{"title": "Universality and Individuality in a Neural Code", "book": "Advances in Neural Information Processing Systems", "page_first": 159, "page_last": 165, "abstract": null, "full_text": "Universality and individuality  in a  neural \n\ncode \n\nElad Schneidman,1,2  Naama Brenner,3  Naftali Tishby,1,3 \n\nRob  R.  de  Ruyter van Steveninck,3  William Bialek3 \n\nISchool of Computer Science and Engineering,  Center for  Neural  Computation and \n\n2Department of Neurobiology,  Hebrew  University,  Jerusalem 91904,  Israel \n\n3NEC  Research Institute, 4 Independence Way,  Princeton, New  Jersey 08540,  USA \n\n{ elads, tishby} @cs.huji. ac. il,  {bialek, ruyter, naama} @research. nj. nec. com \n\nAbstract \n\nThe  problem  of neural  coding  is  to  understand  how  sequences  of \naction potentials (spikes)  are related to sensory stimuli, motor out(cid:173)\nputs,  or  (ultimately)  thoughts  and  intentions.  One clear  question \nis whether the same coding rules are used  by  different  neurons, or \nby  corresponding  neurons  in  different  individuals.  We  present  a \nquantitative formulation of this problem using ideas from  informa(cid:173)\ntion theory, and apply this approach to the analysis of experiments \nin the fly  visual  system.  We  find  significant  individual  differences \nin  the  structure of the  code,  particularly  in  the  way  that tempo(cid:173)\nral  patterns of spikes  are  used  to  convey information  beyond that \navailable from  variations in spike  rate.  On the other hand,  all  the \nflies  in our ensemble exhibit  a  high coding efficiency,  so  that every \nspike carries the same amount of information in all the individuals. \nThus  the  neural  code  has  a  quantifiable  mixture  of individuality \nand universality. \n\n1 \n\nIntroduction \n\nWhen two  people look at the same scene,  do  they see the same things?  This basic \nquestion in the theory of knowledge seems to be beyond the scope  of experimental \ninvestigation.  An accessible version of this question is whether different observers of \nthe same sense data have the same neural representation of these data:  how  much \nof the neural code is  universal,  and how  much is  individual? \n\nDifferences  in  the  neural  codes  of  different  individuals  may  arise  from  various \nsources:  First, different  individuals may use  different  'vocabularies' of coding sym(cid:173)\nbols.  Second, they may use  the same symbols to encode different stimulus features. \nThird,  they  may  have  different  latencies,  so  they  'say' the same things  at  slightly \ndifferent  times.  Finally,  perhaps  the  most  interesting possibility  is  that  different \nindividuals might encode different features of the stimulus, so that they 'talk about \ndifferent  things'. \n\nIf we are to compare neural codes we must give a quantitative definition of similarity \nor divergence among neural responses.  We  shall use  ideas from  information theory \n\n\f[1,  2]  to  quantify  the the  notions  of distinguishability,  functional  equivalence  and \ncontent in the neural code.  This approach does  not require a  metric either on the \nspace  of stimuli  or  on  the  space  of  neural  responses  (but  see  [3]);  all  notions  of \nsimilarity emerge from  the statistical structure of the neural responses. \n\nWe  apply  these methods to  analyze  experiments  on an  identified  motion  sensitive \nneuron in the fly's visual system, the cell HI [4].  Many invertebrate nervous systems \nhave cells that can be named and numbered [5];  in many cases, including the motion \nsensitive  cells  in  the  fly's  lobula  plate,  a  small  number  of neurons  is  involved  in \nrepresenting  a  similarly  identifiable  portion  of the  sensory  world.  It might  seem \nthat  in  these  cases  the  question  of  whether  different  individuals  share  the  same \nneural  representation  of the  visual  world  would  have  a  trivial  answer.  Far  from \ntrivial,  we  shall  see  that  the  neural  code  even  for  identified  neurons  in  flies  has \ncomponents which  are  common  among flies  and  significant  components which  are \nindividual to each fly. \n\n2  Distinguishing flies  according to their spike  patterns \n\nNine different flies are shown precisely the same movie, which is repeated many times \nfor each fly  (Figure Ia).  As we show the movie we  record the action potentials from \nthe  HI  neuron. 1  The details  of the  stimulus  movie  should  not  have  a  qualitative \nimpact on the results, provided that the movie is  sufficiently long and rich to drive \nthe system through a reasonable and natural range of responses.  Figure Ib shows a \nportion of the responses of the different flies  to the visual stimulus - the qualitative \nfeatures of the neural response on long time scales ('\" 100 ms)  are common to almost \nall the flies,  and some aspects of the response are reproducible on a (few)  millisecond \ntime  scale  across multiple  presentations of the movie  to  each fly.  Nonetheless  the \nresponses  are not  identical in  the  different flies,  nor  are they perfectly reproduced \nfrom  trial to trial in the same fly. \n\nTo  analyze  similarities  and  differences  among  the  neural  codes,  we  begin  by  dis(cid:173)\ncretizing the neural  response  into  time  bins  of size  I:l.t  =  2 ms.  At  this  resolution \nthere  are  almost  never  two  spikes  in  a  single  bin,  so  we  can  think  of the  neural \nresponse  as  a  binary string,  as  in Fig.  Ic-d.  We  examine the response in blocks or \nwindows  of time  having  length  T,  so  that  an  individual  neural  response  becomes \na  binary  'word'  W  with  T / I:l.t  'letters'.  Clearly,  any fixed  choice  of T  and  I:l.t  is \narbitrary, and so  we  explore a  range of these parameters. \n\nFigure  If shows  that  different  flies  'speak'  with  similar  but  distinct  vocabularies. \nWe  quantify  the  divergence  among  vocabularies  by  asking  how  much  information \nthe observation of a  single  word W  provides  about the identity of its source,  that \nis  about the identity of the fly  which generates this word: \n\nJ(W -+  identity; T) = 8 Ii. ~ P'(W) log2  pens(w)  bits, \n\n[  pi(W)  ] \n\nN \n\n. \n\n(1) \n\nlThe  stimulus  presented to the flies  is  a  rigidly  moving  pattern of vertical  bars,  ran(cid:173)\ndomly dark or bright,  with average intensity I  ~ 100mW/(m2 \u2022 sr).  The pattern position \nwas  defined by a  pseudorandom sequence,  simulating a  diffusive  motion or random walk. \nRecordings  were  made from  the H1  neuron of immobilized Hies,  using standard methods. \nWe draw attention to three points relevant for  the present analysis:  (1)  The Hies  are freshly \ncaught  female  Calliphora,  so  that our  'ensemble of Hies'  approaches  a  natural  ensemble. \n(2)  In  each  Hy  we  identify  the  H1  cell  as  the  unique spiking  neuron  in  the  lobula  plate \nthat has  a  combination of wide  field  sensitivity,  inward directional  selectivity for  horizon(cid:173)\ntal  motion,  and contralateral projection.  (3)  Recordings are rejected only if raw electrode \nsignals  are excessively noisy or unstable. \n\n\fa \n\nStimulus \n\no~200~ \n'0 \no a; \n>_200 L-----L-----~----~----~----~ \n\n0 \n\nc \n\ne \n\nb \n\nSpike trains \n\nFly 1 \n\n~~~--~~~~\",; \n\nFly 2 \n\n~~~--~H*~~--+4~~-------\u00ad\n\nFly3 \n\n~~U-__ ~~ __ ~ __ ~~~ ______ __ \n\nFly4 \n\n~---------*--~--~~~-------\u00ad\n\nFly5 \n\n~---mrr-----,; \n\nFly 6 \n\n~---*l\u00a5--\u00ad\n\nFly7 \n\n~---'\"\"\"'---------' \n\nFly8 \n\nFly9 \n\n~--.~--~~~~--~ \n\nFly 1 \n\n001000 \n\n. .':\" \n\n: .. \n. \n\n\" \n\nWord distribution @ t \n\npFly 1 (Wlt=3306) \n\n_~~ ____ ~  pFIY'(Wlt=33061 \n\nd \n\nFly 6 \n\nf \n\nTotal word distribution \n\n3L-~=3~,1~~=3~,2-=~-3~,3 \n\nTime (5) \n\n3.4 \n\n3,5 \n\n3306 \n\n3318 \nTime  (ms) \n\n20 \n\n40 \n\n60 \n\nbinary word value \n\nFigure  1:  Different  flies'  spike  trains  and  word  statistics.  (a)  All  flies  view  the \nsame random vertical  bar pattern moving across  their  visual field  with a  time dependent \nvelocity,  part  of  which  is  shown. \nIn  the  experiment,  a  40  sec  waveform  is  presented \nrepeatedly,  90  times.  (b)  A  set  of 45  response  traces  to the part  of the stimulus shown \nin  (a)  from  each  of the  9 flies .  The traces  are  taken from  the segment  of the experiment \nwhere the transient responses have decayed.  (c) Example of construction of the local word \ndistributions.  Zooming  in  on  a  segment  of the  repeated responses  of fly  1  to the  visual \nstimuli, the fly's spike trains are divided into contiguous 2  ms  bins,  and the spikes in each \nof the bins  are counted.  For example,  we  get the 6 letter words  that the fly  used at time \n3306  ms into the input trace.  (d)  Similar  as  (c)  for  fly  6.  (e)  The distributions  of words \nthat flies  1 and 6 used at time t  = 3306 ms from  the beginning of the stimulus.  The time \ndependent  distributions,  pI(Wlt = 3306 ms)  and  p6(Wlt = 3306 ms}  are  presented as  a \nfunction  of the  binary  value  of the  actual  'word',  e.g.,  binary word  value  '17'  stands for \nthe word '010001' .  (f)  Collecting the words  that each  of the flies  used through  all  of the \nvisual stimulus presentations,  we  get the total word distributions for  flies  1 and 6,  pI (W) \nand P6(W} . \n\nwhere  P;.  = 1/ N  is the a  priori probability that we  are recording from fly  i,  pi(W) \nis  the  probability that fly  i  will  generate  (at  some  time)  the  word W  in  response \nto  the  stimulus  movie,  and  pens(w)  is  the  probability  that  any  fly  in  the  whole \nensemble of flies  would generate this word, \n\npens(W) = L p;'pi(W). \n\nN \n\ni=l \n\n(2) \n\nThe  measure  J(W  -+  identity;T)  has  been  discussed  by  Lin  [11]  as  the  'Jensen(cid:173)\nShannon divergence' DJS  among the distributions  pi(W).2 \n\n2Unlike the Kullback- Leibler divergence [2]  (the 'standard' choice for measuring dissim(cid:173)\n\nilarity  among  distributions),  the  Jensen- Shannon  divergence  is  symmetric,  and  bounded \n(see  also  [12]).  Moreover,  DJS  can be used to bound other measures of similarity,  such as \nthe optimal or Bayesian probability of identifying correctly the origin of a  sample. \n\n\fWe  find  that  information about  identity  is  accumulating at  more  or  less  constant \nrate well  before the under sampling limits  of the experiment  are reached  (Fig.  2a). \nThus  I(W  -+  identity; T)  ~ R(W  -+  identity)  . T;  R(W  -+  identity)  ~ 5  bits/s, \nwith a  very weak dependence on the time resolution .t!.t.  Since the mean spike rate \ncan be measured  by  counting the number  of Is in each  word  W,  this  information \nincludes the differences in firing  rate among the different  flies. \n\nEven if flies  use very similar vocabularies, they may differ  substantially in the way \nthat they  associate  words  with  particular  stimulus features.  Since  we  present the \nstimulus repeatedly to each fly,  we  can specify the stimulus precisely by noting the \ntime relative to the beginning of the stimulus.  We  can therefore consider the word \nW  that the ith  fly  will generate at time t.  This word is  drawn from the distribution \npi(Wlt)  which  we  can sample,  as in  Fig.  lc-e,  by looking  across  multiple  presen(cid:173)\ntations of the same  stimulus movie.  In  parallel with the discussion  above,  we  can \nmeasure the information that the word W  observed  at known t  gives  us  about the \nidentity of the fly, \n\n[  pi(Wlt)  ] \nI(W -+ IdentIty It; T) = ~ 11 ~ p  (Wit) log2  pens(Wlt) \n\n. .  \n\nN \n\ni \n\n, \n\n(3) \n\nwhere the distribution of words used at time t  by the whole  ensemble of flies  is \n\npens(Wlt) = L l1Pi(Wlt). \n\nN \n\ni=l \n\nThe natural quantity is  an average over all times t, \n\nI( {W, t} -+  identity; T) = (I(W -+ identity It; T)t bits, \n\n(4) \n\n(5) \n\nwhere  ( .. \u00b7)t  denotes  an average over t. \nFigure 2b shows a plot of I ( {W, t} -+ identity; T) /T as a function of the observation \ntime window  of size  T.  Observing  both the  spike train and the  stimulus together \nprovides 32 \u00b1 1 bits/s about the identity of the fly.  This is  more than six times  as \nmuch information as we can gain by observing the spike train alone, and corresponds \nto gaining one bit in \"\"'  30 ms;  correspondingly, a typical pair of flies  in our ensemble \ncan be distinguished reliably in \"\"'  30 ms.  This is the time scale on which flies actually \nuse  their  estimates  of visual  motion  to  guide  their  flight  during  chasing  behavior \n[6],  so that the neural codes of different  individuals are distinguishable on the time \nscales relevant to behavior. \n\n3  Different flies  encode different  amounts of information \n\nabout  the same stimulus \n\nHaving seen that we  can distinguish reliably among individual flies  using relatively \nshort  samples  of the  neural  response,  we  turn  to  ask  whether  these  substantial \ndifferences  among  codes  have  an  impact  on  the  ability  of  these  cells  to  convey \ninformation about the visual stimulus.  As  discussed in Refs.  [7,  8],  the information \nwhich the neural response of the ith fly provides about the stimulus, Ii(W -+ s(t); T), \nis  determined  by the same probability distributions defined  above:  3 \n\ni(W -+  s(t);T) = (~Pi(Wlt)IOg2 [~~~~)] )t \n\n(6) \n\n3 Again we  note  that our estimate of the information  rate  itself is  independent  of any \nmetric in  the  space  of stimuli,  nor  does  it  depend on  assumptions  about which  stimulus \nfeatures  are most important in the code. \n\n\fa \n\n0 . 05 ,---~-~-~--~-~----r---'] \n\nb \n\n___ --~~~FI~Y 6 __ YS  mixture \n\n\u00a5O.04 \n'\" E \n~ \neO .03 \nf \n\" \"0 \n:;::0.02 \n\" .8 \n'\" \n~001 \n\n---=========== \n\n%L--~5-~1~0 -~15~~2~0 ~-2~5~~3~0 \n\nFly  1 vs mixture \n\nFly 6 vs mixture \n\nWord length (msec) \n\nFly 1 vs  mixture \n\n5 \n\n10 \n\n15 \n\n20 \n\n25 \n\n30 \n\nWord length (msec) \n\nFigure  2:  Distinguishing  one  fly  from  others  based  on  spike  trains.  (a)  The \naverage  rate of information  gained  about  the identity of a fly  from  its word  distribution, \nas  a  function  of  the  word  size  used  (middle  curve).  The  information  rate  is  saturated \neven  before  we  reach  the  maximal  word  length  used.  Also  shown  is  the  average  rate  of \ninformation that the word  distribution of fly  1 (and 6)  gives  about  its identity,  compared \nwith  the  word  distribution  mixture  of  all  of  the  flies.  The  connecting  line  is  used  for \nclarification only.  (b)  Similar to (a) , we  compute the average  amount of information that \nthe distribution  of words  the fly  used  at  a  specific  point  in  time  gives  about  its  identity. \nA veraging over  all  times,  we  show the amount of information gained about the identity of \nfly  1 (and 6)  based on  its time  dependent  word  distributions,  and the average  over  the  9 \nflies  (middle curve).  Error  bars were  calculated as  in  (8) .  A  \"baseline calculation\" , where \nwe subdivided the spike trains of one fly into artificial new individuals, and compared their \nspike trains,  gave  significantly smaller  values  (not  shown) . \n\nFigure  3a shows  that  the  flies  in  our  ensemble  span  a  range  of information  rates \nfrom  ~ 50 to  ~ 150 bits/so  This threefold  range of information rates is  correlated \nwith the range of spike  rates,  so that each of the cells  transmits nearly a  constant \namount  of information  per  spike,  2.39 \u00b1 0.24 bits/spike.  This  universal  efficiency \n(10%  variance over the population, despite three fold  variations in total spike rate), \nreflects that cells with higher firing rates are not generating extra spikes at random, \nbut rather each extra spike is  equally informative about the stimulus. \n\nAlthough  information  rates  are  correlated  with  spike  rates,  this  does  not  mean \nthat  information  is  carried  by  a  \"rate  code\"  alone.  To  address  the  rate/timing \ndistinction  we  compare the  total  information  rate  in  Fig.  3a,  which  includes  the \ndetailed structure of the spike  train,  with the information carried in the temporal \nmodulations of the spike rate.  As explained in Ref.  [10],  the information carried by \nthe arrival time of a single spike can be written as an integral over the time variations \nof the  spike  rate,  and  multiplying  by the  number  of spikes  gives  us  the  expected \ninformation  rate if spikes  contribute  independently;  information  rates larger than \nthis represent synergy among spikes, or extra information in the temporal patterns \nof spike.  For  all  the  flies  in  our  ensemble,  the  total  rate  at  which the  spike  train \ncarries information is  substantially larger than the  'single spike'  information- 2.39 \nvs.  1.64  bits/spike,  on  average.  This extra information is  carried in  the temporal \npatterns of spikes  (Fig.  3b). \n\n4  A  universal codebook? \n\nEven though flies  differ  in  the structures of their neural responses,  distinguishable \nresponses could be functionally equivalent.  Thus it might  be that all flies  could be \n\n\fa \n\n150 \n\n\"Su \no  Q) en \n-g]j  100 \n\u00a78. \n::::l E-..... \n::::l  50 \n.E  .~ \nc  ..... \nen \n_ \n\n~Ul \nctS \n\nI \n\n! \n\nI \n\nI \n\n\u2022 ! \n\nb \n\n100 \n\nE~ \no~ 80 \n..... \n-Q )  \nc \n..... \n0.2  60 \n\"oW  () \nctS \n::::l \nE~ .....  en \n0 - 40 \n-ctS \nc \n..... \n.- 0 \nctSa.  20 \n~E x  Q) \nUJ  ..... \n\nI \nI \nI f \n\n20 \n\n60 \nFiring rate  (spikes/sec) \n\n40 \n\n20 \n\n60 \nFiring rate  (spikes/sec) \n\n40 \n\nFigure  3:  The  information  about  the  stimulus  that  a  fly's  spike  train  carries \nis  correlated  with  firing  rate,  and  yet  a  significant  part  is  in  the  temporal \nstructure.  (a)  The  rate  at  the  HI  spike  train  provides  information  about  the  visual \nstimulus is  shown  as  a function  of the average  spike rate, with each fly  providing a single \ndata point The  linear  fit  of the data points for  the 9 flies  corresponds to  a universal  rate \nof 2.39 \u00b1 0.24 bits/spike, as  noted in the text.  (b)  The extra amount of information that \nthe  temporal  structure  of  the  spike  train  of  each  of the  Hies  carry  about  the  stimulus, \nas  a  function  of  the  average  firing  rate  of  the  fly  (see  [10]).  The  average  amount  of \nadditional  information that is  carried  by  the temporal  structure of the spike  trains,  over \nthe population is  45 \u00b1 17%.  Error bars were calculated as  in  [8] \n\nendowed  (genetically?)  with  a  universal  or  consensus  codebook  that  allows  each \nindividual to make  sense  of her  own  spike  trains,  despite  the  differences  from  her \nconspecifics.  Thus we  want to ask how  much  information we  lose  if the identity of \nthe flies  is  hidden from  us, or equivalently how  much each fly  can gain by knowing \nits own individual code. \nIf we  observe the response of a  neuron but don't know the identity of the individual \ngenerating this response, then we are observing responses drawn from the ensemble \ndistributions defined  above,  pens(WJt)  and  pens(w).  The information that words \nprovide about the visual stimulus then is \n\nIffiiX(W ~ s(t)j T) = ( ~ pens(WJt) 10g2  [~::~~~)] )  t bits. \n\n(7) \n\nOn the other hand, if we know the identity of the fly to be i, we gain the information \nthat  its  spike  train  conveys  about  the  stimulus,  Ji(W  ~ s(t) j T),  Eq.  (6).  The \naverage information loss is then \n\nI~:~(W ~ s(t)j T) =  L lUi(W ~ s(t)j T) - IffiiX(W  ~ s(t)j T). \n\nN \n\n(8) \n\ni= l \n\nAfter some algebra it can be shown that this average information loss is  related to \nthe information that the neural responses give about the identity of the individuals, \nas defined  above: \n\nI( {W, t} ~ identityj T) \n\n-I(W ~ identityj T). \n\n(9) \n\nThe  result  is  that,  on  average,  not  knowing  the  identity  of the  fly  limits  us  to \nextracting only 64  bits/s of information about the visual stimulus.  This should  be \n\n\fcompared with the average information rate of 92.3 bits/s in  our ensemble of flies: \nknowing  her own identity  allows  the  average fly  to  extract  44%  more  information \nfrom  Hl.  Further analysis  shows  that each  individual fly  gains  approximately the \nsame relative amount of information from  knowing its personal codebook. \n\n5  Discussion \n\nWe have found that the flies use similar yet distinct set of 'words' to encode informa(cid:173)\ntion about the stimulus.  The main source of this difference is not in the total set of \nwords  (or spike rates) but rather in how  (i.e.  when)  these words are used to encode \nthe  stimulus;  taking this  into  account  the flies  are  discriminable  on time  scales  of \nrelevance to behavior.  Using their different  codes,  the flies'  HI  spike trains convey \nvery different  amounts of information from the same visual inputs.  Nonetheless, all \nthe flies  achieve a  high and  constant efficiency in their encoding of this information, \nand the temporal structure of their spike trains adds nearly 50%  more information \nthan that carried by the rate. \n\nSo how much is universal and how much is individual?  We find that each individual \nfly would lose'\" 30% of the visual information carried by this neuron if it 'knew' only \nthe  codebook  appropriate to  the  whole  ensemble  of flies.  We  leave  the judgment \nof whether  this  is  high  individuality  or  not  to  the  reader,  but  recall  that  this  is \nthe individuality in  an identified  neuron.  Hence,  we  should  expect  that  all  neural \ncircuits- both vertebrate and invertebrate-express a  degree of universality  and a \ndegree  of individuality.  We  hope  that  the  methods  introduced  here  will  help  to \nexplore this issue of individuality more generally. \n\nThis research was  supported by a  grant from the Ministry of Science,  Israel. \n\nReferences \n[1]  Shannon,  C.  E.  A  mathematical  theory  of  communication,  Bell  Sys.  Tech.  J.  27, \n\n379- 423, 623- 656  (1948) . \n\n[2]  Cover,  T.  &  Thomas J.  Elements  of information theory  (Wiley,  1991). \n[3]  Victor,  J . D.  &  Purpura, K. 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Agnostic  classification  of  Markovian  sequences, \n\nNIPS 10 pp. 465-471  (MIT Press,  1997) . \n\n\f", "award": [], "sourceid": 1894, "authors": [{"given_name": "Elad", "family_name": "Schneidman", "institution": null}, {"given_name": "Naama", "family_name": "Brenner", "institution": null}, {"given_name": "Naftali", "family_name": "Tishby", "institution": null}, {"given_name": "Robert", "family_name": "van Steveninck", "institution": null}, {"given_name": "William", "family_name": "Bialek", "institution": null}]}