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Binding Problem
Rosenblatt’s dilemma (Malsburg ’99)
• One neuron per feature
• Neurons’ ogranization:
 Triangle/Rectangle
 Top/bottom
• One object in the scene
No problem
• Binding problem for 2+
objects: [(triangle, top),
(rectangle, bottom)] ou
[(triangle, bottom), (rectangle,
top)] ?
“Binding” Problem
Temporal Correlation
Local aspects vs. global aspects
Minsky & Papert (1988 or 1969): “No diameter-limited perceptron can
determine whether or not all the parts of any geometric figure are
connnected to one another” (page 12)
Consequence
Computation complexity grows
Exponentially with |R| (retina size)
Source: Minsky & Papert (1988)
Que faire? (1/2)
Introduire l’aspect temporel
Neurone
Inhibiteur global (Contrôleur global)
Que faire? (2/2)
Introduction of temporal aspects
Computational complexity
: 8 (or 4) not proportional to |R|
Inhibitor activity
Source: Wang 99
Double spiral problem?
“If we ask which one of these two figures is
connected, it is difficult to imagine any local
event that could bias a decision toward one
conclusion or the other.” (Minsky & Papert
1988 ou 1969, page 73)
Lang et Witbrock (1988) proved that
this problem cannot be solved with multilayer
perceptrons
Double spirals problem
(Minsky & Papert 88
Or 69)
Que faire?
Introduction of temporal aspects
Source: Chen & Wang 2001
Interior/exterior problem
Point  A  B ?
Simple for humans
(Julesz 1995)
Point  A  B ?
Not simple for humans!!
Not solvable with static neurons
Source: Chen & Wang (2001)
Que faire?
Introduire l’aspect temporel
Source: Chen & Wang 2001
Temporal series approximation
Perceptrons: Function approximation
Adding delays
D
D
Synfire Chain (Abeles 1982)
Computational complexity grows with |R|
(number of points in the series).
Solution: Using spiking neurons
Volterra Series approximation (generalized convolution).
(Maass 2000)