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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)] ? Rosenblatts dilemma (Malsburg 99) Binding Problem

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Temporal Correlation

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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)

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Que faire? (1/2) Introduire laspect temporel Neurone Inhibiteur global (Contrôleur global)

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Que faire? (2/2) Introduction of temporal aspects Computational complexity : 8 (or 4) not proportional to |R| Inhibitor activity Source: Wang 99

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Double spiral problem? Double spirals problem (Minsky & Papert 88 Or 69) 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

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Que faire? Introduction of temporal aspects Source: Chen & Wang 2001

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Interior/exterior problem Source: Chen & Wang (2001) Point ? ? Simple for humans Not simple for humans!! Not solvable with static neurons (Julesz 1995)

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Que faire? Introduire laspect temporel Source: Chen & Wang 2001

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Temporal series approximation Perceptrons: Function approximation Adding delays Computational complexity grows with |R| (number of points in the series). DD Synfire Chain (Abeles 1982) Solution: Using spiking neurons Volterra Series approximation (generalized convolution). (Maass 2000)

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