Neural Models for Part-Whole Hierarchies
Authors: Peter Dayan Maximilian Riesenhuber
Published in: Advances in Neural Information Processing Systems 9  (NIPS 1996) (Main Conference Track), 1996

Abstract: We present a connectionist method for  representing images that ex(cid:173) plicitly addresses their hierarchical nature.  It blends data from neu(cid:173) roscience about whole-object viewpoint sensitive cells in inferotem(cid:173) poral  cortex8  and  attentional  basis-field  modulation  in  V43  with  ideas  about  hierarchical  descriptions  based  on  microfeatures.5,11  The resulting model makes critical use of bottom-up and top-down  pathways for  analysis and synthesis.6  We  illustrate the model  with  a simple example of representing information about faces. 
1  Hierarchical Models 
Images  of objects  constitute an  important  paradigm case of a  representational  hi(cid:173) erarchy, in  which  'wholes', such as faces,  consist of 'parts', such as eyes,  noses  and  mouths.  The  representation and manipulation of part-whole hierarchical informa(cid:173) tion  in  fixed  hardware  is  a  heavy  millstone  around  connectionist  necks,  and  has  consequently been the inspiration for  many interesting proposals, such as  Pollack's  RAAM.l1 
We  turned to the  primate visual  system for  clues.  Anterior  inferotemporal  cortex  (IT) appears to construct representations of visually presented objects.  Mouths and  faces  are both objects, and so require fully  elaborated representations,  presumably  at  the level  of anterior IT,  probably using  different  (or  possibly  partially overlap(cid:173) ping) sets of cells.  The natural way to represent the part-whole relationship between  mouths and faces is to have a neuronal hierarchy, with connections bottom-up from  the mouth units to the face units so that information about the mouth can be used  to help  recognize  or  analyze  the  image  of a  face,  and  connections  top-down  from  the face  units to the mouth units expressing the generative or synthetic knowledge  that if there is a face in a scene, then there is  (usually) a  mouth too.  There is little 
We thank Larry Abbott, Geoff Hinton, Bruno Olshausen, Tomaso Poggio, Alex Pouget, 
Emilio Salinas and Pawan Sinha for  discussions  and comments. 
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M.  Riesenhuberand P.  Dayan 
empirical support for  or against such a  neuronal hierarchy,  but it seems extremely  unlikely  on the grounds that arranging for  one with  the correct set of levels for  all  classes of objects seems  to be impossible. 
There  is  recent  evidence  that  activities  of cells  in  intermediate  areas  in  the  visual  processing hierarchy  (such  as  V4)  are  influenced  by  the locus  of visual  attention. 3  This  suggests  an  alternative  strategy  for  representing  part-whole  information,  in  which  there  is  an  interaction,  subject  to  attentional  control,  between  top-down  generative  and  bottom-up  recognition  processing.  In  one  version  of our example,  activating units in IT that represent a  particular face  leads,  through the top-down  generative  model,  to a  pattern of activity  in  lower  areas  that  is  closely  related  to  the  pattern  of activity  that  would  be  seen  when  the  entire  face  is  viewed.  This  activation  in  the  lower  areas  in  turn  provides  bottom-up input  to the  recognition  system.  In the bottom-up direction, the attentional signal controls which aspects of  that activation are actually processed, for example, specifying that only the activity  reflecting  the lower  part of the face  should  be  recognized.  In this  case,  the mouth  units in IT can then recognize this restricted pattern of activity as being a particular  sort of mouth.  Therefore,  we  have provided a  way  by  which  the visual system can  represent the part-whole relationship between faces  and mouths. 
This describes just one of many possibilities.  For instance, attentional control could  be mainly active during the top-down phase instead.  Then it would create in VI  (or  indeed in  intermediate areas)  just the  activity  corresponding to  the  lower  portion  of the face  in the first  place.  Also the focus  of attention need  not be so ineluctably  spatial. 
The overall scheme is  based  on  an hierarchical top-down  synthesis  and  bottom-up  analysis model for  visual  processing, as in  the Helmholtz machine6  (note that  "hi(cid:173) erarchy"  here refers  to a  processing hierarchy rather than the part-whole hierarchy  discussed above)  with a  synthetic model forming  the effective map: 
'object' 18)  'attentional eye-position'  -t 'image' 
(1) 
(shown  in  cartoon form  in  figure  1)  where  'image'  stands in  for  the  (probabilities  over the)  activities of units at various levels in the system that would be caused by  seeing the aspect of the 'object' selected by placing the focus  and scale of attention  appropriately.  We  use this  generative model during synthesis in  the way  described  above to traverse the hierarchical  description  of any particular image.  We  use  the  statistical inverse of the synthetic model as the way of analyzing images to determine  what  objects  they  depict.  This  inversion  process  is  clearly  also  sensitive  to  the  attentional  eye-position - it actually determines  not only  the nature of the object  in  the scene,  but  also the  way  that it is  depicted  (ie  its instantiation parameters)  as  reflected  in the attentional eye  position. 
In  particular,  the  bottom-up  analysis  model  exists  in  the  connections  leading  to  the  2D  viewpoint-selective  image  cells  in  IT reported  by  Logothetis  et  al8  which  form  population  codes  for  all  the  represented  images  (mouths,  noses,  etc).  The  top-down synthesis model exists in the connections leading in the reverse direction.  In generalizations of our scheme, it may,  of course, not be necessary to generate an  image all  the way down in VI. 
The map  (1)  specifies a  top-down  computational task very  like  the  bottom-up one  addressed  using  a  multiplicatively  controlled synaptic matrix in  the shifter  model 
Neural Modelsfor Part-Whole Hierarchies 
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attentional  eye  position e  =(c;, tyl t%)