  indication  that \nthe same computational elements  used  to encode  the first  inverse \ndynamics  map  are  being  used  to  learn  the  second  mapping.  We \npredict  that this leads to a forgetting  of the initially learned skill. \n\n1 \n\nIntroduction \n\nIn tasks where we use our hands to interact with a tool, our motor system develops \na  model  of the  dynamics of that  tool  and  uses  this  model  to  control  the  coupled \ndynamics of our arm and the tool  (Shadmehr and Mussa-Ivaldi  1994).  In physical \nsystems theory, the tool is a mechanical analogue of an admittance, mapping a force \nas  input  onto  a  change  in  state  as  output  (Hogan  1985).  In  this  framework,  the \n\n\u00b7Currently at  Dept.  Biomedical  Eng,  Johns  Hopkins  Univ,  Baltimore,  MD  21205 \ntCurrently at Dept. Physiology,  Northwestern Univ Med Sch (M211),  Chicago, IL 60611 \n\n\f1118 \n\nReza Shadmehr,  Tom  Brashers-Krug,  Ferdinando Mussa-Ivaldi \n\nFigure  1:  The experimental  setup.  The robot  is \na  very  low  friction  planar  mechanism  powered  by \ntwo  torque  motors  that  act  on  the  shoulder  and \nelbow  joints.  Subject  grips  the  end-point  of  the \nrobot  which  houses  a  force  transducer  and  moves \nthe hand to a series of targets displayed  on a moni(cid:173)\ntor facing the subject (not shown) .  The function of \nthe  robot is  to  produce  novel  force  fields  that  the \nsubject  learns  to  compensate  for  during  reaching \nmovements. \n\nmodel developed  by the motor control system during the learning process  needs  to \napproximate  an  inverse  of this  mapping.  This  inverse  dynamics  map is  called  an \ninternal model of the tool. \n\nWe  have  been  interested  in  understanding  the  representations  that  the  nervous \nsystem  uses  in  learning  and  storing  such  internal  models.  In  a  previous  work  we \nmeasured the  way  a  learned  internal model extrapolated beyond  the training data \n(Shadmehr and Mussa-Ivaldi 1994).  The results suggested that the coordinate sys(cid:173)\ntem of the learned map was in intrinsic (e.g., joint or muscles based)  rather than in \nextrinsic (e.g., hand based)  coordinates.  Here we  present  a mathematical technique \nto estimate the  input-output properties  of the  learned  map.  We  then  explore  the \nissue  of how  the  motor  memory might store  two  maps which  have  similar inputs \nbut different  outputs. \n\n2  Quantifying the internal model \n\nIn  our  paradigm,  subjects  learn  to  control  an  artificial  tool:  the  tool  is  a  robot \nmanipulandum which  has  torque  motors  that  can  be  programmed  to  produce  a \nvariety  of dynamical environments  (Fig.  1).  The  task  for  the  subject  is  to  grasp \nthe end-effector  and make point to point reaching movements to a series of targets. \nThe environments are represented  as force fields  acting on the subject's hand, and a \ntypical case is shown in Fig. 2A.  A typical experiment begins with the robot motors \nturned off.  In  this  \"null\"  environment subjects move their hand to the targets in  a \nsmooth, straight line fashion.  When the force field is introduced, the dynamics of the \ntask change  and the hand trajectory is significantly altered  (Shadmehr and Mussa(cid:173)\nIvaldi  1994).  With  practice  (typically hundreds  of movements),  hand  trajectories \nreturn to their straight line path.  We have suggested that practice leads to formation \nof an  internal model which  functions  as  an  inverse  dynamics mapping, i.e., from  a \ndesired  trajectory  (presumably in  terms of hand position  and  velocity,  Wolpert et \nal. 1995) to a prediction of forces  that will be encountered  along the trajectory.  We \ndesigned  a  method  to  quantify  these  forces  and estimate the  output  properties  of \nthe internal model. \nIf we  position a force  transducer at the interaction point between  the robot and the \nsubject,  we  can write the dynamics of the four link system in Fig. 1 in terms of the \n\n\fInterference in  Learning Internal Models of Inverse  Dynamics in  Humans \n\n1119 \n\nfollowing coupled vector  differential equations: \n\nIr(P)P + Gr(p,p)p =  E(p,p) + J'{ F \nIII (q)q + GII(q, q)q = C(q, q, q*(t\u00bb  - f; F \n\n(1) \n(2) \nwhere  I  and  G  are  inertial  and  Corriolis/centripetal  matrix functions,  E  is  the \ntorque field  produced  by  the  robot's  motors,  i.e.,  the environment,  F  is  the force \nmeasured at the handle of the robot,  C is the controller implemented by  the motor \nsystem of the subject,  q*(t)  is the reference  trajectory planned by the motor system \nof the subject,  J  is  the  Jacobian  matrix describing  the  differential  transformation \nof coordinates from  endpoint  to joints,  q  and  p  are  joint  positions  of the subject \nand the robot,  and the subscripts sand r  denote subject or robot  matrices. \n\nIn  the  null  environment,  i.e.,  E  = \u00b0 in  Eq.  (1),  a  solution  to  this  coupled  system \n\nis  q =  q*(t)  and the  arm follows the reference  trajectory  (typically a straight  hand \npath with a  Gaussian tangential velocity profile).  Let  us  name the controller which \naccomplishes this task C = Co  in  Eq.  (2).  When  the robot  motors are producing a \nforce  field  E  # 0,  it  can  be  shown  that the solution is  q =  q*(t)  if and only if the \nnew controller in Eq.  (2) is C =  C1  =  Co + f[ J;T E.  The internal model composed \nby  the  subject  is  C1  - Co,  i.e.,  the  change  in  the  controller  after  some  training \nperiod.  We  can estimate this quantity by  measuring the  change  in  the interaction \nforce  along  a  given  trajectory  before  and  after  training.  If we  call  these  functions \nFo  and FI,  then  we  have: \n\nFo(q, q, ij, q*(t\u00bb \nFI(q,q,ij,q*(t\u00bb \n\nJ;T(Co - IlIq - Gllq) \nJII-T(Co+f;J;TE-Illq-Gllq) \n\n(3) \n(4) \nThe functions  Fo  and  FI  are  impedances of the subject's  arm as  viewed  from  the \ninteraction  port.  Therefore,  by  approximating the  difference  FI  - Fo,  we  have  an \nestimate of the change in the controller.  The crucial assumption is that the reference \ntrajectory  q*(t)  does  not  change during the training process. \nIn  order  to  measure  Fo,  we  had  the  subjects  make  movements  in  a  series  of en(cid:173)\nvironments.  The  environments  were  unpredictable  (no  opportunity  to  learn)  and \ntheir  purpose  was  to  perturb  the  controller  about  the  reference  trajectory  so  we \ncould  measure  Fo  at  neighboring  states.  Next,  the  environment  in  Fig.  2A  was \npresented  and the subject given  a practice period  to adapt.  After  training,  FI  was \nestimated in a similar fashion as Fo.  The difference between these two functions was \ncalculated along all measured arm trajectories and the results were  projected onto \nthe  hand velocity  space.  Due to  computer limitations, only  9 trajectories  for  each \ntarget  direction  were  used  for  this  approximation.  The resulting  pattern  of forces \nwere  interpolated  via a  sum of Gaussian  radial  basis  functions,  and  are  shown  in \nFig.  2B.  This is  the  change in  the  impedance of the  arm and estimates the input(cid:173)\noutput  property of the internal model that was  learned  by  this subject.  We  found \nthat this subject,  which provided some of best  results in the test group, learned to \nchange the effective  impedance of his arm in a way that approximated the imposed \nforce  field.  This would be a  sufficient  condition for  the  arm to compensate for  the \nforce field and allow the hand to follow the desired trajectory.  An alternate strategy \nmight have been to simply co-contract arm muscles:  this would lead to an increased \nstiffness  and an ability to resist  arbitrary environmental forces.  Figure 2B  suggests \nthat practice  led  to formation of an internal model specific  to the dynamics of the \nimposed force  field. \n\n\f1120 \n\nReza Shadmehr,  Tom  Brashers-Krug,  Ferdinando Mussa-Ivaldi \n\nA \n\n-200 \n\n0 \n\n200 \n..... _<...-) \n\n... \n\nB \n\n\",\",,-<...-) \n\nFigure 2:  Quantification  of the change in impedance  of a  subject's arm  after learning  a \nforce  field.  A:  The force  field  produced  by  the robot  during  the  training  period.  B: The \nchange  in  the subject's arm impedance  after the training  period,  i.e.,  the internal  model. \n\n2.1  Formation of the internal model in long-term memory \n\nHere we  wished to determine whether subjects retained the internal model in long(cid:173)\nterm  motor memory.  We  tested  16  naive subjects.  They  were  instructed  to  move \nthe  handle  of the  robot  to  a  sequence  of targets  in  the  null  environment.  Each \nmovement  was  to  last  500  \u00b1 50  msec.  They  were  given  visual  feedback  on  the \ntiming of each movement.  After  600  movements, subjects were  able to consistently \nreach  the targets in proper time.  These  trajectories  constituted  a  baseline set. \nSubjects  returned  the  next  day  and  were  re-familiarized  with  the  timing  of  the \ntask.  At  this  point  a  force  field  was  introduced  and  subjects  attempted  to  per(cid:173)\nform  the exact  task as  before:  get to the target in  proper time.  A sequence  of 600 \ntargets was given.  When first  introduced, the forces  perturbed the subject's trajec(cid:173)\ntories,  causing  them  to  deviate  from  the straight  line  path.  As  noted  in  previous \nwork  (Shadmehr and  Mussa-Ivaldi 1994), these  deviations decreased  with practice. \nEventually, subject's trajectories in the presence of the force  field  came to resemble \nthose of the  baseline,  when  no  forces  were  present.  The convergence  of the trajec(cid:173)\ntories  to  those  performed  at  baseline  is  shown  for  all  16  subjects  in  Fig.  3A.  The \ntiming performance of the subjects  while moving in  the field  is shown  in  Fig.  3B. \n\nIn  order  to  determine  whether  subjects  retained  the  internal  model  of the  force \nfield  in  long-term memory, we  had them return  the next day  (24 to 30  hours later) \nand  once  again  be  tested  on  a  force  field.  In  half of the  subjects,  the  force  field \npresented  was  one  that  they  had trained  on in  the previous  day  (call this field  1). \nIn  the other half,  it was  a force  field  which  was  novel  to  the subjects,  field  2.  Field \n2  had  a  correlation  value  of -1 with  respect  to  field  1  (i.e.,  each  force  vector  in \nfield  2 was  a  180  degree  rotation of the respective  vector  in field  1).  Subjects  who \nwere  tested on a field  that they had trained on before performed significantly better \n(p  < 0.01)  than  their initial performance (Fig. 4A), signifying retention.  However, \nthose  who  were  given  a  field  that  was  novel  performed  at  naive  levels  (Fig.  4B). \nThis result  suggested  that the internal model formed  after practice in a given  field \nwas  (1)  specific to that field:  performance on the untrained field  was no better than \n\n\fInterference  in Learning Internal  Models  of Inverse  Dynamics in Humans \n\n1121 \n\n0.9 \n\n0.85 \n\n.~  0.8 \n:\u00a7 \n~ 0.75 \n8 \n\n0.7 \n\n0.85 \n\nA \n\n0 \n\n100 \n\n200 \n\n300 \n\n400 \n\n500 \n\n600 \n\nMovemen1 N!mber \n\n-; 0.9 \n\n\u00a5 \n~ i 08 \n~ 0.7 \n\nB \n\n0.6 \n\n0 \n\n100 \n\n200 \n\n300 \n\n400 \n\n500 \n\n600 \n\nMovement Number \n\nFigure 3:  Measures  of performance  during  the  training  period  (600  movements)  for  16 \nnaive  subjects.  Short  breaks  (2  minutes)  were  given  at intervals  of 200  movements.  A : \nMean  \u00b1 standard  error  (SE)  of the  correlation  coefficient  between  hand  trajectory  in  a \nnull  environment  (called  baseline  trajectories,  measured  before exposure  to the field) , and \ntrajectory in  the force  field.  Hand trajectories in the field  converge to that in the null field \n(i.e. , become straight,  with a bell shaped velocity profile).  B: Mean \u00b1 SE of the movement \nperiod  to reach  a  target.  The goal  was  to reach the target in  0.5 \u00b1 0.05  seconds. \n\nI  1 \n\n.,  0.9 \nE \n\ni= I:: \\ \n\n:::;;  0.6  ~ , ~ ', \n\nA \n\n;  0) \nY!1y~ \n200 \n\n100 \n\no \n\n~iIJIJ ,l,ll,lI\" \n\n\"T'  I,.\", 1f11T'1 \n600 \n400 \n\n500 \n\n300 \n\nMovement Number \n\n0.8 \n\n10.75 \n., \nE  0.7 \ni= \n~ 0.65 \nE \n~  0.8 \n:::;; \n0.55 \n\nB \n\n0 \n\n1 00 \n\n200 \n\n300 \n\n400 \n\n500 \n\n600 \n\nMovement Number \n\nFigure 4:  Subjects learned  an internal model specific  to the field  and  retained it in long(cid:173)\nterm memory.  A:  Mean  \u00b1 standard  error  (SE)  of the movement  period  in  the force  field \n(called  field  1)  during  initial  practice  session  (upper  trace)  and  during  a  second  session \n24-30  hours  after  the  initial  practice  (lower  trace).  B:  Movement  period  in  a  different \ngroup of subjects during initial  training  (dark line)  in field  1 and test in an anti-correlated \nfield  (called  field  2)  24-30  hours  later  (gray  line). \n\nperformance  recorded  in a  separate set  of naive subjects who were  given than field \nin their initial training day;  and (2)  could be retained, as evidenced by performance \nin the following  day. \n\n2.2 \n\nInterference effects of the motor memory \n\nIn our experiment the  \"tool\"  that subjects  learn  to control is rather unusual , nev(cid:173)\nertheless,  subjects  learn  its  inverse  dynamics and  the  memory is  used  to  enhance \nperformance  24  hours  after  its  initial  acquisition.  We  next  asked  how  formation \nof this  memory affected  formation of subsequent  internal  models.  In  the  previous \nsection  we  showed  that when  a  subject  returns  a  day  after  the initial training,  al(cid:173)\nthough the memory of the learned internal model is present, there is no interference \n(or  decrement  in  performance)  in  learning  a  new,  anti-correlated  field .  Here  we \nshow  that  when  this  temporal  distance  is  significantly  reduced,  the just  learned \n\n\f1122 \n\nReza Shadmehr,  Tom Brashers-Krug,  Ferdinanda Mussa-Ivaldi \n\n200 \n\n300 \n\n400 \n\nMovement Number \n\nFigure 5:  Interference in  sequential  learning  of two  uncorrelated  force  fields:  The lower \ntrace is the mean and standard error of the movement periods of a  naive group of subjects \nduring initial  practice in a force field  (called field  1).  The upper trace is  the movement pe(cid:173)\nriod of another group of naive subjects in field  1,  5 minutes after practicing 400 movements \nin field  2,  which  was anti-correlated  with field  1. \n\nmodel interferes  with learning of a  new  field. \n\nSeven  new  subjects  were  recruited.  They  learned  the  timing of the task  in  a  null \nenvironment and in  the following day were given 400  targets in a force  field  (called \nfield  1).  They showed  improvement in  performance as  before.  After  a short  break \n(5-10  minutes in  which  they  walked  about  the lab or read  a  magazine),  they  were \ngiven  a  new  field:  this field  was  called field  2 and  was  anti-correlated  with respect \nto field  1.  We found  a significant reduction  (p < 0.01)  in  their ability to learn field \n2 (Fig. 5)  when  compared to a subject group which had not initially trained in field \n1.  In  other  words,  performance in  field  2 shortly  after  having  learned  field  1 was \nsignificantly worse than that of naives.  Subjects seemed surprised by their inability \nto master the task  in field  2.  In order  to demonstrate that field  2  in  isolation was \nno more difficult to learn than field  1,  we  had a new set of subjects  (n =  5)  initially \nlearn field  2,  then field  1.  Now  we  found  a  very  large  decrement  in  learn ability of \nfield  1. \nOne way to explain the decrement in performance shown in  Fig. 5 is to assume that \nthe same  \"computational elements\"  that represented  the internal model of the first \nfield were being used to learn the second field.!  In other words, when the second field \nwas given, because the forces were opposite to the first  field,  the internal model was \nbadly biased against representing this second field:  muscle torque patterns predicted \nfor  movement to a given  target were  in the wrong direction. \nIn  the  connectionist  literature  this  is  a  phenomenon  called  temporal  interference \n(Sutton  1986).  As  a  network  is  trained,  some of its elements acquire  large weights \nand  begin  to  dominate  the  input-output  transformation.  When  a  second  task  is \npresented  with a new  and conflicting map (mapping similar inputs to different out(cid:173)\nputs),  there  are large errors  and the network  performs more poorly  than a  \"naive\" \nnetwork.  As  the network  attempts to learn the new  task,  the errors  are fed  to each \nelement  (i.e.,  pre-synaptic input).  This causes  most activity in  those elements that \n\n1 Examples  of  computational  elements  used  by  the  nervous  system  to  model  inverse \ndynamics  of a  mechanical  system were found  by  Shidara et al.  (1993),  where it was shown \nthat the firing  patterns of a  set of Purkinje cells  in the cerebellum  could  be reconstructed \nby  an inverse  dynamic  representation  of the eye. \n\n\fInterference in Learning Internal Models of Inverse Dynamics in  Humans \n\n1123 \n\nhad the largest synaptic weight.  If the learning algorithm is  Hebbian , i.e.,  weights \nchange  in  proportion  to  co-activation  of the  pre- and  the  post-synaptic  element, \nthen  the  largest  weights  are  changed  the  most, effectively  causing  a  loss  of what \nwas  learned  in  the  first  task.  Therefore,  from  a  computational  stand  point,  we \nwould expect  that the internal model of field  1 as learned by our subjects should be \ndestroyed  by  learning of field  2.  Evidence  for  \"catastrophic interference\"  in  these \nsubjects  is  presented  elsewhere  in  this volume (Brashers-Krug  et al.  1995). \n\nThe  phenomenon  of interference  in  sequential  learning  of two  stimulus-response \nmaps has been termed proactive interference or negative transfer in the psychological \nliterature.  In  humans,  interference  has  been  observed  extensively  in  verbal  tasks \ninvolving short-term declarative memory (e.g., tasks involving recognition of words \nin  a  list  or  pairing  of non-sense  syllables,  Bruce  1933,  Melton  and  Irwin  1940, \nSears  and  Hovland  1941).  It has  been  found  that interference  is  a  function  of the \nsimilarity of the stimulus-response maps in the two tasks:  if the stimulus in the new \nlearning task requires a response very different than what was recently learned, then \nthere is significant interference.  Interestingly, it has been shown  that the amount of \ninterference  decreases  with increased learning (or practice) on the first  map (Siipola \nand Israel  1933). \n\nIn tasks involving procedural memory (which includes motor learning, Squire 1986), \nthe  question  of interference  has  been  controversial:  Although  Lewis  et  al.  (1949) \nreported interference in sequential learning of two motor tasks which involved mov(cid:173)\ning levers  in  response  to a set  of lights,  it has  been  suggested  that the interference \nthat  they  observed  might  have  been  due  to  cognitive  confusion  (Schmidt  1988). \nIn  another  study,  Ross  (1974)  reported  little interference  in  subjects  learning  her \nmotor tasks. \n\nWe  designed  a  task  that  had  little  or  no  cognitive  components.  We  found  that \nshortly  after  the  acquisition  of a  motor memory,  that  memory strongly  interfered \nwith learning of a  new,  anti-correlated input-output mapping.  However,  this inter(cid:173)\nference  was  not  significant  24  hours  after  the memory was  initially acquired .  One \npossible explanation is that the initial learning has taken  place in  a temporary and \nvulnerable  memory  system.  With  time  and/or  practice,  the  information  in  this \nmemory had transferred  to long-term storage (Brashers-Krug  et  al.  1995) . \nBrain imaging studies during motor learning suggest  that as subjects  become more \nproficient  in  a  motor  task,  neural  fields  in  the  motor  cortex  display  increases  in \nactivity (Grafton et al.  1992)  and new fields  are recruited  (Kawashima et al.  1994) . \nIt has  been  reported  that  when  a  subject  attempts  to  learn  two  new  motor tasks \nsuccessively  (in this case the tasks consisted of two sequences of finger  movements), \nthe neural activity in the  motor cortex is  lower for  the second  task , even  when  the \norder ofthe tasks is reversed (Jezzard et al. 1994).  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