TIPE 2009 - Étude d'un réseau de neurones
Adrien Vergé, Lucien Giraud et Paul Tessier

Créer un nouveau réseau de neurones

Nombre de couches :     1  + 

Nombre d'entrées :         Laisser 25 pour pouvoir tester les images de 5*5=25 pixels représentant les chiffres.

Couche 1 :     neurones, fonction

Les coefficients de la matrice et du vecteur seuil seront remplis aléatoirement. C'est l'entrainement qui mènera vers les coefficients adaptés.

Tester le réseau de neurones actuel
Entrée
0
1
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3
4
5
6
7
8
9

0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
Couche 1
0.96-0.48-1.72-0.80.31.46-0.52-0.38-0.38-0.141.92-1.060.38-1.88-0.6-1.28-1.42-0.580.541.461.581.52-1.340.841.06
1.420.18-0.461.06-0.6-1.340.020.94-1.041.22-0.78-1.58-1.320.860.040.540.780.98-1.080.9-1.62-0.341.5-0.2-1.82
0.96-0.621.71.62-1.780.761.040.42-1.70.11.82-1.02-1.880.74-0.041.341.980.38-1.980.84-1.580.58-0.41.421.5
-1.51.82-0.86-2-0.38-0.660.961-0.960.581.241.82-0.4-0.36-1.91.72-0.54-0.91.84-1.821.061.18-1.84-0.561.2
1.02-0.12-0.24-1.38-0.72-0.76-0.88-0.920.4-0.880.721.74-1.92-0.3-1.240.66-1.08-1.44-1.740.58-1.321.98-1.98-0.221.8
-1.78-1.160.96-1.60.280.161.42-1.861.92-1.98-0.56-0.84-0.840.541.580.3-0.761.30.380.96-1.94-0.981.9-1.38-0.72
0.46-0.7-0.740.481.1-0.940.721.94-1.981.120.220.180.540.360.10.561.821.281.740.360.840.021.60.14-1.6
0.540.2-0.560.440.820.74-1.12-1.8821.381.22-0.960.11.16-0.94-0.8-0.641.261.741.74-0.660.31.54-1.40.02
-0.121.46-1.96-0.52-0.42-1.54-1.981.8-0.10.460.6-1.381.360.74-1.380.74-0.04-0.34-1.18-0.90.740.040.48-0.02-0.22
0.21.32-1.94-0.261.940.11.641.40.16-0.9-1.020.62-0.86-1.24-1.481.621.38-0.860.980.1-0.24-0.28-1.941.440.54
-0.820.16-1.421.66-1.880.36-0.141.460.421.61.4-1.481.240.780.68-1.681.76-0.7-0.52-1.5-0.18-0.921.880.98-1.94
-0.02-1.28-0.220.06-1.84-1.681.240.32-1.10.90.461.26-1.26-0.08-0.32-1.66-0.70.221.58-1.92-1.121.921.840.18-0.62
-1.6620.48-1.780.960.540.221.7-1.7-1.741.88-1.381.50.18-0.460.38-1.36-1.21.140.560.51.481.88-1.31.04
1.96-0.420.941.81.78-1.7-1.861.780.8-1.640.74-0.680.580.44-0.360.840.30.280.34-1.521.82-1.3-0.88-1.381.86
1.71.121.321.561.820.341.52-0.6-0.741.3-0.82-0.421.44-1.06-1.641.821.7-0.30.40.121.36-0.78-1.6-0.381.58
-1.12-0.56-1.720.020.06-1.88-0.28-0.821.44-0.74-1.02-0.22-1.220.41.06-1.921.58-1.381.52-1.48-11.34-1.80.72-0.28
0.340.060.960.761.70.521.66-0.860.8-0.341.20.921.38-1.640.36-1.36-0.64-1.88-0.581.781.18-0.51.361.82-0.98
1.88-1.2-1.64-1.921.540.080.44-0.4-0.96-0.82-0.721.56-1.180.420.360.48-0.38-0.72-0.1401.640.521.381.781.94
1.140.94-0.560.480.740.480.361.560.840.461.1-1.1-1.12-1.32-0.040.06-0.02-0.50.88-1.61.88-0.640.02-0.861.24
-1.98-1.22-0.261.4-1.46-0.320.541.51.12-10.24-0.421.38-0.2-1.6-0.18-1.12-0.680.7-0.441.28-1.241.56-1.221.64
1.96-1.36-1-0.04-0.2-1.7800.58-0.02-0.621.141.661.940.620.76-1.08-1.16-1.66-1.70.64-1.260.121.520.06-1.2
-0.92-0.66-0.42-1.380.12-0.8-1.420.760.220.56-1.440.46-1.461.14-1.58-0.060.26-1.92-0.14-1.120.840.8-0.281.21.1
-1.641.94-0.81.900.02-1.021.341.6-0.38-0.54-1.20.2-1.781.04-1.26-1.22-0.52-0.721.94-0.081.220.20-0.92
1.08-1.161.88-1.2-1.980.96-0.841.98-1.84-0.94-0.020.180.04-0.68-0.221.660.780.58-0.161-0.380.581.81.11.88
1.72-0.981.1-0.11.04-1.84-1.021.9-1.96-0.221.9210.961.91.18-2-0.14-0.660.041.181.14-0.32-0.06-0.281.54
-1.061.340.12-1.280.440-1.561.46-0.920.360.48-0.741.340.38-0.7-0.90.3-1.7-1.960.181.48-1.94-1.96-1.180.1
1.221.981.8-0.84-0.321.320.12-1-0.580.841.441.421.30.9-1.5-0.36-0.62-0.22-1.041.761.10.080.041.420.14
-1.780.90.2-1.741.72-1.71.481.7-1.92-1.36-0.641.420.760.38-1.16-0.4-0.18-1.76-1.12-1.28-1.240.540.10.541.5
-0.14-0.36-0.421.92-0.961.72-1.881.94-0.08-1.621.660.221.881.340.32-1.48-1.32-0.281.281.080.56-1.12-1.120.82-0.22
-0.41.58-1.71.720.121.82-0.441.76-0.62-0.52-1.2-0.92-0.4-1.2810-1.64-0.78-0.141.71.540.4-1.62-0.76-0.34
1.461.820.54-1.660.62-1.7-0.040.2-1.38-0.34-1.68-1.581.24-1.92-0.2-1.3-1.120.90.32-0.4-0.1-1.7-0.021.120.18
-0.340.66-1.440.061.90.24-0.481.72-1.22-0.120.32-0.91.84-1.48-0.28-0.5-1.140.14-1.26-1.061.96-0.54-0.180.841.8
1.44-1.28-1.92-0.61.860.281.080.50.86-0.860.4-0.920.660.1-0.12-1.46-1.580.98-1.64-1.06-1.32-0.12-0.20.840.64
0.760.78-1.92-1.44-0.381.88-20.341.98-0.580.20.26-1.5-1.32-0.9-0.361.10.2-1.7-0.82-1.94-1.16-0.41.06-0.78
0.561.761.1-1.640.58-0.281.12-0.66-0.181.70.96-0.321.7-0.7-0.34-0.881.521.92-0.38-1.8-11.261.31.221.56
-1.541.28-1.620.080.34-0.4-1.360.08-1.3-1-1.360.44-1.90-1.761.8-1.04-0.061.50.281.6-1.4-0.221.50.22
-0.02-1.52-0.52-0.741.7-0.98-0.260.98-0.581.84-0.681.04-1.521.41.76-0.52-1.980.18-0.40.040.42-0.61-1.66-1.12
-0.721.96-0.51.061.441.74-0.961.94-0.80.321.640.22-1.940.61.661.91.920.68-1.641.320.42-0.141.34-1.41.46
-0.621.04-1.16-1.621.4-0.26-0.341.341.24-1.30.760.98-0.260.68-1.84-1.940.30.4-1.88-1.10.04-1.98-1.18-1.28-1.6
-1.881.160.261.481.76-0.28-1.160.780.58-0.780.16-1.70.9-0.521.561.6-1.760.52-0.660.940.7-0.6-0.78-0.92-0.46
0.141.12-0.440.961.86-0.021.11-1.780.560.76-0.041.42-0.48-1.48-1.361.7-1.161.54-0.82-1.621.14-0.580.92-1.54
-1.66-0.4-0.12-0.420.71.441.72-0.2-1.020.68-0.340.96-0.24-1.361.2-1.681.42-0.861.74-1.08-0.32-1.64-1.380.521.92
-0.180.921.041.24-0.181.521.61.44-0.62-0.820.12-1.18-1.11.94-0.21.58-0.42-1.24-0.660.241.98-0.34-0.36-0.9-0.6
0.580.8-0.241.22-0.7-0.32-0.98-1.8-1.3-1.740.04-1.81.88-0.54-0.4-0.961.60.42-0.061.52-1.78-0.48-0.9-10.86
1.36-1.04-1.48-1.020.06-0.081.58-1.161.70.780.16-0.641.820.360.08-1.94-1.60.281.94-0.121.9-1.04-0.540.320.92
-1.020.56-1.580.081.561.3-0.58-1.51.820.420.58-0.2801.44-0.6-1.24-0.420.78-1.441.96-1.16-1.36-1.641.14-1.44
0.241.04-0.461.7-0.64-1.56-1.321.92-1.120.781.46-1.82-1.81.98-20.620.54-0.26-1.4-0.021.16-0.621.56-0.08-0.04
1.520.760.621.88-0.11.180.1-1.08-1.28-0.20.28-0.820.480.20.08-0.74-0.360.26-0.54-0.380.28-1.94-1.86-2-1.32
0.121.160.08-0.32-0.94-1.96-0.821.840.66-0.94-0.26-0.161.180.680.56-1.04-1.061.741.461.16-0.2-1.3-1.22-1.940.18
0.40.340.240.560.360.94-1.32-0.5-0.980.360.58-0.941.560.421.74-1.4-1.86-0.441.80.84-1.88-1.261.81.88-1.8
0.94-0.32-1.081.72-0.261.10.12-1.92-0.66-1.320.44-1.72-0.641.96-0.71.720.540.381.28-1.060.121.9-0.91.71.68
1.941.82-1.581.721.7-1.360.64-0.64-0.420.361.12-1.34-1.521.220.02-0.84-0.340.320.52-0.41.640.24-1.880-0.48
-0.92-1.88-0.60.21.82-0.920.121.64-0.48-0.161.320.16-1.52-1.341.740.861.8-1.61.3410.44-1.5-1.36-1.261.04
0.26-1.64-0.720.40.380.81.480.5-1.8-0.340.3-0.71.8-0.060.82-0.36-0.76-1.040.12-0.08-1.3-1.02-0.3-0.88-1.7
-1.321.58-1.2-0.68-1.71.861.6-1.32-0.88-0.021.061.92-0.54-0.44-1.881.141.88-0.580.92-0.2-1.78-1.441.06-0.80.68
-1.04-0.11.660.661.041.981.360.6-1.22-1.320.9-1.38-1.741.6-0.260.240.66-0.341.7-1.8-0.220.82-1.921.2-0.26
-0.11.420.3-1.06-1.4-1.02-0.10.52-1.36-1.44-0.46-1.381.92-1.88-0.6-1.421.040.02-1.160.621.781.1-0.72-0.580.78
-0.51.2-0.4-0.420.381.361.48-0.2-0.34-1.580.40.640.32-1.11.30.880.441.920.80.58-0.71.38-0.381.34-1.8
-1.761.11.3-0.48-1.480.081.021.721.7-1.40.11.04-1.941.9-1.32-1.520.281.340.821.20.62-0.3-0.360.52-1.52
-1.81.841.86-0.161.16-1.940.080.261.381.60.78-0.540.60.5-0.861.2-1.4-1.821.28-1.52-1.121.780.78-1.780.6
-0.020.84-1.721.62-0.64-1.221.84-0.8-1.38-0.34-1.64-1.31.740.62-1.941.32-0.6-0.48-0.081.920.68-0.88-1.50.88-1.6
-11.76-1.841.7820.76-0.260.841.06-0.64-1.821.84-0.82-0.62-1.540.86-0.24-0.840.58-1.64-0.76-0.1-0.220.761.84
-0.3-0.56-1.040.2-1.7-0.641.22-1.94-0.480.98-1.96-1.72-1.280.881.360.11.081.181.3-1.541.640.140.22-1.2-1.28
0.60.040.64-1.62-1.20.460.080.241.42-1.740.56-1.221.480.620.30.460.680.61.2-0.44-0.06-0.72-1.36-0.88-1.44
-0.9-1.240.721.34-0.441.44-0.081.60.060.3-1.62-1.48-1.640.641.96-1.36-0.82-1.28-1.881.821.040.60.5-0.38-0.2
-1.961.581.08-1.32-1.321.66-0.2-0.540.38-0.881.02-0.21.060.621.88-0.641-1.62-0.28-0.36-1.680.380.84-0.960.52
0.64-1.94-0.9-0.86-0.30.9-0.8-0.74-0.02-0.1-0.04-0.361.71.42-2-1.180.44-0.21.88-0.96-0.32-0.78-1.960.060.96
-0.320.4-0.68-1.51.441.861.161.52-1.06-1.72-0.81.86-0.520.48-0.161.38-1.561.481.081.881.51.90.3-0.71.78
1.360.98-1.021.4-0.981.96-0.941.42-0.72-0.420.86-0.88-1.280.380.08-0.981.6-0.080.50.081.76-0.120.521.24-1.06
0.40.72-1.16-1.3-2-1.4-1.960.98-0.41.46-2-0.46-1.51.440.840.080.31.960.82-1.340.021.84-1.761.940.34
0.321.7-1.8-1.160.92-0.841.26-0.380.021.98-0.360.64-2-1.38-1.781.46-1.38-0.221.98-1.96-1.40.060.34-1.44-1.14
1.020.58-1.31.260.521.04-0.420.21.260.44-0.88-1.6-0.30.760.44-0.34-1.62-0.94-0.32-1-0.7-0.86-0.361.08-0.9
-0.31.71.18-1.96-1.76-1.961.060.84-1.260.32-0.661.781.921.561.020.34-1.321.44-1.961.46-0.14-0.31.860.941.38
-1.16-1.78-1.480.51.32-0.36-1.821-1.2-1.781.26-1.161.280.1-0.42-0.41.46-0.64-0.51.02-1.621.861.71.841.9
1.14-0.3-0.40.98-1.38-1.021.84-1.14-0.50.32-1.841.140.521.181.940.760.44-1.220.02-1.480.381.641.981.74-0.88
0.98-1.88-1.040.681.96-1.14-0.18-0.340.46-1.220.281.44-1.381.14-1.080.961.32-1.96-0.540.482-1.8-1.08-1.240.24
-0.561.14-0.12-0.580.881-1.611.981.10.96-1.18-1.1-1.41.28-0.320.880.720.320.021.64-0.74-0.661.70.74
1.841.680.96-1.26-1.56-0.80.21.61.081.620.460.06-1.98-0.560.041.12-1.60.86-2-10.14-0.31.9-1.16-2
-0.08-1.54-0.721.26-1.84-21.081.860.981.84-1.72-1.840.021.881.24-0.360.34-0.7-0.341.781.34-1.22-1.820.18-1.22
-0.82-1.680.5-0.94-0.840.520.98-0.361.80.24-0.21.82-0.68-0.360.78-0.86-0.060.941.16-0.180.18-1.22-1.861.480.46
1.940.821.24-1.9-1-2-0.72-0.680.520.360.48-0.98-0.66-1.9-1.21.58-0.08-1.38-1.121.561.40.02-0.50.34-0.82
1.32-1.48-0.041.46-2-1.61.380.821.661.51.821.68-1.24-0.860.181.141.621.2-1.541.74-2-1.98-0.36-1.38-1.08
-0.8-20.960.720.36-1.880.020.880.1-0.520.880.52-1.14-0.30.16-1.66-0.48-0.18-0.880.662-1.760.281.2-1.3
01.2-1.261.661.82-0.32-1.141.84-1.381.580.18-1.24-0.4-0.940.861.11.96-0.621.96-0.361.54-1.721.18-0.64-0.6
-0.18-0.64-0.34-1.9-1.460.360.121.741.12-0.241.56-1.220.641.38-0.580.22-0.440.181.840.64-0.960.920.580.420.86
-1.78-0.061.161.41.32-1.44-0.78-1.340.22-0.66-0.8-1.421.46-1.061.7-0.78-1.52-1.521.861.88-0.10.08-0.56-1.92-0.1
-1.94-0.88-1.20.641.541.660.88-0.520.820.28-1.221.381.52-0.56-0.42-1.160.660.18-1.721.6-0.14-0.5-1.920.36-0.64
1.96-1.761.44-0.62-1.68-0.68-0.54-0.540.12-1.92-1-0.220.980.48-1.42-0.761.281.98-1.26-1.28-0.46-0.421.381.74-0.14
0.98-0.421.381.061.94-1.281.02-1.82-1.86-1.6-1.48-0.52-0.14-0.021.6-0.040.98-0.62-1.08-0.54-0.020.18-1.26-0.060.92
-0.541.5-1.5-1.161.220.381.82-1.2-0.260.88-1.260.46-0.1-1.080.620.32-0.54-1.92-1.821.461.70.140.44-0.941.08
1.921.06-0.76-1.36-1.02-1.840.1-1.52-1.340.961.71.040.76-1.5-1.22-0.36-0.761.241.560.18-0.14-0.141.64-0.060.04
1.1-0.38-1.82-0.480.71.28-0.58-0.26-1.480.060.74-1.3-1.841.22-0.641.120.92-1.6-0.121.42-0.821.52-1.36-1.581.08
0.820.28-1.080.46-1.80.98-0.46-0.161.181.08-1.480.44-1.520.280.980.56-11.680.72-1.78-0.96-0.161.14-0.561.72
0.540.641.241.21.080.30.02-0.661.24-1.54-0.440.20.021.4-0.62-0.921.941.82-0.420.220.78-1.881.240.460.86
1.461.5-1.320.6-1.06-1.6-0.861.581.66-1.680.64-0.040.342-0.820.82-0.461.4-1.16-1.06-1.24-0.08-1.12-1.421.52
1.11.381.640.34-0.180.48-0.22-0.71.18-1.620.241.58-0.48-0.181.24-0.16-1.56-0.82-1.82-1.580.361.02-0.02-0.241.86
0.920.54-0.221.821.12-0.720.90.48-1.08-0.78-1.721.421.02-0.40.581.41.860.16-1.08-0.34-0.620.780.120.560.96
0.54-1.08-0.02-1.480.68-0.161.46-0.81.641.26-1.68-1.080.160.8-0.161.41.1-0.760.42-1.31.82-0.18-1.46-0.020.74
0.21.36-0.5-1.7-0.1-1.540.860.820.441.38-0.5-1.720.840.71.920.081.02-1.18-1.76-0.180.661.64-1.081.920.04
-0.381.741.860.16-0.30.6-1.64-0.96-1.92-1.340.96-1.441.54-0.241.020.921.281.3-0.26-0.021.221.84-1.02-1.98-1.94

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0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
    sigmoide
Sortie
0.58
0.86
1
0.03
0.03
0.09
0.85
0.97
0.05
0.02
0.94
0.1
0.97
0
0.87
0
1
0.1
0.34
0.01
0.11
0
0.99
0.99
0.28
0
1
0
0.71
0.87
0
0.08
0
0.02
0.98
0.03
0.04
1
0
0.96
0.56
0.02
0.97
0.05
0
0.29
0.87
0.06
0
1
0.94
0.22
0.04
0.03
0.5
0.83
0.01
0.99
0.17
0.96
0.04
0.08
0.01
0.01
0.97
0.98
0
0.84
0.98
0.07
0.01
0.4
0.97
0.81
0.98
0
0.99
0.94
0.03
0.02
0.57
0.62
0.03
0.95
0.62
0.38
0.04
0
0.05
0.59
0.33
0.35
0.48
0.35
0
0.9
0.82
0
0.91
0.99
Chiffre le plus probable :
37
Sortie idéale

Entrainer le réseau de neurones actuel

Cette option va entrainer le réseau pendant 100 itérations. Pendant chaque itération on soumet au réseau une des 10 images représentant les chiffres (aléatoirement), on compare le résultat à la sortie idéale (qui devrait être obtenue, par exemple pour l'image du zéro on souhaite obtenir la sortie [1,0,0,0,0,0,0,0,0,0]) puis on corrige les coefficients de chaque couche du réseau par la méthode de rétropropagation du gradient. Pour chaque itération on affiche la norme de l'erreur obtenue (erreur = sortie obtenue - sortie idéale).

Nombre d'itérations

Vitesse d'apprentissage η =     Attention une vitesse trop grande peut empêcher la convergence du réseau vers un état sans erreur.

Présenter les exemples :