{"title": "Plasticity of Center-Surround Opponent Receptive Fields in Real and Artificial Neural Systems of Vision", "book": "Advances in Neural Information Processing Systems", "page_first": 159, "page_last": 165, "abstract": null, "full_text": "Plasticity of Center-Surround Opponent \nReceptive Fields  in Real and Artificial \n\nNeural  Systems of Vision \n\nS.  Yasui \n\nKyushu Institute of Technology \n\nlizuka 820,  Japan \n\nT.  Furukawa \n\nKyushu Institute of Technology \n\nlizuka 820, Japan \n\nM.  Yamada \n\nElectrotechnical Laboratory \n\nTsukuba 305,  Japan \n\nT.  Saito \n\nTsukuba University \nTsukuba 305, Japan \n\nAbstract \n\nDespite  the  phylogenic  and  structural  differences,  the  visual  sys(cid:173)\ntems of different species, whether vertebrate or invertebrate, share \ncertain functional properties.  The center-surround opponent recep(cid:173)\ntive field  (CSRF)  mechanism represents  one  such example.  Here, \nanalogous  CSRFs  are  shown  to  be  formed  in  an  artificial  neural \nnetwork which learns to localize contours (edges)  of the luminance \ndifference.  Furthermore,  when  the  input  pattern  is  corrupted  by \na  background noise,  the CSRFs of the hidden  units  becomes shal(cid:173)\nlower and broader with decrease of the signal-to-noise ratio (SNR). \nThe same kind of SNR-dependent plasticity is present in the CSRF \nof real visual neurons; in bipolar cells of the carp retina as is shown \nhere  experimentally,  as  well  as  in  large  monopolar  cells  of the  fly \ncompound eye  as  was  described  by others.  Also,  analogous  SNR(cid:173)\ndependent  plasticity  is  shown  to  be  present  in  the  biphasic  flash \nresponses  (BPFR) of these  artificial  and  biological visual systems . \nThus,  the spatial  (CSRF)  and  temporal  (BPFR) filtering  proper(cid:173)\nties with  which a  wide variety of creatures see the world appear to \nbe optimized for  detectability of changes in space  and time. \n\nINTRODUCTION \n\n1 \nA  number  of  learning  algorithms  have  been  developed  to  make  synthetic  neural \nmachines be trainable to function in  certain optimal ways.  If the brain and nervous \nsystems  that  we  see  in  nature  are  best  answers  of the  evolutionary  process,  then \none  might  be  able  to  find  some  common  'softwares'  in  real  and  artificial  neural \nsystems.  This  possibility is  examined in this  paper,  with  respect  to  a  basic  visual \n\n\f160 \n\nS. Y ASUI, T. FURUKAWA, M.  YAMADA, T. SAITO \n\nmechanism  relevant  to  detection  of  brightness  contours  (edges).  In  most  visual \nsystems of vertebrate and invertebrate, one finds interneurons which possess center(cid:173)\nsurround  opponent  receptive  fields  (CSRFs).  CSRFs  underlie  the  mechanism of \nlateral inhibition which produces edge enhancement effects  such  as  Mach  band.  It \nhas also been shown in the fly compound eye that the CSRF of large monopolar cells \n(LMCs)  changes its shape in  accordance with SNR;  the CSRF becomes  wider with \nincrease of the noise level in the sensory environment.  Furthermore, whereas CSRFs \ndescribe  a  filtering  function  in  space,  an  analogous  observation  has  been  made \nin  LMCs  as  regards  the  filtering  property  in  the  time  domain;  the  biphasic  flash \nresponse  (BPFR)  lasts  longer  as  the  noise  level  increases  (Dubs,  1982;  Laughlin, \n1982). \n\nA  question  that  arises  is whether similar  SNR-dependent spatia-temporal filtering \nproperties might be present in  vertebrate visual  cells.  To investigate this,  we  made \nan  intracellular recording experiment  to  measure  the CSRF  and  BPFR profiles  of \nbipolar  cells  in  the  carp  retina  under  appropriate  conditions,  and  the  results  are \ndescribed  in  the  first  part  of this  paper.  In  the  second  part,  we  ask  the  same \nquestion  in a  3-layer feedforward  artificial  neural  network  (ANN)  trained  to detect \nand  localize spatial and  temporal  changes in  simulated visual inputs  corrupted  by \nnoise.  In this case, the ANN wiring structure evolves from an initial random state so \nas to minimize the detection error,  and we look  into the internal ANN  organization \nthat  emerges  as  a  result  of training.  The  findings  made  in  the  real  and  artificial \nneural systems are  compared and discussed in  the final  section. \n\nIn  this study,  the  backpropagation  learning  algorithm  was  applied  to  update  the \nsynaptic parameters of the ANN. This algorithm was used as a  means for  the com(cid:173)\nputational optimization.  Accordingly,  the  present choice is  not necessarily  relevant \nto the question of whether the error backpropagation pathway actually might exist \nin  real  neural systems( d.  Stork & Hall,  1989). \n\n2  THE CASE OF A  REAL NEURAL SYSTEM: \n\nRETINAL BIPOLAR CELL \n\nBipolar cells occur as  a second order neuron in the vertebrate retina, and they have \na  good  example  of CSRF  Here  we  are  interested in  the  possibility  that the CSRF \nand  BPFR of bipolar  cells  might change  their size  and  shape  as  a  function  of the \nvisual  environment,  particularly  as  regards  the  dark- versus  light-adapted  retinal \nstates which correspond to low versus high SNR conditions as explained later.  Thus, \nthe following  intracellular recording experiment was  carried out . \n\n2.1  MATERIAL AND  METHOD \n\nThe retina was  isolated  from  the  carp  which  had  been  kept  in  complete  darkness \nfor  2  hrs  before  being  pithed  for  sacrifice.  The  specimen  was  then  mounted  on \na  chamber  with  the  receptor  side  up,  and  it  was  continuously  superfused  with  a \nRinger  solution  composed of (in  mM)  102  NaCI,  28  NaHC03 ,  2.6  KCI,  1 CaCh,  1 \nMgCh and 5 glucose, maintained at pH=7 .6 and aerated with a gas mixture of 95% \nO2  and 5% CO 2 \u2022  Glass micropipettes filled with 3M  KCI and having tip resistances \nof about  150  Mn  were  used  to  record  the  membrane  potential.  Identification  of \nbipolar  cell  units was  made on  the  basis of presence  or  absence of CSRF .  For  this \npreliminary test, the center and peripheral responses were examined by using flashes \nof a  small  centered spot  and  a  narrow  annular ring.  To  map  their  receptive  field \nprofile,  the  stimulus  was  given  as  flashes  of a  narrow  slit  presented  at  discrete \npositions 60  pm apart on the retina.  The slit of white light was 4 mm long and 0.17 \nmm  wide,  and  its  flash  had  intensity  of 7.24  pW /cm2  and  duration  of 250  msec. \nThe CSRF  measurement  was made  under  dark- and  light- adapted  conditions.  A \n\n\fPlasticity  of Center-Surround  Opponent  Receptive  Fields \n\n161 \n\n(b)  1.0 \n\no  . \n\naUght \n\u2022  Dark \n\n-1.0 \n\ni \n\n-1.0 \n\ni \n0 \n\n\".\". \n\ni \n1.0 \n\n(c) \n\nI 5mV \n\n(a) \n\nLighl \n\nt CCnler \n\n\"'/I~~I~~1~!.yvr\"\"'~ \n\n_0 _\n\n_  ._._._._._ 0_0_0_0_._ \"_\n\n\"- \". \n\nI ~ I \n\nn.,k \n\n~~H\u00b7\\J)rl .. i  !rt~~\\ .. +,~ \n\nSIIlV _ ._\n\n. _ ___  0_0_ \"_\"_\n\n0_ ._0_\"_._\n\n\" \n\nGO/1m \n\nI Osee \n\n~ \n\nlsec \n\nFigure  1:  (a)  Intracellular  recordings  from  an  ON-center  bipolar  cell  of the  carp \nretina  with  moving  slit  stimuli  under  light  and  dark  adapted  condition.  (b)  The \nreceptive field  profiles plotted from the recordings.  (c)  The response  recorded when \nthe slit was positioned at the receptive field  center. \n\nsteady  background light of 0.29  JJW /cm2  was provided for  light adaptation. \n\n2.2  RESULTS \n\nFig.la shows  a  typical set  of records  obtained  from  a  bipolar  cell.  The  response \nto each flash  of slit was  biphasic  (i.e.,  BPFR), consisting of a  depolarization  (ON) \nfollowed by a hyperpolarization(OFF) . The ON  response was the major component \nwhen  the  slit  was  positioned  centrally  on  the  receptive  field,  whereas  the  OFF \nresponse  was  dominant at peripheral locations  and somewhat sluggish.  The CSRF \npattern  was  portrayed  by  plotting  the  response  membrane  potential  measured  at \nthe  time  just  prior  to  the  cessation  of each  test  flash.  The  result  compiled  from \nthe  data  of  Figola  is  presented  in  Fig.lb,  showing  that  the  CSRF  of  the  dark(cid:173)\nadapted state was shallow and broad as opposed to the sharp profile produced during \nlight adaptation.  The records  with  the slit  positioned  at the  receptive field  center \nare  enlarged  in  Fig.lc,  indicating  that  the  OFF  part of the  BPFR  waveform  was \nshallower and broader when the retina was  dark adapted than when  light  adaptedo \n\n3  THE CASE OF  ARTIFICIAL NEURAL NETWORKS \n\nVisual  pattern  recognition  and  imagery  data  processing  have  been  a  traditional \napplication  area of ANNs.  There  are also  ANNs that deal with time series signals. \nThese both types of ANNs  are  considered here, and  they are trained  to detect and \nlocalize spatial or  temporal changes of the input signal corrupted  by  noise. \n\n\f162 \n\nS.  Y ASUI, T. FURUKAWA, M.  YAMADA, T. SAITO \n\n3.1  PARADIGMS AND  METHODS \n\nThe  ANN  models  we  used  are  illustrated  in  Figs.2.  The  model  of  Fig.2a  deals \nIt  consists  of three  layers  (input,  hidden, \nwith  one-dimensional  spatial  signals. \noutput),  each  having  the  same  number  of 12  or  20  neuronal  units.  The  pattern \ngiven to the input layer represents the brightness distribution of light.  The network \nwas  trained  by  means  of the  standard  backpropagation  algorithm,  to  detect  and \nlocalize step-wise  changes  (edges)  which  were  distributed on each  training pattern \nin  a  random fashion  with  respect  to  the  number,  position  and  height.  The  mean \nlevel  of the  whole  pattern  was  varied  randomly  as  well.  In  addition,  there  was \na  background  noise  (not  illustrated  in  Figs.2);  independent  noise  signals  of  the \nsame statistics were given to the all input units, and the maximum noise amplitude \n(NL:  noise  level)  remained  constant throughout each training session.  The teacher \nsignal  was the  \"true\"  edge  positions which  were  subject to obscuration due  to the \nbackground  noise;  the  learning  was  supervised  such  that  each  output  unit  would \nrespond with  1 when  a step-wise change not due to the  background noise  occurred \nat  the  corresponding position,  and  respond  with  -1 otherwise.  The  value of each \nsynaptic weight parameter was given randomly at the outset and updated by using \nthe  backpropagation  algorithm  after  presentation  of each  training  pattern.  The \ntraining session  was terminated when  the  mean square error stopped decreasing. \n\nTo  process time series  inputs, the ANN  model  of Fig.2b  was  constructed  with  the \nbackpropagation  learning  algorithm.  This  temporal  model  also  has  three  layers, \nbut the meaning of this is  quite different from the spatial network model of Fig.2a. \nThat  is,  whereas  each  unit  of  each  layer  in  the  spatial  model  is  an  anatomical \nentity,  this  is  not  the  case  with  respect  to  the  temporal  model.  Thus,  each  layer \nrepresents a  single neuron so  that  there are actually  only three  neuronal  elements, \ni.e.,  a  receptor,  an  interneuron,  and  an  output  cell.  And,  the  units  in  the  same \nlayer represent  activity states of one  neuron  at different  time slices;  the  rightmost \nunit  for  the  present  time,  the  next  one  for  one  time  unit  ago,  and  so  on.  As  is \napparent from  Fig.2b, therefore,  there is  no  convergence from  the future  (right) to \nthe  past  (left).  Each  cell  has  memory  of T-units  time.  Accordingly,  the  network \nrequires 2T - 1 units in  the input layer, T  units in  the  hidden layer and  1 units in \nthe output layer to  calculate  the output at present time.  The input was a  discrete \ntime series in  which step-wise changes took  place  randomly  in  a  manner analogous \nto the spatial input  of Fig.2a.  As  in the spatial case,  there was a  background noise \n\n(b) \n\nInput \n\nCorreetiom \n\nCorrectiom \n\nFigure 2:  The neural network architectures.  Spatial  (a)  and temporal model  (b). \n\n\fPlasticity  of Center-Surround  Opponent Receptive  Fields \n\n163 \n\n(8) \n\n11I1JJ11JJ111 \niFJiiii \u2022 \u2022  \n\nOulput ut,i'\" \n\n0.1 \n\n0.2 \n\n2000 \n\n4000 \n\n10000 \n\n30000 \n\n0.0 01.O-=~~~~4~.0~!!iI!!:!II\"'''-'l8.0xl04 \n\nIterations \n\nFigure  3:  Development  of receptive  fields.  Synaptic  weights  (a)  and  mean square \nerror  (b),  both as a  function  of the number of iterations. \nadded  to  the  input.  The  network  was  trained  to  respond  with  + 1/ -1  when  the \noriginal input signal increased/decreased, and  to respond  with  0 otherwise. \n\n3.2  RESULTS \n\nSpatial case:  Emergence of CSRFs with SNR-dependent plasticity \n\nHIddm  Layer \n\n\\'---\n\nAs  regards the edge  detection learning by the \nANN  model  of  Fig.2a,  the  results  without \nthe  background  noise  are  described  first  (Fu(cid:173)\nrukawa  &  Yasui,  1990;  Joshi  &  Lee,  1993). \nFig.3a  illustrates  how  the  synaptic  connec(cid:173)\ntions developed from the initial random state. \nIf the final  distribution of synaptic weight pa(cid:173)\nrameters is examined from input units to any \nhidden  unit  and  also  from  hidden  units  to \nany  output  unit,  then  it  can  be  seen  in  ei(cid:173)\nther case  that the central and  peripheral con(cid:173)\nnections  are opposite in  the  polarity of their \nweight  parameters;  the  central group  had  ei-\nther  positive  (ON-center)  or  negative  (OFF-\ncenter)  values,  but  the  reversed  profiles  are \nshown in the drawing of Fig.3a for  the OFF -center case.  In any event, CSRFs were \nformed  inside  the network as  a  result of the edge  detection  learning.  Fig.3b shows \nthe performance improvement during a learning session.  FigA shows the activation \npattern  of each  layer  in  response  to  a  sample  input,  and  edge  enhancement  like \nthe  Mach band effect  can  be observed in  the  hidden  layer.  Fig.5a presents sample \ninput patterns corrupted by the background noise of various NL  values, and Fig.5b \nshows  how  a  hidden  unit  was connected  to  the  input  layer  at  the end  of training. \nCSRFs were still formed  when  the environment suffered  from  the  noise.  However, \nthe  structure of the  center-surround antagonism changed  as  a  function  of NL;  the \nCSRFs became shallow and broad as  NL  increased,  i.e., as the SNR decreased. \n\nFigure  4:  A  Sample  of  activity \npattern of each layer \n\nI  I \n\nOutput  Layer \n\nTemporal case:  Emergence of BPFRs with SNR-dependent plasticity \n\nWith  reference  to  the  learning paradigm of Fig.2b,  Fig.5c  reveals  how  a  represen(cid:173)\ntative hidden  unit  made synaptic connections with the input  units  as  a function of \nNL;  the weight  parameters are plotted  against  the elapsed  time.  Each trace would \ncorrespond  to the response of the hidden  unit to  a flash  of light,  and it  consists of \n\n\f164 \n\nS.  Y ASUI, T. FURUKAWA, M.  YAMADA, T. SAITO \n\ntwo phases of ON  and OFF, i.e., BPFRs (biphasic flash  responses)  emerged in  this \nANN  as  a  result  of learning,  and  the  biphasic  time  course  changed  depending  on \nNL;  the  negative-going phase  became shallower and longer  with  decrease  of SNR. \n\n4  DISCUSSION:  Common Receptive Field Properties in \n\nVertebrate, Invertebrate and Artificial Systems \n\nA  CSRF  profile  emerges after  differentiating twice in space  a  small  patch of light, \nand CSRF  is  a  kind of point spreading function.  Accordingly,  the response  to any \ninput  distribution  can  be  obtained  by  convolving  the  input  pattern  with  CSRF. \nThe double differentiation of this spatial filtering  acts to locate edge  positions.  On \nthe  other  hand,  the  waveform of BPFR appears by  differentiating  once  in  time  a \nshort  flash  of light.  Thus,  the  BPFR is  an  impulse  response  function  with  which \nto  convolve  the  given  input  time  series  to obtain  the  response  waveform.  This  is \na  derivative  filtering,  which  subserves  detection  of temporal  changes  in  the  input \nvisual signal.  While both CSRF and BPFR occur in visual neurons of a wide variety \nof vertebrates and invertebrates, the first part of the present study shows that these \nspatial and temporal filtering functions  can develop  autonomously  in our ANNs. \n\nThe  neural  system  of visual  signal  processing  encounters  various  kinds  of  noise. \nThere are  non-biological  ones such as  a  background noise  in  the visual  input itself \nand the  photon noise  which  cannot be ignored when the light intensity is  low.  En(cid:173)\ndogenous sources of noise include spontaneous photoisomerization in photoreceptor \ncells,  quantal transmitter release at synaptic sites, open/close activities of ion chan(cid:173)\nnels and so on.  Generally speaking, therefore, since the surroundings are dim when \nthe retina is dark adapted, SNR in the neuronal environment tends to be low during \ndark adaptation.  According to the present experiment on the carp retina, the CSRF \nof bipolar cells widens in space and the BPFR is  prolonged in time when the retina \nis  dark  adapted,  that  is,  when  SNR  is  presumably  low.  Interestingly,  the  same \nSNR-dependent  properties have  also  been  described  in  connection  with  the  CSRF \nand  BPFR of large  monopolar  cells  in  the  fly  compound  eye.  These  spatial  and \ntemporal  observations are  both in  accord  with  a  notion  that  a  method  to remove \nnoise is smoothing which requires averaging for  a sufficiently long interval.  In other \nwords,  when  SNR is  low,  the  signal  averaging  takes  place  over  a  large  portion  of \nthe spatio-temporal domain comprised of CSRF and BPFR. Smoothing and differ(cid:173)\nentiation are  entirely opposite in  the signal  processing role.  The  SNR dependency \nof the CSRF and BPFR profiles can  be viewed as  a compromise between these two \noperations,  for  the  need  to  detect  signal  changes in  the  presence  of noise.  These \n\n(a) \n\n(b) \n\n(c) \n\n~ 0 \n\n-io \n\n10 \n\n20 \n\n0 \n\n10 \n\n10 \n\n20 \n\nFigure  5:  (a)  A  sample  set  of  training  patterns  with  different  background  noise \nlevels  (NLs).  The  NLs  are  0.0,  0.4,  1.0  from  bottom  to  top.  The  receptive  field \nprofiles  (b)  and flash  responses (c)  after training with each NL.  The ordinate scale \nis  linear  but in  arbitrary unit, with  the zero  level  indicated  by dotted lines. \n\n\fPlasticity  of Center-Surround Opponent  Receptive  Fields \n\n165 \n\npoints  parallel  the  results  of information-theoretic  analysis  by  Atick  and  Redlich \n(1992)  and by  Laughlin  (1982). \n\n5  CONCLUDING  REMARKS \nWe  have  learnt  from  this  study  that  the  same  software  is  at  work  for  the  SNR(cid:173)\ndependent control of the  spati~temporal visual  receptive field  in  entirely different \nhardwares; namely, vertebrate, invertebrate and  artificial  neural systems.  In other \nwords, the plasticity scheme represents nature's optimum answer to the visual func(cid:173)\ntional  demand,  not  a  result  of compromise  with  other factors  such as  metabolism \nor  morphology.  Some  mention  needs  to  be  made  of the  standard  regularization \ntheory.  If the  theory  is  applied  to  the  edge  detection  problem,  then  one  obtains \nthe  Laplacian-Gaussian filter  which  is  a  well-known  CSRF example(Torre  &  Pog(cid:173)\ngio,  1980).  And,  the  shape  of this spatial  filter  can  be  made  wide  or  narrow  by \nmanipulating  the  value of a  constant  usually  referred  to  as  the  regularization  pa(cid:173)\nrameter.  This parameter choice corresponds to the compromise that our ANN  finds \nautonomously between smoothing and differentiation.  The present type of research \naided by trainable artificial neural networks seems to be a useful top-down approach \nto gain insight into the brain and neural mechanisms.  Earlier, Lehky and Sejnowski \n(1988) were able to create neuron-like units similar to the complex cells of the visual \ncortex by using the backpropagation algorithm, however, the CSRF mechanism was \ngiven a priori to an early stage in their ANN  processor.  It should also be noted that \nLinsker  (1986)  succeeded in self-organization of CSRFs in  an  ANN  model  that op(cid:173)\nerates under the learning law of Hebb.  Perhaps, it remains to be examined whether \nthe  CSRFs formed  in  such  an  unsupervised  learning  paradigm might  also  possess \nan  SNR-dependent plasticity similar  to  that described  in  this  paper. \n\nReferences \nAtick, J .J. & Redlich, A.N . (1992)  What does the retina know about natural scenes? \nNeural  Computation,  4,  196-210. \nDubs, A.  (1982) The spatial integration of signals in the retina and lamina of the fly \ncompound  eye  under  different  conditions of luminance.  1.  Compo  Physiol A,  146, \n321-334. \nFurukawa, T. & Yasui, S. (1990) Development of center-surround opponent receptive \nfields  in a neural network through backpropagation training.  Proc. Int.  Con/.  Fuzzy \nLogic  &  Neural Networks  (Iizuka,  Japan) 473-490. \nJoshi, A.  & Lee,  C.H . (1993) Backpropagation learns Marr's operator Bioi.  Cybern., \n10, 65-73. \nLaughlin, S.  B.  (1982)  Matching coding to scenes to enhance efficiency.  In Braddick \nOJ,  Sleigh  AC(eds)  The  physical  and  biological  processing  of images  (pp.42-52). \nSpringer,  Berlin,  Heidelberg New  York. \nLehky, S. R. & Sejnowski, T. J. (1988) Network model of shape-from shading:  neural \nfunction  arises from  both receptive and  projective fields .  Nature,  333,  452-454. \n\nLinsker, R. (1986)  From basic network principles to neural architecture:  Emergence \nof spatial-opponent cells.  Proc. Natl.  Acad. Sci.  USA,  83,  7508-7512. \nStork,  D.  G.  & Hall,  J.  (1989)  Is  backpropagation biologically  plausible?  Interna(cid:173)\ntional  Join  Con/.  Neural Networks,  II (Washington  DC),  241-246. \nTorre,  V.  & Poggio,  T.  A.  (1986)  On  edge  detection.  IEEE  Trans.  Pattern  Anal. \nMachine  Intel. ,  PAMI-8,  147-163. \n\n\f\fPART III \nTHEORY \n\n\f\f", "award": [], "sourceid": 1094, "authors": [{"given_name": "S.", "family_name": "Yasui", "institution": null}, {"given_name": "T.", "family_name": "Furukawa", "institution": null}, {"given_name": "M.", "family_name": "Yamada", "institution": null}, {"given_name": "T.", "family_name": "Saito", "institution": null}]}