• 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)] ?Rosenblatt’s dilemma (Malsburg ’99)

Binding Problem

“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 growsExponentially with |R| (retina size)

Source: Minsky & Papert (1988)

Que faire? (1/2)Que faire? (1/2)

Introduire l’aspect temporel

Neurone

Inhibiteur global (Contrôleur global)

Que faire? (2/2)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?Double spiral problem?

Double spirals problem (Minsky & Papert 88Or 69)

“If we ask which one of these two figures is connected, it is difficult to imagine any localevent that could bias a decision toward one conclusion or the other.” (Minsky & Papert 1988 ou 1969, page 73)

Lang et Witbrock (1988) proved thatthis problem cannot be solved with multilayer perceptrons

Que faire?Que faire?

Introduction of temporal aspects

Source: Chen & Wang 2001

Interior/exterior problemInterior/exterior problem

Source: Chen & Wang (2001)

Point BA ?

Point ?BA

Simple for humans

Not simple for humans!!

Not solvable with static neurons

(Julesz 1995)

Que faire?Que faire?

Introduire l’aspect temporel

Source: Chen & Wang 2001

Temporal series approximationTemporal series approximation

Perceptrons: Function approximation

Adding delays

Computational complexity grows with |R| (number of points in the series).

D DSynfire Chain (Abeles 1982)

Solution: Using spiking neurons Volterra Series approximation (generalized convolution). (Maass 2000)