! les réseaux de neurones artificiels · – +si apprentissage stochastique (après présentation...
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Les Réseaux de Neurones Artificiels""
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Introduction
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Les réseaux à une couche
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• Méthode d’exploration de H"
– Recherche par gradient • Minimisation de la fonction d’erreur
– Algorithme :
si la forme est correctement classée : ne rien faire !
sinon : !
boucler sur les formes d’apprentissage jusqu’à critère d’arrêt !
w(t + 1) = w(t) ! " xi ui
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Les réseaux multi-couches
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Composants et structure
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g(a) = 11 + e! a
yl = g wjk ! jj= 0, d"
#
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Fonction à base radiale
Fonction sigmoïde
Fonction à seuil
Fonction à rampe
Activation ai
Sortie zi
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L’apprentissage
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Objectif :
– Algorithme (rétro-propagation de gradient) : descente de gradient
Algorithme itératif :
Cas hors-ligne (gradient total) :
où :
Cas en-ligne (gradient stochastique) :
w( t ) = w( t!1) ! "# Ew(t )
wij (t) = wij (t !1)!"(t) 1m
#RE (xk ,w)#wijk=1
m
$
wij (t) = wij (t !1)!"(t) #RE(xk,w)#wij
RE(xk,w) = [tk ! f (xk ,w)]2
!
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1m
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1. Présentation d’un exemple parmi l’ensemble d’apprentissage Séquentielle, aléatoire, en fonction d’un critère donné
2. Calcul de l’état du réseau
3. Calcul de l’erreur = fct(sortie - sortie désirée) (e.g. = (yl - ul)2)
4. Calcul des gradients Par l’algorithme de rétro-propagation de gradient
5. Modification des poids synaptiques
6. Critère d’arrêt Sur l’erreur. Nombre de présentation d’exemples, ...
7. Retour en 1
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1. Evaluation de l’erreur Ej (ou E) due à chaque connexion :
Idée : calculer l’erreur sur la connexion wji en fct de l’erreur après la cellule j
– Pour les cellules de la couche de sortie :
– Pour les cellules d’une couche cachée :
! El
! wij
!k = " El
" ak = g' (ak )
" El
" yk = g' (ak ) # uk(xl) $ yk( )
! j = " El
" aj =
" El
" ak
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# = ! k
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",5""V"activation de la cellule i
"w5""V"sortie de la cellule i
"!5""V"erreur attachée à la cellule i
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• 2. Modification des poids
– On suppose gradient à pas (constant ou non ): !8>="
– Si apprentissage stochastique (après présentation de chaque exemple)
– Si apprentissage total (après présentation de l’ensemble des exemples)
!
"wij = #(t) $ j yi
!
"wij = #(t) $ jn zi
n
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m
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• Efficacité en apprentissage
– En O(w) pour chaque passe d’apprentissage, w = nb de poids
– Il faut typiquement plusieurs centaines de passes (voir plus loin)
– Il faut typiquement recommencer plusieurs dizaines de fois un
apprentissage en partant avec différentes initialisations des poids
• Efficacité en reconnaissance
– Possibilité de temps réel
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Questions pratiques
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Apprentissage(s) Reseau non lineaire a une couche
Reseau non lineaire a une couche (1)
Introduction d’une fonction ϕ non lineaire
On a donc Y = ϕ(WX), et les MC ne sont plus applicables
On va appliquer une methode de descente de gradient → rappels !
Algorithme iteratif :
On choisit un Wt=0 aleatoire
Bonne direction = celle ou le critere
baisse
Avancer un peu, mais pas trop
Wt+1 ← Wt − ηdJ (W)
dW
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avec :
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clement.chatelain@insa-rouen.fr () Reseaux de Neurones 9 fevrier 2012 23 / 49
Apprentissage(s) Reseaux multicouches
Reseaux multicouches (6)
Remarques :
On peut sommer les erreurs sur toute la base et retropropager une
seule fois :
→ mode Batch (plus rapide)
Question du pas ... 2eme ordre ? Cf. cours gradient
Quand stopper l’algorithme ? Attention au surapprentissage
clement.chatelain@insa-rouen.fr () Reseaux de Neurones 9 fevrier 2012 33 / 49
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• 1 neurone de sortie
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Presented by Martin Ho, Eddy Li, Eric Wong and Kitty Wong - Copyright© 2000
- Developed in 1993.
- Performs driving with Neural Networks.
- An intelligent VLSI image sensor for road following.
- Learns to filter out image details not relevant to driving.
Hidden layer
Output units
Input units
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• [Le Cun et al., 1989, ...] (ATT Bell Labs : très forte équipe)
• ! 10000 exemples de chiffres manuscrits
• Segmentés et redimensionnés sur matrice 16 x 16
• Technique des poids partagés (“weight sharing”)
• Technique du optimal brain damage
• 99% de reconnaissance correcte (sur l’ensemble d’apprentissage)
• 9% de rejet (pour reconnaissance humaine)
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!
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input
features
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features
Output f(X) six
Target Y
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Supervised Fine-Tuning
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output neuronactivation y n( )
teacherd n( )
wi
"reservoir" with three traces x ni( )
B
A
!
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! G
output neuronactivation y n( )
teacherd n( )
wi
"reservoir" with three traces x ni( )
B
A
!
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
(&,%.%.C!*&&/&! !),'!0%.%0%R*-!S'!! !! !
!"
G555
4554
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" $$ $()*$" "'#"! " $""#O!,+(%9,(%/.!/H!(3*!$U(3!%.(*&.,7!.*6&/.!,(!(%0*!"V;!L3%'!%'!,!'%0:7*!7%.*,&!&*C&*''%/.;!!!
! G
output neuronactivation y n( )
teacherd n( )
wi
"reservoir" with three traces x ni( )
B
A
!
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
(&,%.%.C!*&&/&! !),'!0%.%0%R*-!S'!! !! !
!"
G555
4554
D4555
4#"#"D555T4IKN
" $$ $()*$" "'#"! " $""#O!,+(%9,(%/.!/H!(3*!$U(3!%.(*&.,7!.*6&/.!,(!(%0*!"V;!L3%'!%'!,!'%0:7*!7%.*,&!&*C&*''%/.;!!!
! G
output neuronactivation y n( )
teacherd n( )
wi
"reservoir" with three traces x ni( )
B
A
!
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
(&,%.%.C!*&&/&! !),'!0%.%0%R*-!S'!! !! !
!"
G555
4554
D4555
4#"#"D555T4IKN
" $$ $()*$" "'#"! " $""#O!,+(%9,(%/.!/H!(3*!$U(3!%.(*&.,7!.*6&/.!,(!(%0*!"V;!L3%'!%'!,!'%0:7*!7%.*,&!&*C&*''%/.;!!!
! G
&"^4B1)"7"
X5?0,6"M"&",KK*(0/*("7"
output neuronactivation y n( )
teacherd n( )
wi
"reservoir" with three traces x ni( )
B
A
!
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
(&,%.%.C!*&&/&! !),'!0%.%0%R*-!S'!! !! !
!"
G555
4554
D4555
4#"#"D555T4IKN
" $$ $()*$" "'#"! " $""#O!,+(%9,(%/.!/H!(3*!$U(3!%.(*&.,7!.*6&/.!,(!(%0*!"V;!L3%'!%'!,!'%0:7*!7%.*,&!&*C&*''%/.;!!!
! G
X1*2("
/+)5*+("
!"#$"
'()"*+)(,-."M"0(-*10()"5NK-6)5100(6)"
• 90&N&*:,*%42#!,*%)?(2N6,
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!"#$"
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%: G+>B1/("/O50/-4210")-K(*Z5)+(">*W)"Z(*),26("
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– ;(*>,50(N(0>"K,)"-0"N1/W6("U5161?5S-("
P: 9KK*(02)),?("/(N,0/,0>"/-")150"
• ;B15."/("6O,*4B5>(4>-*("
• 9KK*(02)),?("6(0>Y")-<(>"M"N505N,"614,-."
Q: &"]K,45>+"7"
– \5r456("/O50>(*K*+>(*"6()"*+)(,-.",KK*5)"
– \5r456("/("N(h*("/("6,"4100,5)),04("#,02&(2&"
I#"G,)>(*"DXD"!";1-*)"DXDlQ""C""F+)(,-."/("0(-*10()",*2345(6)"
!"#$"
Références bibliographiques
• 90>150(";]FE{Év]'X"(>"',-*(0>"GD;'^A"
O002%*+66#:%,#2+P.&%!Q,R(*.%0)6,%),#!:(2&)<7%6"
^_*166()Y"P$%$"
• b:"\*(_L-)"(>",6:"
O002%*+66#:%,6)#+6+S4%Q,T16%#4;,-%,*%42(*%6Q,R#2)%6,)(0(!(:&S4%6Q,U#.<&*%6,V,
L%.)%426,6400(2)"
^_*166()Y"P$$I:"8G,6?*+"6("2>*("?+0+*,6Y"Z*,5N(0>"/+/5+",-."FE)="
• X5N10"a9cÑDE"
W%42#!,W%)?(2N6Q,O,.(702%<%*6&L%,3(4*-#+(*"
@*(024("a,66Y"%###"
• X5N10"a9cÑDE"
W%42#!,W%)?(2N6,#*-,X%#2*&*:,U#.<&*%6"
@*(024("a,66Y"P$$#:"8F(,66_"/5m(*(0>"L*1N">B("%###O)"10(="
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