{"metadata":{"kernelspec":{"language":"python","display_name":"Python 3","name":"python3"},"language_info":{"name":"python","version":"3.12.12","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"},"kaggle":{"accelerator":"none","dataSources":[{"sourceType":"datasetVersion","sourceId":14413364,"datasetId":9205632,"databundleVersionId":15229372}],"dockerImageVersionId":31286,"isInternetEnabled":true,"language":"python","sourceType":"notebook","isGpuEnabled":false}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"markdown","source":"# Deep learning 1 - Neurones linéaires(FR) v2.3\n\n```python\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nimport pandas as pd\n\nimport plotly.express as px\n\nfrom sklearn.metrics import *\nfrom sklearn.model_selection import train_test_split, cross_val_score\nfrom sklearn.preprocessing import StandardScaler, MinMaxScaler\nfrom sklearn.pipeline import Pipeline\n```\n","metadata":{}},{"cell_type":"code","source":"import numpy as np\nimport matplotlib.pyplot as plt\n\nimport pandas as pd\n\nimport plotly.express as px\n\nfrom sklearn.metrics import *\nfrom sklearn.model_selection import train_test_split, cross_val_score\nfrom sklearn.preprocessing import StandardScaler, MinMaxScaler\nfrom sklearn.pipeline import Pipeline","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T00:13:02.386948Z","iopub.execute_input":"2026-05-13T00:13:02.387246Z","iopub.status.idle":"2026-05-13T00:13:07.018890Z","shell.execute_reply.started":"2026-05-13T00:13:02.387215Z","shell.execute_reply":"2026-05-13T00:13:07.017880Z"}},"outputs":[],"execution_count":1},{"cell_type":"markdown","source":"## Neurone linéaire à 1 entrée\n\n![linearneuron.png](attachment:5d09a579-a3e3-4b41-ad09-5a6581d90767.png)\n\nUn neurone linéaire simple calcule:\n\nu = a x + b\n\noù:\n- x est une entrée scalaire\n- a est un poids (weight)\n- b est un biais (bias)\n- u est la sortie (prediction)\n\nOn va apprendre a et b en minimisant l’erreur quadratique moyenne (MSE).\n","metadata":{},"attachments":{"5d09a579-a3e3-4b41-ad09-5a6581d90767.png":{"image/jpeg":"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"}}},{"cell_type":"markdown","source":"## Descente de gradient\n\n![GradientDescent.png](attachment:c23adde3-3192-4ef3-9ca3-39c203a3ce9a.png)\n\nOn veut minimiser une fonction de coût E(a,b).\nIci, on prend la MSE:\n\n$$\n E(a,b) = \\frac{1}{n}\\sum_{i=1}^{n}\\left(y_i - (a x_i + b)\\right)^2\n$$\n\n### Principe\n\nOn cherche à minimiser une fonction de coût E(a,b) qui mesure l’erreur du modèle.\n\nLe gradient ∇E indique la direction dans laquelle E augmente le plus rapidement.\nEn se déplaçant dans la direction opposée au gradient, on fait décroître la valeur de E.\n\nLa descente de gradient consiste donc à ajuster les paramètres par petits pas\ndans la direction de plus forte diminution de la fonction de coût,\njusqu’à atteindre (ou approcher) un minimum.\n\n### Descente de gradient (batch)\n\nOn met à jour les paramètres du modèle dans la direction opposée au gradient de la fonction de coût:\n\n$$\n\\begin{aligned}\na &\\leftarrow a - \\eta ,\\frac{\\partial E}{\\partial a} \\\\\nb &\\leftarrow b - \\eta ,\\frac{\\partial E}{\\partial b}\n\\end{aligned}\n$$\n\noù $\\eta$ est le **learning rate**.\n\nUne **epoch** correspond à une itération complète où le gradient est calculé en utilisant **tous** les points du jeu d’apprentissage.\n\n\n### Learning rate\n\nLe learning rate contrôle **l’amplitude de chaque mise à jour** des paramètres.\n\nS’il est trop petit, les mises à jour sont très faibles:\nla convergence est lente et peut nécessiter un grand nombre d’epochs.\n\nS’il est trop grand, les mises à jour dépassent le minimum:\nla fonction de coût peut osciller ou diverger.\n\nLe learning rate ne change pas la direction du gradient,\nil change uniquement la **distance parcourue** à chaque itération.\n\n\n\n### Epochs\n\nUne epoch correspond à **un passage complet sur l’ensemble des données d’apprentissage**.\n\nÀ chaque epoch:\n\n* on calcule le gradient (batch, SGD ou minibatch)\n* on met à jour les paramètres\n* la loss est réévaluée\n\nAugmenter le nombre d’epochs permet au modèle d’approcher le minimum de la fonction de coût,\nmais au-delà d’un certain point, cela n’améliore plus la performance sur les données de test.","metadata":{},"attachments":{"c23adde3-3192-4ef3-9ca3-39c203a3ce9a.png":{"image/jpeg":"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"}}},{"cell_type":"markdown","source":"> #### Exercice \n> En partant de $E_i = 1/2 (y_i - u_i)^2$ et $u_i = a x_i + b$, recalculer $\\frac{\\partial E_i}{\\partial b}$. \n> Puis écrire dE/db en version batch (moyenne sur i=1..n). ","metadata":{}},{"cell_type":"markdown","source":"","metadata":{}},{"cell_type":"code","source":"np.random.uniform()","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T00:26:06.177348Z","iopub.execute_input":"2026-05-13T00:26:06.177641Z","iopub.status.idle":"2026-05-13T00:26:06.183830Z","shell.execute_reply.started":"2026-05-13T00:26:06.177617Z","shell.execute_reply":"2026-05-13T00:26:06.182647Z"}},"outputs":[{"execution_count":5,"output_type":"execute_result","data":{"text/plain":"0.6312343444143639"},"metadata":{}}],"execution_count":5},{"cell_type":"markdown","source":"## Neurone linéaire from scratch (batch Gradient Descent)\n\nL’objectif est de recoder un neurone linéaire “à la main” pour comprendre précisément ce que fait l’entraînement.\n\nLa classe contient des paramètres apprenables et des méthodes qui reproduisent le cycle standard entraînement/prédiction.\n\n- `__init__` initialise et stocke les paramètres du modèle, ici aa et bb. \n Ces paramètres seront modifiés au fil des epochs par descente de gradient.\n\n- `forward` calcule la prédiction du neurone à partir des entrées. \n Pour une entrée xx, on obtient:\n $$\n u = a x + b\n $$\n Dans le code, `forward` doit fonctionner sur un vecteur de valeurs xx (tous les points du train) pour permettre le calcul batch.\n\n- `fit` réalise l’apprentissage. \n À chaque epoch, on calcule les gradients $\\frac{\\partial E}{\\partial a}$ et $\\frac{\\partial E}{\\partial b}$,\n puis on met à jour $a$ et $b$ en batch (gradient moyen sur l’ensemble des points d’apprentissage).\n\nEn enregistrant la loss à chaque epoch, on peut visualiser la convergence et diagnostiquer des problèmes de learning rate\n(divergence, oscillations, convergence lente).\n","metadata":{}},{"cell_type":"markdown","source":"### 💡 Syntaxe à reprendre\n\n_Repère syntaxique pour aborder l'exercice ci-dessous._\n\n```python\nnp.random.uniform()\n```\n","metadata":{}},{"cell_type":"markdown","source":">#### Exercice \n> Implémenter une classe Python `LinearNeuron1D` correspondant à un neurone linéaire à une entrée.\n>\n> La classe doit contenir:\n> - une méthode `__init__` qui initialise les paramètres aa et bb (valeurs aléatoires ou nulles)\n> - une méthode `forward(x)` qui calcule la prédiction:\n> $$\n u = a x + b\n $$\n> où `x` est un vecteur de données\n> - une méthode `fit(x, y, lr, epochs)` qui entraîne le neurone par descente de gradient batch\n>\n> À chaque epoch, la méthode `fit` devra:\n> - calculer la prédictions $u$\n> - calculer les gradients $\\frac{\\partial E}{\\partial a}$ et $\\frac{\\partial E}{\\partial b}$\n> - mettre à jour les paramètres:\n> $$\n a \\leftarrow a - lr\\,\\frac{\\partial E}{\\partial a}\n \\qquad\n b \\leftarrow b - lr\\,\\frac{\\partial E}{\\partial b}\n $$\n>\n> Stocker la valeur de la loss à chaque epoch afin de pouvoir visualiser la convergence.\n>\n> Tester la classe sur le jeu de données `abalone_mini` en prédisant `Rings` à partir de `Length`.\n","metadata":{}},{"cell_type":"code","source":"class NeuroneLineaire:\n def __init__(self):\n self.a = np.random.uniform()\n self.b = np.random.uniform()\n self.history = []\n\n def predict(self, x):\n return self.a*x + self.b\n\n def fit(self, x, y, learning_rate=0.1, epochs=100):\n for i in range(epochs):\n u = self.predict(x)\n grad_a = np.mean((u-y)*x)\n grad_b = np.mean(u-y)\n self.a = self.a - learning_rate*grad_a\n self.b = self.b - learning_rate*grad_b\n self.history.append(np.mean((u-y)**2))","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T00:52:21.867714Z","iopub.execute_input":"2026-05-13T00:52:21.868112Z","iopub.status.idle":"2026-05-13T00:52:21.876397Z","shell.execute_reply.started":"2026-05-13T00:52:21.868080Z","shell.execute_reply":"2026-05-13T00:52:21.875256Z"}},"outputs":[],"execution_count":19},{"cell_type":"code","source":"np.random.choice(len(y))","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T00:56:13.281077Z","iopub.execute_input":"2026-05-13T00:56:13.282069Z","iopub.status.idle":"2026-05-13T00:56:13.288399Z","shell.execute_reply.started":"2026-05-13T00:56:13.282030Z","shell.execute_reply":"2026-05-13T00:56:13.287373Z"}},"outputs":[{"execution_count":29,"output_type":"execute_result","data":{"text/plain":"2511"},"metadata":{}}],"execution_count":29},{"cell_type":"code","source":"class NeuroneLineaireStochastique:\n def __init__(self):\n self.a = np.random.uniform()\n self.b = np.random.uniform()\n self.history = []\n\n def predict(self, x):\n return self.a*x + self.b\n\n def fit(self, x, y, learning_rate=0.1, epochs=100):\n for i in range(epochs):\n n = len(y)\n u = self.predict(x)\n i_random = np.random.choice(n)\n grad_a = (u[i_random]-y[i_random])*x[i_random]\n grad_b = u[i_random]-y[i_random]\n self.a = self.a - learning_rate*grad_a\n self.b = self.b - learning_rate*grad_b\n self.history.append(np.mean((u-y)**2))","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T00:58:04.831752Z","iopub.execute_input":"2026-05-13T00:58:04.832135Z","iopub.status.idle":"2026-05-13T00:58:04.839267Z","shell.execute_reply.started":"2026-05-13T00:58:04.832104Z","shell.execute_reply":"2026-05-13T00:58:04.838209Z"}},"outputs":[],"execution_count":30},{"cell_type":"code","source":"def MAE(y, y_bar):\n # Mean absolute error\n return np.mean(abs(y-y_bar))\n\ndef MAPE(y, y_bar):\n # Mean absolute percentage error\n return np.mean(abs((y-y_bar)/y))\n\ndef MSE(y, y_bar):\n # Mean squared error\n return np.mean((y-y_bar)**2)\n\ndef RMSE(y, y_bar):\n # Root mean squared error\n return np.sqrt(MSE(y,y_bar))\n\ndef R2(y, y_hat):\n y = np.array(y)\n y_hat = np.array(y_hat)\n \n y_mean = np.mean(y)\n \n ss_res = np.sum((y - y_hat) ** 2)\n ss_tot = np.sum((y - y_mean) ** 2)\n \n return 1 - ss_res / ss_tot\n","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T00:58:07.970059Z","iopub.execute_input":"2026-05-13T00:58:07.970414Z","iopub.status.idle":"2026-05-13T00:58:07.976648Z","shell.execute_reply.started":"2026-05-13T00:58:07.970385Z","shell.execute_reply":"2026-05-13T00:58:07.975768Z"}},"outputs":[],"execution_count":31},{"cell_type":"code","source":"df = pd.read_csv('/kaggle/input/datasets/pyim59/mini-datasets/abalone_mini.csv')\n\nx = df['Length']\ny = df['Rings']\n\nmodel = NeuroneLineaireStochastique()\nmodel.fit(x, y, epochs=100)\ny_hat = model.predict(x)\n\nprint('RMSE :', RMSE(y, y_hat))\nprint('MAE :', MAE(y, y_hat))\nprint('MAPE :', MAPE(y, y_hat))\nprint('R2 :', R2(y, y_hat))\n\nplt.plot(model.history)\nplt.show()\n\n# Visualisation : réel vs prédit\nfig = px.scatter(x=x, y=y)\nfig.add_scatter(\n x=x,\n y=y_hat,\n mode=\"lines\",\n name=\"Valeurs prédites\"\n)\nfig.show()\n\n# Résidus\nresidus = y - y_hat\n\nfig = px.scatter(\n x=x,\n y=residus,\n labels={\"x\": \"Consommation\", \"y\": \"Résidu\"},\n title=\"Résidus de la régression linéaire\"\n)\n\nfig.add_hline(\n y=0,\n line_color=\"red\"\n)\n\nfig.show()","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T00:58:19.845015Z","iopub.execute_input":"2026-05-13T00:58:19.845746Z","iopub.status.idle":"2026-05-13T00:58:20.087061Z","shell.execute_reply.started":"2026-05-13T00:58:19.845708Z","shell.execute_reply":"2026-05-13T00:58:20.086396Z"}},"outputs":[{"name":"stdout","text":"RMSE : 2.926101047218973\nMAE : 2.0974583968921188\nMAPE : 0.22522608150304807\nR2 : 0.17615213642485228\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"
","image/png":"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\n"},"metadata":{}},{"output_type":"display_data","data":{"text/html":"\n\n\n
\n
\n\n"},"metadata":{}},{"output_type":"display_data","data":{"text/html":"\n\n\n
\n
\n\n"},"metadata":{}}],"execution_count":33},{"cell_type":"code","source":"(x - x.mean())/x.std()","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T01:03:43.446679Z","iopub.execute_input":"2026-05-13T01:03:43.447046Z","iopub.status.idle":"2026-05-13T01:03:43.456632Z","shell.execute_reply.started":"2026-05-13T01:03:43.447013Z","shell.execute_reply":"2026-05-13T01:03:43.455684Z"}},"outputs":[{"execution_count":40,"output_type":"execute_result","data":{"text/plain":"0 -1.199497\n1 -0.748059\n2 -2.266531\n3 -0.132463\n4 -0.337662\n ... \n3197 -0.830139\n3198 -0.624940\n3199 -0.460781\n3200 -0.624940\n3201 -0.296622\nName: consumption, Length: 3202, dtype: float64"},"metadata":{}}],"execution_count":40},{"cell_type":"code","source":"df = pd.read_csv('/kaggle/input/datasets/pyim59/mini-datasets/co2_mini.csv')\n\nx = df['consumption']\ny = df['co2']\n\n# Normalisation des entrées\nx = (x - x.mean())/x.std()\n\nmodel = NeuroneLineaireStochastique()\nmodel.fit(x, y, learning_rate=0.1, epochs=100)\ny_hat = model.predict(x)\n\nprint('RMSE :', RMSE(y, y_hat))\nprint('MAE :', MAE(y, y_hat))\nprint('MAPE :', MAPE(y, y_hat))\nprint('R2 :', R2(y, y_hat))\n\nplt.plot(model.history)\nplt.show()\n\n# Visualisation : réel vs prédit\nfig = px.scatter(x=x, y=y)\nfig.add_scatter(\n x=x,\n y=y_hat,\n mode=\"lines\",\n name=\"Valeurs prédites\"\n)\nfig.show()\n\n# Résidus\nresidus = y - y_hat\n\nfig = px.scatter(\n x=x,\n y=residus,\n labels={\"x\": \"Consommation\", \"y\": \"Résidu\"},\n title=\"Résidus de la régression linéaire\"\n)\n\nfig.add_hline(\n y=0,\n line_color=\"red\"\n)\n\nfig.show()","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T01:04:09.165631Z","iopub.execute_input":"2026-05-13T01:04:09.166046Z","iopub.status.idle":"2026-05-13T01:04:09.406332Z","shell.execute_reply.started":"2026-05-13T01:04:09.166015Z","shell.execute_reply":"2026-05-13T01:04:09.405432Z"}},"outputs":[{"name":"stdout","text":"RMSE : 2.9372275196400772\nMAE : 2.2928761589886566\nMAPE : 0.008509324685853654\nR2 : 0.9973152341609375\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"
","image/png":"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\n"},"metadata":{}},{"output_type":"display_data","data":{"text/html":"\n\n\n
\n
\n\n"},"metadata":{}},{"output_type":"display_data","data":{"text/html":"\n\n\n
\n
\n\n"},"metadata":{}}],"execution_count":41},{"cell_type":"code","source":"","metadata":{"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"> #### Exercice \n> Modifier la classe `LinearNeuron1D` afin de mémoriser l’évolution de la fonction de coût au cours de l’apprentissage.\n>\n> Ajouter un attribut `history`, initialisé comme une liste vide dans la méthode `__init__`.\n>\n> À chaque epoch de la méthode `fit`, calculer la fonction de coût:\n> $$\n E(a,b) = \\frac{1}{n}\\sum_{i=1}^{n}(y_i - u_i)^2\n $$\n> puis ajouter sa valeur à la liste `history`.\n>\n> Rappels Python:\n> - une liste se crée avec `[]`\n> - on ajoute un élément à la fin d’une liste avec la méthode `append`\n> - par exemple:\n> `L.append(valeur)`\n>\n> Après l’entraînement, utiliser `history` pour tracer la courbe de la loss en fonction du nombre d’epochs.\n","metadata":{}},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"### SGD et minibatch\n\nJusqu’ici, la descente de gradient est effectuée en mode *batch*.\nÀ chaque epoch, le gradient est calculé comme la moyenne des contributions de **tous** les exemples du jeu d’apprentissage.\nLa mise à jour des paramètres est donc déterministe, mais elle peut être coûteuse lorsque le dataset est volumineux.\n\nEn **Stochastic Gradient Descent (SGD)**, la mise à jour des paramètres est effectuée à partir d’un **seul exemple** tiré aléatoirement.\nLe gradient est alors une estimation bruitée du gradient batch.\nLes mises à jour sont plus rapides, mais la trajectoire de la descente devient irrégulière et la loss peut fluctuer d’une itération à l’autre.\n\nLe **minibatch gradient descent** constitue un compromis entre les deux approches.\nÀ chaque mise à jour, on sélectionne un sous-ensemble de taille $B$ du jeu d’apprentissage, par exemple B=16B=16 ou B=32B=32,\net on utilise la moyenne des gradients calculés sur ce minibatch.\nCette stratégie permet de réduire le bruit du gradient tout en conservant un coût de calcul raisonnable.\n\nDans les bibliothèques de deep learning, l’entraînement est presque toujours réalisé en minibatch,\ncar cette approche est bien adaptée au calcul vectorisé et aux accélérateurs matériels (GPU).\n\n","metadata":{}},{"cell_type":"markdown","source":"### 💡 Syntaxe à reprendre\n\n_Repère syntaxique pour aborder l'exercice ci-dessous._\n\n```python\nclass LinearNeuron1D:\n\n def __init__(self):\n self.a = np.random.uniform()\n self.b = np.random.uniform()\n self.history = []\n\n def forward(self, x):\n return self.a * x + self.b\n\n def fit(self, x, y, lr=0.1, epochs=10, mode='batch', batch_size=32):\n n = len(x)\n for _ in range(epochs):\n if mode == 'batch':\n idx = np.array(range(0, n))\n elif mode == 'sgd':\n idx = np.array(np.random.randint(n))\n elif mode == 'minibatch':\n idx = np.array(np.random.choice(n, size=batch_size))\n else:\n print('ERREUR : mode non reconnu')\n u = self.forward(x[idx])\n grad_a = ((u - y[idx]) * x[idx]).mean()\n grad_b = (u - y[idx]).mean()\n self.a -= lr * grad_a\n self.b -= lr * grad_b\n self.history.append(((y[idx] - u) ** 2).mean())\n return self.history\n```\n","metadata":{}},{"cell_type":"markdown","source":"> Exercice \n> Étendre la méthode `fit` de la classe `LinearNeuron1D` afin de permettre différentes stratégies de descente de gradient,\n> de manière cohérente avec ce qui est fait en pratique dans PyTorch.\n>\n> Ajouter un paramètre `mode` à la méthode `fit`, pouvant prendre les valeurs `\"batch\"`, `\"sgd\"` ou `\"minibatch\"`.\n>\n> - En mode `\"batch\"`, le gradient est calculé à partir de l’ensemble des données d’apprentissage (comportement actuel).\n> - En mode `\"sgd\"`, à chaque mise à jour, un seul exemple (xi,yi)(x_i, y_i) est tiré aléatoirement et utilisé pour calculer le gradient.\n> - En mode `\"minibatch\"`, à chaque mise à jour, un sous-ensemble de taille BB est tiré aléatoirement et le gradient est calculé\n> comme la moyenne des gradients sur ce sous-ensemble.\n>\n> Ajouter un paramètre `batch_size` utilisé uniquement lorsque `mode=\"minibatch\"`.\n>\n> Rappels sur les tirages aléatoires avec NumPy:\n> - `np.random.randint(0, n)` tire un entier aléatoire entre `0` et `n-1`\n> - `np.random.choice(n, size=B, replace=False)` tire `B` indices distincts entre `0` et `n-1`\n> - `np.arange(n)` crée un tableau contenant les entiers de `0` à `n-1`\n> - `x[idx]` et `y[idx]` permettent d’extraire les sous-ensembles correspondant aux indices tirés où `idx` désigne un tableau d’indices entiers correspondant aux exemples sélectionnés\n>\n> Vérifier que, pour un même learning rate et un même nombre d’epochs,\n> la trajectoire de la loss est plus bruitée en SGD qu’en batch,\n> et que le minibatch constitue un compromis entre les deux.\n","metadata":{}},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"## Neurone linéaire à entrées multiples\n\n![MultipleLinearNeuron.png](attachment:7a4881fc-db00-4411-8ace-d79ad0effdb7.png)\n\nJusqu’ici, le neurone linéaire ne traitait qu’une seule variable d’entrée.\nDans ce cas, le paramètre du modèle était un scalaire $a$.\nPour prendre en compte plusieurs variables explicatives, on généralise naturellement ce modèle.\n\nPour un ensemble de $n$ observations décrites par $m$ variables,\nles données sont regroupées dans une matrice:\n\n$$\nX \\in \\mathbb{R}^{n \\times m}\n$$\n\nChaque ligne de $X$ correspond à un exemple,\nchaque colonne à une variable d’entrée.\n\nLe neurone linéaire à entrées multiples calcule alors la prédiction:\n\n$$\nu = X w + b\n$$\n\noù:\n- $w \\in \\mathbb{R}^{m}$ est le vecteur des poids du neurone\n- $b$ est un biais scalaire\n- $u \\in \\mathbb{R}^{n}$ est le vecteur des prédictions\n\nLa fonction de coût reste la MSE batch:\n\n$$\nE(w,b) = \\frac{1}{n}\\sum_{i=1}^{n}(y_i - u_i)^2\n$$\n\nLe calcul du gradient se généralise directement à ce cadre vectoriel.\nPour le vecteur des poids, on obtient:\n\n$$\n\\frac{\\partial E}{\\partial w}\n= X^T (u - y)\n$$\n\nCette expression correspond à l’accumulation, pour chaque poids,\ndes contributions de toutes les observations.\n\nPour le biais, le gradient est:\n\n$$\n\\frac{\\partial E}{\\partial b}\n= \\frac{1}{n}\\sum_{i=1}^{n}(u_i - y_i)\n$$\n\nCes formules sont la version vectorisée exacte du cas à une entrée.\nElles constituent le cœur de l’apprentissage des couches linéaires\ndans les bibliothèques de deep learning.\n","metadata":{},"attachments":{"7a4881fc-db00-4411-8ace-d79ad0effdb7.png":{"image/jpeg":"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"}}},{"cell_type":"markdown","source":"### 💡 Syntaxe à reprendre\n\n_Repère syntaxique pour aborder l'exercice ci-dessous._\n\n```python\nX\n```\n","metadata":{}},{"cell_type":"markdown","source":"> #### Exercice \n> Implémenter une classe Python `LinearNeuron` correspondant à un neurone linéaire\n> à entrées multiples.\n>\n> Le neurone doit calculer la prédiction:\n> $$\nu = X w + b\n$$\n> où $X$ est une matrice de données de taille $(n,m)$,\n> $w$ est un vecteur de poids de taille $(m,)$\n> et $b$ est un biais scalaire.\n>\n> La classe doit contenir:\n> - une méthode `__init__` qui initialise les attributs du modèle\n> - une méthode `forward(X)` qui calcule les prédictions\n> - une méthode `fit(X, y, lr, epochs)` qui entraîne le neurone par descente de gradient batch\n>\n> **Indication importante** \n> La dimension $m$ des entrées peut être déduite directement de la matrice $X$.\n> Il n’est donc pas nécessaire de la fournir explicitement lors de l’initialisation.\n> Les poids $w$ peuvent être initialisés lors du premier appel à `fit`,\n> à partir de la dimension de $X$.\n>\n> **Indications pour l’implémentation** \n> - remplacer le scalaire $a$ par un vecteur de poids $w$ \n> - remplacer l’expression $a x$ par le produit matrice-vecteur `X @ w` \n> - coder le gradient des poids sous la forme:\n> $$\n \\texttt{grad\\_w = X.T @ (u - y) / n}\n $$\n> - conserver le biais $b$ et son gradient $\\partial E / \\partial b$\n>\n> À chaque epoch, la méthode `fit` devra:\n> - calculer les prédictions $u$\n> - calculer la fonction de coût:\n> $$\n E(w,b) = \\frac{1}{n}\\sum_{i=1}^{n}(y_i - u_i)^2\n $$\n> - calculer les gradients:\n> $$\n \\frac{\\partial E}{\\partial w} = \\frac{1}{n} X^T (u - y)\n \\qquad\n \\frac{\\partial E}{\\partial b} = \\frac{1}{n}\\sum_{i=1}^{n}(u_i - y_i)\n $$\n> - mettre à jour les paramètres $w$ et $b$\n>\n> Rappels NumPy utiles:\n> - `np.zeros(m)` crée un vecteur de $m$ zéros\n> - `X[:, j]` extrait la colonne $j$ de la matrice $X$\n> - `X.T` est la transposée de $X$\n> - `X @ w` calcule le produit matrice-vecteur\n>\n> Tester la classe sur le jeu de données `abalone_mini`\n> en prédisant `Rings` à partir de plusieurs variables explicatives.\n","metadata":{}},{"cell_type":"code","source":"df = pd.read_csv('/kaggle/input/datasets/pyim59/mini-datasets/abalone_mini.csv')\n\nX = np.array(df.drop(columns='Rings'))\ny = np.array(df['Rings']","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T01:09:59.227434Z","iopub.execute_input":"2026-05-13T01:09:59.227895Z","iopub.status.idle":"2026-05-13T01:09:59.239231Z","shell.execute_reply.started":"2026-05-13T01:09:59.227864Z","shell.execute_reply":"2026-05-13T01:09:59.238436Z"}},"outputs":[],"execution_count":44},{"cell_type":"code","source":"X.shape[0]","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T01:10:18.608975Z","iopub.execute_input":"2026-05-13T01:10:18.609824Z","iopub.status.idle":"2026-05-13T01:10:18.614829Z","shell.execute_reply.started":"2026-05-13T01:10:18.609791Z","shell.execute_reply":"2026-05-13T01:10:18.613944Z"}},"outputs":[{"execution_count":48,"output_type":"execute_result","data":{"text/plain":"4177"},"metadata":{}}],"execution_count":48},{"cell_type":"code","source":"X[:,1]","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T01:55:16.254593Z","iopub.execute_input":"2026-05-13T01:55:16.254903Z","iopub.status.idle":"2026-05-13T01:55:16.260782Z","shell.execute_reply.started":"2026-05-13T01:55:16.254877Z","shell.execute_reply":"2026-05-13T01:55:16.259821Z"}},"outputs":[{"execution_count":113,"output_type":"execute_result","data":{"text/plain":"array([-0.43214879, -1.439929 , 0.12213032, ..., 0.67640943,\n 0.77718745, 1.48263359])"},"metadata":{}}],"execution_count":113},{"cell_type":"code","source":"class NeuroneLineaireMultiple:\n def __init__(self):\n self.b = np.random.uniform()\n self.history = []\n\n def predict(self, X):\n return X@self.w + self.b\n\n def fit(self, X, y, learning_rate=0.1, epochs=100):\n n = X.shape[0]\n m = X.shape[1]\n self.w = np.random.uniform(size=m)\n grad_w = np.zeros(m)\n for i in range(epochs):\n u = self.predict(X)\n for j in range(m):\n grad_w[j] = np.mean((u-y)*X[:,j])\n self.w[j] -= learning_rate*grad_w[j]\n grad_b = np.mean(u-y)\n self.b = self.b - learning_rate*grad_b\n self.history.append(np.mean((u-y)**2))","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T01:55:37.876169Z","iopub.execute_input":"2026-05-13T01:55:37.877249Z","iopub.status.idle":"2026-05-13T01:55:37.884538Z","shell.execute_reply.started":"2026-05-13T01:55:37.877199Z","shell.execute_reply":"2026-05-13T01:55:37.883664Z"}},"outputs":[],"execution_count":114},{"cell_type":"code","source":"from sklearn.metrics import *\nfrom sklearn.preprocessing import *\n\ndf = pd.read_csv('/kaggle/input/datasets/pyim59/mini-datasets/abalone_mini.csv')\n\nX = np.array(df.drop(columns='Rings'))\ny = np.array(df['Rings'])\n\nscaler = StandardScaler()\nX = scaler.fit_transform(X)\n\nmodel = NeuroneLineaireMultiple()\nmodel.fit(X,y, learning_rate=0.1, epochs=100)\ny_hat = model.predict(X)\n\nplt.plot(model.history)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T01:55:50.159547Z","iopub.execute_input":"2026-05-13T01:55:50.159875Z","iopub.status.idle":"2026-05-13T01:55:50.495737Z","shell.execute_reply.started":"2026-05-13T01:55:50.159846Z","shell.execute_reply":"2026-05-13T01:55:50.494916Z"}},"outputs":[{"execution_count":116,"output_type":"execute_result","data":{"text/plain":"[]"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"
","image/png":"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\n"},"metadata":{}}],"execution_count":116},{"cell_type":"code","source":"","metadata":{"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"> #### Exercice \n> Tester la classe `LinearNeuron` sur le jeu de données `house_mini`\n>\n> Remarques ?","metadata":{}},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"## Pourquoi faut-il normaliser les entrées pour une descente de gradient ?\n\nPour comprendre la nécessité de la normalisation, on commence par le cas **le plus simple possible**:\nune fonction de coût dépendant d’un **seul paramètre**.\nCe cadre permet de comprendre l’idée sans matrices ni formalisme lourd.\n\n\n\n### Cas à une dimension\n\nConsidérons une fonction de coût quadratique:\n\n$$\nE(a) = \\frac{1}{2} k (a - a^*)^2\n$$\n\noù:\n\n* $a$ est le paramètre à apprendre\n* $a^*$ est la valeur optimale\n* $k > 0$ mesure la **courbure** de la fonction de coût\n\nDans ce cas, le Hessien se réduit à un scalaire égal à $k$.\n\n\n\n### Descente de gradient en 1D\n\nLe gradient est:\n\n$$\n\\frac{dE}{da} = k (a - a^*)\n$$\n\nLa descente de gradient s’écrit:\n\n$$\na_{t+1} = a_t - \\eta \\frac{dE}{da}\n$$\n\nsoit:\n\n$$\na_{t+1} = a_t - \\eta k (a_t - a^*)\n$$\n\nEn notant l’erreur $e_t = a_t - a^*$, on obtient:\n\n$$\ne_{t+1} = (1 - \\eta k), e_t\n$$\n\n\n\n### Condition de convergence et vitesse\n\nPour que la descente converge, il faut:\n\n$$\n|1 - \\eta k| < 1\n$$\n\nce qui impose:\n\n$$\n0 < \\eta < \\frac{2}{k}\n$$\n\nLa **vitesse de convergence** dépend directement du facteur $|1 - \\eta k|$.\n\n* si $k$ est grand (fonction très raide), $\\eta$ doit être très petit\n* si $k$ est petit (fonction très plate), la convergence est lente\n\nAinsi, en une dimension, la vitesse de convergence dépend directement de la **courbure**, c’est à dire du Hessien.\n\n\n\n### Lien avec les données et la normalisation\n\nDans une régression linéaire à une entrée:\n\n$$\nE(a) = \\frac{1}{n}\\sum_{i=1}^{n}(y_i - a x_i - b)^2\n$$\n\nla courbure par rapport à $a$ est proportionnelle à:\n\n$$\nk \\propto \\frac{1}{n}\\sum_{i=1}^{n} x_i^2\n$$\n\nSi la variable $x$ prend des valeurs très grandes ou très petites,\nla courbure de la fonction de coût change fortement.\n\nNormaliser $x$ permet de contrôler cette courbure,\net donc de rendre la descente de gradient plus stable et plus rapide.\n\n\n\n### Généralisation au cas multidimensionnel\n\nLorsque le modèle dépend de plusieurs paramètres,\nla courbure n’est plus décrite par un scalaire,\nmais par une **matrice Hessienne** $H$,\nqui contient les dérivées secondes par rapport à tous les paramètres.\n\nDans ce cas:\n\n* chaque direction de l’espace des paramètres a sa propre courbure\n* la vitesse de convergence dépend du contraste entre ces courbures\n* ce contraste est mesuré par le **conditionnement** du Hessien\n\nSi les variables d’entrée ne sont pas normalisées,\nle Hessien est mal conditionné et la descente de gradient converge lentement.\n\nLa normalisation réduit ce déséquilibre,\naméliore le conditionnement du Hessien,\net accélère la convergence.\n\n\n","metadata":{}},{"cell_type":"markdown","source":"## Méthodes de normalisation dans `sklearn` (Rappels)\n\nLa normalisation vise à mettre les variables d’entrée sur des échelles comparables\nafin d’améliorer la stabilité et la vitesse de la descente de gradient.\n\n\n### MinMaxScaler\n\nLe **MinMaxScaler** met chaque variable dans un intervalle fixé, en général $[0,1]$.\n\nPrincipe:\n\n$$\nx_{\\text{scaled}} = \\frac{x - x_{\\min}}{x_{\\max} - x_{\\min}}\n$$\n\nCaractéristiques:\n\n* conserve la forme de la distribution\n* sensible aux valeurs aberrantes\n* souvent utilisé lorsque les bornes ont un sens physique\n\nEn pratique:\n\n```python\nfrom sklearn.preprocessing import MinMaxScaler\n\nscaler = MinMaxScaler()\nX_scaled = scaler.fit_transform(X)\n```\n\n\n### StandardScaler\n\nLe **StandardScaler** centre les données et les réduit\n(moyenne nulle, variance unitaire).\n\nPrincipe:\n\n$$\nx_{\\text{scaled}} = \\frac{x - \\mu}{\\sigma}\n$$\n\nCaractéristiques:\n\n* données centrées autour de 0\n* bien adapté aux modèles linéaires et au deep learning\n* sensible aux outliers\n\nEn pratique:\n\n```python\nfrom sklearn.preprocessing import StandardScaler\n\nscaler = StandardScaler()\nX_scaled = scaler.fit_transform(X)\n```\n\n\n### RobustScaler\n\nLe **RobustScaler** utilise des statistiques robustes\n(médiane et intervalle interquartile).\n\nPrincipe:\n\n$$\nx_{\\text{scaled}} = \\frac{x - \\text{median}}{\\text{IQR}}\n$$\n\noù $\\text{IQR} = Q_3 - Q_1$.\n\nCaractéristiques:\n\n* beaucoup moins sensible aux outliers\n* utile lorsque les données contiennent des valeurs extrêmes\n* la distribution résultante n’est pas forcément centrée en 0\n\nEn pratique:\n\n```python\nfrom sklearn.preprocessing import RobustScaler\n\nscaler = RobustScaler()\nX_scaled = scaler.fit_transform(X)\n```\n\n### Choix\n\n> * **StandardScaler**: choix par défaut pour la descente de gradient\n> * **MinMaxScaler**: utile quand on veut borner explicitement les variables\n> * **RobustScaler**: à privilégier en présence d’outliers\n\n```python\ndf = pd.read_csv('/kaggle/input/datasets/pyim59/mini-datasets/house_mini.csv')\n\nX = df.drop(columns='price').to_numpy()\ny = df['price'].to_numpy()\n\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n\nscaler = StandardScaler()\nX_train = scaler.fit_transform(X_train)\nX_test = scaler.transform(X_test)\n\nmodel = LinearNeuron()\nmodel.fit(X_train,y_train,mode=\"minibatch\",epochs=500, lr=0.01, batch_size=32)\ny_hat = model.forward(X_test)\n\nprint(f\"MAE : {mean_absolute_error(y_test,y_hat):.2f}\")\nprint(f\"RMSE : {np.sqrt(mean_squared_error(y_test,y_hat)):.2f}\")\nprint(f\"MAPE : {mean_absolute_percentage_error(y_test,y_hat):.4f}\")\nprint(f\"R2 : {r2_score(y_test,y_hat):.3f}\")\n\nplt.plot(model.history)\n```\n\n```python\ny.reshape(-1,1)\n```\n","metadata":{}},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"### En pratique: séparation train / test\n\nDans un contexte d’apprentissage supervisé,\non **ne normalise jamais l’ensemble du dataset d’un seul coup**.\n\nOn procède toujours en deux étapes:\n\n```python\nscaler = StandardScaler()\nX_train = scaler.fit_transform(X_train)\nX_test = scaler.transform(X_test)\n```\n\n\n### Pourquoi cette distinction `fit` / `transform` ?\n\n* `fit`\n calcule les statistiques de normalisation\n (moyenne, écart-type, min/max, médiane, etc.)\n\n* `transform`\n applique ces statistiques aux données\n\n\n### Raison fondamentale\n\nLes statistiques de normalisation **doivent être calculées uniquement\nà partir du jeu d’apprentissage**.\n\nSi l’on faisait:\n\n```python\nscaler.fit_transform(X)\n```\n\navant la séparation train / test,\non introduirait une **fuite d’information** (*data leakage*):\nles données de test influenceraient indirectement l’apprentissage.\n\n\n> Le jeu de test doit rester totalement “inconnu” du modèle.\n\nNormaliser avec les statistiques du test reviendrait à\nutiliser de l’information future pour entraîner le modèle,\nce qui biaise l’évaluation des performances.\n\n\n","metadata":{}},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"> Exercice \n> Sans scaling, trouver un lr qui ne diverge pas (souvent très petit). \n> Avec StandardScaler, augmenter lr (0.01, 0.1, 0.5, 1.0). \n> Conclure","metadata":{}},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"code","source":"y.reshape(-1,1)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T02:03:42.664573Z","iopub.execute_input":"2026-05-13T02:03:42.664918Z","iopub.status.idle":"2026-05-13T02:03:42.671190Z","shell.execute_reply.started":"2026-05-13T02:03:42.664891Z","shell.execute_reply":"2026-05-13T02:03:42.670424Z"}},"outputs":[{"execution_count":118,"output_type":"execute_result","data":{"text/plain":"array([[15],\n [ 7],\n [ 9],\n ...,\n [ 9],\n [10],\n [12]])"},"metadata":{}}],"execution_count":118},{"cell_type":"markdown","source":"## Introduction à PyTorch\n\nPyTorch est une bibliothèque de deep learning qui automatise deux éléments clés\nque nous avons programmés à la main jusqu’ici:\n\n* le calcul des gradients (autograd)\n* la mise à jour des paramètres (optimizers)\n\nL’idée fondamentale reste strictement la même:\nun modèle, une fonction de coût, une descente de gradient.\n\nLa différence est que PyTorch fournit une structure standard,\nrobuste et réutilisable pour implémenter ces étapes,\ndes modèles linéaires simples jusqu’aux réseaux profonds.\n\n## Neurone linéaire en PyTorch\n\nLe neurone linéaire que nous avons implémenté *from scratch*\ncorrespond en PyTorch à une couche `nn.Linear`.\n\nPour une entrée de dimension $m$, le modèle calcule:\n\n$$\nu = X w + b\n$$\n\nexactement comme notre classe `LinearNeuron`.\n\n\n### Import des modules PyTorch\n\n```python\nimport torch\nimport torch.nn as nn\n```\n\n* `torch` fournit les tenseurs et le calcul numérique\n* `torch.nn` contient les briques de réseaux de neurones\n\n\n### Données sous forme de tenseurs\n\nPyTorch travaille avec des **tenseurs**.\n\nUn tenseur est une généralisation des tableaux NumPy:\n\n* un scalaire → tenseur 0D\n* un vecteur → tenseur 1D\n* une matrice → tenseur 2D\n\nPar rapport à NumPy, les tenseurs PyTorch peuvent en plus:\n\n* stocker des gradients\n* participer à un graphe de calcul (autograd)\n* être placés sur CPU ou GPU\n\n\n\n### Conversion des données en tenseurs\n\n```python\nX_train = torch.tensor(X_train, dtype=torch.float32)\ny_train = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)\n\nX_test = torch.tensor(X_test, dtype=torch.float32)\ny_test = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)\n```\n\nAprès conversion:\n\n* `X_train` est de forme `(n, m)`\n* `y_train` est de forme `(n, 1)`\n\n\n### Pourquoi `view(-1, 1)` pour `y` ?\n\nÀ l’origine, la variable cible `y` est souvent un **vecteur NumPy**\nde forme `(n,)`.\n\nEn NumPy, on écrirait typiquement:\n\n```python\ny = y.reshape(-1, 1)\n```\n\nEn PyTorch, l’équivalent est:\n\n```python\ny = y.view(-1, 1)\n```\n\nLes deux opérations ont exactement le même objectif:\n\n> transformer un vecteur 1D en une colonne 2D.\n\n\n### Compatibilité avec `nn.Linear`\n\nUne couche définie par:\n\n```python\nnn.Linear(m, 1)\n```\n\nproduit une sortie de forme `(n, 1)`.\n\nPour que le calcul de la loss soit correct,\nles prédictions et les cibles doivent avoir **la même forme**.\n\n`view(-1, 1)` garantit donc la compatibilité:\n\n* avec `nn.Linear`\n* avec les fonctions de coût (`nn.MSELoss`, etc.)\n\n\n### Détail sur `view`\n\n* `-1` signifie: *“déduire automatiquement la taille”*\n* `1` impose une colonne\n* aucune copie mémoire n’est faite (changement de vue)\n\n\n### Définition du modèle\n\n```python\nmodel = nn.Linear(X_train.shape[1], 1)\n```\n\nCette ligne remplace:\n\n* l’initialisation manuelle de $w$\n* l’initialisation manuelle de $b$\n* l’écriture explicite de la méthode `forward`\n\nPyTorch crée automatiquement:\n\n* un vecteur de poids `model.weight`\n* un biais `model.bias`\n\n\n### `forward` et appel du modèle\n\nDans PyTorch, la méthode `forward` décrit le calcul du modèle,\nmais **on ne l’appelle jamais directement**.\n\nOn utilise toujours:\n\n```python\ny_hat = model(X_train)\n```\n\net non:\n\n```python\ny_hat = model.forward(X_train)\n```\n\n`model(X)` passe par la mécanique interne de `nn.Module`,\nqui gère correctement l’autograd, les modes `train()` / `eval()`,\net d’autres mécanismes internes.\n\n\n### Fonction de coût\n\n```python\ncriterion = nn.MSELoss()\n```\n\n* correspond exactement à la MSE utilisée précédemment\n* calcule automatiquement la moyenne sur le batch\n\n\n### Optimiseur (descente de gradient)\n\n```python\noptimizer = torch.optim.SGD(model.parameters(), lr=0.1)\n```\n\n* `model.parameters()` fournit tous les paramètres entraînables\n* `SGD` implémente la descente de gradient\n* `lr` joue le même rôle que précédemment (learning rate)\n\n\n### Boucle d’entraînement\n\n```python\nepochs = 30\nloss_history = []\n\nfor _ in range(epochs):\n optimizer.zero_grad()\n\n y_hat = model(X_train)\n loss = criterion(y_hat, y_train)\n\n loss.backward()\n optimizer.step()\n\n loss_history.append(loss.item())\n```\n\nDécomposition logique:\n\n1. `optimizer.zero_grad()`\n remet les gradients à zéro (ils sont accumulés par défaut)\n\n2. `model(X_train)`\n calcule les prédictions via `forward`\n\n3. `loss.backward()`\n calcule automatiquement les gradients par rétropropagation\n\n4. `optimizer.step()`\n met à jour les paramètres du modèle\n\n```python\nimport torch\nimport torch.nn as nn\n\ndf = pd.read_csv('/kaggle/input/datasets/pyim59/mini-datasets/house_mini.csv')\n\nX = df.drop(columns='price').to_numpy()\ny = df['price'].to_numpy()\n\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n\nscaler = StandardScaler()\nX_train = scaler.fit_transform(X_train)\nX_test = scaler.transform(X_test)\n\nX_train_t = torch.tensor(X_train, dtype=torch.float32)\ny_train_t = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)\n\nX_test_t = torch.tensor(X_test, dtype=torch.float32)\ny_test_t = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)\n\nprint(X_train.shape)\nprint(y_train.shape)\n\nmodel = nn.Linear(X_train_t.shape[1], 1)\ncriterion = nn.MSELoss()\noptimizer = torch.optim.SGD(model.parameters(), lr=0.1)\n\nepochs = 100\nloss_history = []\nfor _ in range(epochs):\n optimizer.zero_grad()\n\n u = model(X_train_t)\n loss = criterion(u, y_train_t)\n\n loss.backward()\n optimizer.step()\n\n loss_history.append(loss.item())\n\nplt.plot(loss_history)\nplt.show()\n\nwith torch.no_grad():\n y_hat = model(X_test_t)\n\ny_hat = y_hat.cpu().numpy().reshape(-1)\n\nprint(f\"MAE : {mean_absolute_error(y_test,y_hat):.2f}\")\nprint(f\"RMSE : {np.sqrt(mean_squared_error(y_test,y_hat)):.2f}\")\nprint(f\"MAPE : {mean_absolute_percentage_error(y_test,y_hat):.4f}\")\nprint(f\"R2 : {r2_score(y_test,y_hat):.3f}\")\n```\n","metadata":{}},{"cell_type":"code","source":"import torch\nimport torch.nn as nn\n\ndf = pd.read_csv('/kaggle/input/datasets/pyim59/mini-datasets/house_mini.csv')\n\nX = df.drop(columns='price').to_numpy()\ny = df['price'].to_numpy()\n\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n\nscaler = StandardScaler()\nX_train = scaler.fit_transform(X_train)\nX_test = scaler.transform(X_test)\n\nX_train_t = torch.tensor(X_train, dtype=torch.float32)\ny_train_t = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)\n\nX_test_t = torch.tensor(X_test, dtype=torch.float32)\ny_test_t = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)\n\nprint(X_train.shape)\nprint(y_train.shape)\n\nmodel = nn.Linear(X_train_t.shape[1], 1)\ncriterion = nn.MSELoss()\noptimizer = torch.optim.SGD(model.parameters(), lr=0.1)\n\nepochs = 100\nloss_history = []\nfor _ in range(epochs):\n optimizer.zero_grad()\n\n u = model(X_train_t)\n loss = criterion(u, y_train_t)\n\n loss.backward()\n optimizer.step()\n\n loss_history.append(loss.item())\n\nplt.plot(loss_history)\nplt.show()\n\nwith torch.no_grad():\n y_hat = model(X_test_t)\n\ny_hat = y_hat.cpu().numpy().reshape(-1)\n\nprint(f\"MAE : {mean_absolute_error(y_test,y_hat):.2f}\")\nprint(f\"RMSE : {np.sqrt(mean_squared_error(y_test,y_hat)):.2f}\")\nprint(f\"MAPE : {mean_absolute_percentage_error(y_test,y_hat):.4f}\")\nprint(f\"R2 : {r2_score(y_test,y_hat):.3f}\")","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T02:14:38.649387Z","iopub.execute_input":"2026-05-13T02:14:38.649761Z","iopub.status.idle":"2026-05-13T02:14:38.854486Z","shell.execute_reply.started":"2026-05-13T02:14:38.649729Z","shell.execute_reply":"2026-05-13T02:14:38.853499Z"}},"outputs":[{"name":"stdout","text":"(17290, 6)\n(17290,)\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"
","image/png":"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\n"},"metadata":{}},{"name":"stdout","text":"MAE : 169500.07\nRMSE : 254558.14\nMAPE : 0.3481\nR2 : 0.507\n","output_type":"stream"}],"execution_count":121},{"cell_type":"markdown","source":"### Évaluation et prédictions\n\nAprès l’entraînement, on utilise le modèle pour produire des prédictions\nsur un jeu de données **jamais vu pendant l’apprentissage**: le jeu de test.\n\nCette phase est appelée **évaluation** ou **inférence**.\n\n\n#### Passage en mode évaluation\n\n```python\nmodel.eval()\n```\n\nCette instruction met le modèle en **mode évaluation**.\n\nElle ne modifie pas les poids du modèle.\nElle indique simplement à PyTorch que le modèle n’est plus en phase d’apprentissage.\n\nPour un neurone linéaire seul, cela ne change rien numériquement,\nmais pour des modèles plus complexes, certaines couches\n(seulement actives pendant l’entraînement) se comportent différemment\nen phase d’évaluation.\n\n\n#### Désactivation du calcul des gradients\n\n```python\nwith torch.no_grad():\n y_hat = model(X_test)\n```\n\nPar défaut, PyTorch construit un **graphe de calcul**\npour toutes les opérations impliquant des paramètres entraînables.\nCe graphe est nécessaire pour la rétropropagation.\n\nPendant l’évaluation, on n’a **pas besoin de gradients**.\nLe bloc `with torch.no_grad():` indique donc à PyTorch:\n\n> “N’enregistre pas les opérations, je ne ferai pas de backward.”\n\nConséquences:\n\n* moins de mémoire utilisée\n* calcul plus rapide\n* possibilité de convertir les résultats en NumPy\n\n\n#### Sortie du modèle\n\nÀ ce stade, `y_hat` est un tenseur PyTorch de forme `(n, 1)`,\noù `n` est le nombre d’exemples du jeu de test.\n\nCette forme est naturelle en PyTorch,\ncar les couches `nn.Linear` produisent des sorties à deux dimensions.\n\n\n#### Conversion vers NumPy pour l’évaluation\n\nLes fonctions d’évaluation classiques (`sklearn`, `matplotlib`)\nattendent des tableaux NumPy 1D.\n\nOn convertit donc explicitement la sortie:\n\n```python\ny_hat = y_hat.cpu().numpy().reshape(-1)\n```\n\nDécomposition:\n\n* `y_hat.cpu()`\n garantit que les données sont sur le CPU\n (indispensable si le modèle est sur GPU)\n\n* `.numpy()`\n convertit le tenseur PyTorch en tableau NumPy\n\n* `.reshape(-1)`\n transforme la sortie de `(n, 1)` en `(n,)`\n\n\n\n#### Résumé \n\nCette séquence d’instructions:\n\n```python\nmodel.eval()\nwith torch.no_grad():\n y_hat = model(X_test)\n\ny_hat = y_hat.cpu().numpy().reshape(-1)\n```\n\nsignifie:\n\n> “Utiliser le modèle en mode prédiction,\n> sans calcul de gradients,\n> puis convertir proprement la sortie PyTorch\n> en un format exploitable pour l’évaluation.”\n\n\n### Correspondance avec le neurone *from scratch*\n\n| From scratch | PyTorch |\n| --------------------------- | ------------------ |\n| `forward(X)` | `model(X)` |\n| calcul manuel des gradients | `loss.backward()` |\n| mise à jour de `w`, `b` | `optimizer.step()` |\n| boucle `epochs` | boucle `epochs` |\n| stockage de la loss | `loss.item()` |\n\n","metadata":{}},{"cell_type":"markdown","source":"### 💡 Syntaxe à reprendre\n\n_Repère syntaxique pour aborder l'exercice ci-dessous._\n\n```python\nimport torch\nimport torch.nn as nn\nscaler = StandardScaler()\nX_train = scaler.fit_transform(X_train)\nX_test = scaler.transform(X_test)\nX_train_t = torch.tensor(X_train, dtype=torch.float32)\ny_train_t = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)\nX_test_t = torch.tensor(X_test, dtype=torch.float32)\ny_test_t = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)\nmodel = nn.Linear(X_train_t.shape[1], 1)\ncriterion = nn.MSELoss()\noptimizer = torch.optim.SGD(model.parameters(), lr=0.1)\nepochs = 100\nloss_history = []\nfor _ in range(epochs):\n optimizer.zero_grad()\n u = model(X_train_t)\n loss = criterion(u, y_train_t)\n loss.backward()\n optimizer.step()\n loss_history.append(loss.item())\nwith torch.no_grad():\n y_hat = model(X_test_t)\ny_hat = y_hat.cpu().numpy().reshape(-1)\n```\n","metadata":{}},{"cell_type":"markdown","source":"> #### Exercice \n> Appliquer le neurone linéaire PyTorch sur le jeu de données `house_mini`.\n>\n> Charger `house_mini.csv`, choisir une variable cible `y` (par exemple `Price` si elle existe),\n> puis construire la matrice d’entrée `X` avec les autres colonnes numériques.\n>\n> Séparer les données en apprentissage et test avec `train_test_split`.\n>\n> Normaliser les entrées avec un scaler `sklearn` (StandardScaler recommandé),\n> en faisant `fit` sur `X_train` uniquement, puis `transform` sur `X_train` et `X_test`.\n>\n> Convertir `X_train`, `y_train`, `X_test`, `y_test` en tenseurs PyTorch (`torch.tensor`)\n> avec le type `torch.float32`, et mettre `y` au format `(n,1)` avec `.view(-1,1)`.\n>\n> Définir le modèle PyTorch:\n> - `model = nn.Linear(m, 1)` où `m = X_train.shape[1]`\n> - `criterion = nn.MSELoss()`\n> - `optimizer = torch.optim.SGD(model.parameters(), lr=...)`\n>\n> Entraîner le modèle pendant un nombre d’epochs fixé.\n> Stocker la loss (`loss.item()`) à chaque epoch dans une liste `loss_history`.\n>\n> Évaluer le modèle sur le jeu de test avec une métrique de régression\n> (par exemple MSE ou $R^2$) et comparer avec la version \"from scratch\".\n>\n> Varier le learning rate et observer:\n> - divergence si trop grand\n> - convergence lente si trop petit\n> - stabilité et vitesse avec la normalisation\n","metadata":{}},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"df = pd.read_csv('/kaggle/input/datasets/pyim59/mini-datasets/house_mini.csv')\n\nX = df.drop(columns='price').to_numpy()\ny = df['price'].to_numpy()\n\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n\nscaler = StandardScaler()\nX_train = scaler.fit_transform(X_train)\nX_test = scaler.transform(X_test)\n\nX_train_t = torch.tensor(X_train, dtype=torch.float32)\ny_train_t = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)\n\nX_test_t = torch.tensor(X_test, dtype=torch.float32)\ny_test_t = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T02:19:16.138284Z","iopub.execute_input":"2026-05-13T02:19:16.138595Z","iopub.status.idle":"2026-05-13T02:19:16.173489Z","shell.execute_reply.started":"2026-05-13T02:19:16.138568Z","shell.execute_reply":"2026-05-13T02:19:16.172639Z"}},"outputs":[],"execution_count":125},{"cell_type":"code","source":"from torch.utils.data import TensorDataset, DataLoader\n\ntrain_dataset = TensorDataset(X_train_t, y_train_t)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T02:19:22.355476Z","iopub.execute_input":"2026-05-13T02:19:22.355809Z","iopub.status.idle":"2026-05-13T02:19:22.360351Z","shell.execute_reply.started":"2026-05-13T02:19:22.355783Z","shell.execute_reply":"2026-05-13T02:19:22.359587Z"}},"outputs":[],"execution_count":126},{"cell_type":"code","source":"train_dataset[0]","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T02:19:46.598396Z","iopub.execute_input":"2026-05-13T02:19:46.599196Z","iopub.status.idle":"2026-05-13T02:19:46.606072Z","shell.execute_reply.started":"2026-05-13T02:19:46.599135Z","shell.execute_reply":"2026-05-13T02:19:46.605354Z"}},"outputs":[{"execution_count":127,"output_type":"execute_result","data":{"text/plain":"(tensor([-0.3962, -1.4550, -1.1687, -0.1466, -0.9172, -1.0499]),\n tensor([180000.]))"},"metadata":{}}],"execution_count":127},{"cell_type":"code","source":"batch_size = 32\n\ntrain_loader = DataLoader(\n train_dataset,\n batch_size=batch_size,\n shuffle=True\n)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T02:22:15.912270Z","iopub.execute_input":"2026-05-13T02:22:15.912628Z","iopub.status.idle":"2026-05-13T02:22:15.917778Z","shell.execute_reply.started":"2026-05-13T02:22:15.912601Z","shell.execute_reply":"2026-05-13T02:22:15.916729Z"}},"outputs":[],"execution_count":128},{"cell_type":"code","source":"Xb, yb = next(iter(train_loader))\n\nprint(\"Xb shape:\", Xb.shape)\nprint(\"yb shape:\", yb.shape)\n\nXb[:5], yb[:5]","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T02:22:30.818500Z","iopub.execute_input":"2026-05-13T02:22:30.818818Z","iopub.status.idle":"2026-05-13T02:22:30.837125Z","shell.execute_reply.started":"2026-05-13T02:22:30.818791Z","shell.execute_reply":"2026-05-13T02:22:30.836188Z"}},"outputs":[{"name":"stdout","text":"Xb shape: torch.Size([32, 6])\nyb shape: torch.Size([32, 1])\n","output_type":"stream"},{"execution_count":129,"output_type":"execute_result","data":{"text/plain":"(tensor([[ 0.6657, 0.1730, 0.5575, -0.0286, 0.9289, -1.3686],\n [ 0.6657, -0.4782, 0.4701, -0.1800, -0.9172, -0.8625],\n [-1.4581, -1.4550, -1.0267, -0.2254, -0.9172, 0.5247],\n [-0.3962, 0.4985, -0.4476, -0.2350, 0.9289, -0.4126],\n [ 0.6657, 0.4985, 0.0222, 0.1070, 0.0059, -0.4313]]),\n tensor([[925000.],\n [285000.],\n [249900.],\n [348000.],\n [207000.]]))"},"metadata":{}}],"execution_count":129},{"cell_type":"markdown","source":"## Le `DataLoader` en PyTorch\n\nLe `DataLoader` est un composant central de PyTorch pour gérer l’accès aux données pendant l’entraînement.\nIl ne change pas l’algorithme d’apprentissage.\nIl automatise simplement ce que l’on ferait à la main: mélanger les données,\nles découper en minibatchs et itérer proprement.\n\n\n### Données d’entrée du DataLoader\n\nÀ ce stade du notebook, on suppose disposer déjà de:\n\n* `X_train` : données d’entrée d’apprentissage, sous forme de **tenseur PyTorch** de taille `(n, m)`\n* `y_train` : cibles associées, sous forme de **tenseur PyTorch** de taille `(n, 1)`\n\nCes tenseurs ont été obtenus après:\n\n* séparation train / test\n* normalisation éventuelle\n* conversion NumPy vers PyTorch\n\nCe sont ces deux objets qui vont être fournis au `DataLoader`.\n\n\n### Dataset puis DataLoader\n\nEn PyTorch, on distingue deux niveaux:\n\n* le `Dataset`: une collection d’exemples unitaires\n* le `DataLoader`: un itérateur qui regroupe ces exemples en minibatchs\n\nLorsque les données sont déjà sous forme de tenseurs,\non utilise `TensorDataset`.\n\n```python\nfrom torch.utils.data import TensorDataset, DataLoader\n\ntrain_dataset = TensorDataset(X_train, y_train)\n```\n\nConceptuellement, `train_dataset` représente une collection de paires:\n\n$$\n(X_i,; y_i)\n$$\n\nOn peut accéder à un exemple individuel:\n\n```python\ntrain_dataset[0]\n```\n\n\n### Création du DataLoader\n\n```python\nbatch_size = 32\n\ntrain_loader = DataLoader(\n train_dataset,\n batch_size=batch_size,\n shuffle=True\n)\n```\n\nSignification des paramètres principaux:\n\n* `batch_size`: nombre d’exemples par minibatch\n* `shuffle=True`: mélange les données à chaque epoch\n (équivalent à une permutation aléatoire des indices)\n\n\n### Ce que produit un DataLoader\n\nUn `DataLoader` est un **itérateur**.\nÀ chaque itération, il renvoie un minibatch:\n\n```python\nfor Xb, yb in train_loader:\n ...\n```\n\nTypiquement:\n\n* `Xb` a une forme `(B, m)`\n* `yb` a une forme `(B, 1)`\n* `B` vaut `batch_size` (sauf éventuellement pour le dernier batch)\n\nSi `shuffle=True`, les minibatchs ne sont pas identiques d’une epoch à l’autre.\n\n\n### Visualiser un DataLoader\n\nOn ne “voit” pas directement un `DataLoader` comme un tableau.\nOn visualise ce qu’il produit.\n\nVisualiser un premier minibatch:\n\n```python\nXb, yb = next(iter(train_loader))\n\nprint(\"Xb shape:\", Xb.shape)\nprint(\"yb shape:\", yb.shape)\n\nXb[:5], yb[:5]\n```\n\nParcourir une epoch et afficher les tailles des lots:\n\n```python\nfor i, (Xb, yb) in enumerate(train_loader):\n print(f\"Batch {i}: Xb shape = {Xb.shape}, yb shape = {yb.shape}\")\n```\n\nObserver l’effet du `shuffle`:\n\n```python\nXb1, yb1 = next(iter(train_loader))\nXb2, yb2 = next(iter(train_loader))\n\nXb1[:3], yb1[:3], Xb2[:3], yb2[:3]\n```\n\n```python\nfrom torch.utils.data import TensorDataset, DataLoader\n\ndf = pd.read_csv('/kaggle/input/datasets/pyim59/mini-datasets/abalone_mini.csv')\n\nX = df.drop(columns='Weight').to_numpy()\ny = df['Weight'].to_numpy()\n\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n\nscaler = StandardScaler()\nX_train = scaler.fit_transform(X_train)\nX_test = scaler.transform(X_test)\n\nX_train_t = torch.tensor(X_train, dtype=torch.float32)\ny_train_t = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)\n\nX_test_t = torch.tensor(X_test, dtype=torch.float32)\ny_test_t = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)\n\nprint(X_train.shape)\nprint(y_train.shape)\n\ntrain_dataset = TensorDataset(X_train_t, y_train_t)\n\nbatch_size = 32\n\ntrain_loader = DataLoader(\n train_dataset,\n batch_size=batch_size,\n shuffle=True\n)\n\nmodel = nn.Linear(X_train_t.shape[1], 1)\ncriterion = nn.MSELoss()\noptimizer = torch.optim.SGD(model.parameters(), lr=0.1)\n\nepochs = 100\nloss_history = []\nfor _ in range(epochs):\n nb=0\n epoch_loss=0\n for Xb, yb in train_loader:\n optimizer.zero_grad()\n u = model(Xb)\n loss = criterion(u, yb)\n loss.backward()\n optimizer.step()\n epoch_loss += loss.item()\n nb += 1\n loss_history.append(epoch_loss/nb)\n\nplt.plot(loss_history)\nplt.show()\n\nwith torch.no_grad():\n y_hat = model(X_test_t)\n\ny_hat = y_hat.cpu().numpy().reshape(-1)\n\nprint(f\"MAE : {mean_absolute_error(y_test,y_hat):.2f}\")\nprint(f\"RMSE : {np.sqrt(mean_squared_error(y_test,y_hat)):.2f}\")\nprint(f\"MAPE : {mean_absolute_percentage_error(y_test,y_hat):.4f}\")\nprint(f\"R2 : {r2_score(y_test,y_hat):.3f}\")\n\nplt.scatter(X_test[:,1], y_test)\nplt.scatter(X_test[:,1], y_hat, c='red')\nplt.show()\n```\n","metadata":{}},{"cell_type":"code","source":"df = pd.read_csv('/kaggle/input/datasets/pyim59/mini-datasets/abalone_mini.csv')\n\nX = df.drop(columns='Weight').to_numpy()\ny = df['Weight'].to_numpy()\n\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n\nscaler = StandardScaler()\nX_train = scaler.fit_transform(X_train)\nX_test = scaler.transform(X_test)\n\nX_train_t = torch.tensor(X_train, dtype=torch.float32)\ny_train_t = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)\n\nX_test_t = torch.tensor(X_test, dtype=torch.float32)\ny_test_t = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)\n\nprint(X_train.shape)\nprint(y_train.shape)\n\ntrain_dataset = TensorDataset(X_train_t, y_train_t)\n\nbatch_size = 32\n\ntrain_loader = DataLoader(\n train_dataset,\n batch_size=batch_size,\n shuffle=True\n)\n\nmodel = nn.Linear(X_train_t.shape[1], 1)\ncriterion = nn.MSELoss()\noptimizer = torch.optim.SGD(model.parameters(), lr=0.1)\n\nepochs = 100\nloss_history = []\nfor _ in range(epochs):\n nb=0\n epoch_loss=0\n for Xb, yb in train_loader:\n optimizer.zero_grad()\n u = model(Xb)\n loss = criterion(u, yb)\n loss.backward()\n optimizer.step()\n epoch_loss += loss.item()\n nb += 1\n loss_history.append(epoch_loss/nb)\n\nplt.plot(loss_history)\nplt.show()\n\nwith torch.no_grad():\n y_hat = model(X_test_t)\n\ny_hat = y_hat.cpu().numpy().reshape(-1)\n\nprint(f\"MAE : {mean_absolute_error(y_test,y_hat):.2f}\")\nprint(f\"RMSE : {np.sqrt(mean_squared_error(y_test,y_hat)):.2f}\")\nprint(f\"MAPE : {mean_absolute_percentage_error(y_test,y_hat):.4f}\")\nprint(f\"R2 : {r2_score(y_test,y_hat):.3f}\")\n\nplt.scatter(X_test[:,1], y_test)\nplt.scatter(X_test[:,1], y_hat, c='red')\nplt.show()","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T02:27:26.779305Z","iopub.execute_input":"2026-05-13T02:27:26.780303Z","iopub.status.idle":"2026-05-13T02:27:33.677992Z","shell.execute_reply.started":"2026-05-13T02:27:26.780256Z","shell.execute_reply":"2026-05-13T02:27:33.677231Z"}},"outputs":[{"name":"stdout","text":"(3341, 4)\n(3341,)\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"
","image/png":"iVBORw0KGgoAAAANSUhEUgAAAiwAAAGdCAYAAAAxCSikAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjAsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvlHJYcgAAAAlwSFlzAAAPYQAAD2EBqD+naQAAYX9JREFUeJzt3Xl8FPX9P/DXHsluzg0k5CQQ7nAmkEAIHmiJBEQlai1SFES01aJi8yutoIKttcEqFFuwfLXijSCtoiKiGARBwhXCEe47AbI5CLnv3fn9sTuT3WST3cmxE/D1fDzyeMBmspmdJDvveX/e7/eoBEEQQERERNSFqZXeASIiIiJnGLAQERFRl8eAhYiIiLo8BixERETU5TFgISIioi6PAQsRERF1eQxYiIiIqMtjwEJERERdnlbpHegIZrMZV65cgZ+fH1QqldK7Q0RERC4QBAHl5eUIDw+HWt16DuWGCFiuXLmCyMhIpXeDiIiI2iA3Nxc9e/ZsdZsbImDx8/MDYHnB/v7+Cu8NERERuaKsrAyRkZHSebw1N0TAIi4D+fv7M2AhIiK6zrhSzsGiWyIiIuryGLAQERFRl8eAhYiIiLo8BixERETU5TFgISIioi6PAQsRERF1eQxYiIiIqMtjwEJERERdHgMWIiIi6vIYsBAREVGXx4CFiIiIujwGLERERNTl3RA3P+ws9SYz0jadgMlsxsIpg6HTapTeJSIiop8lZlhaIQjA6p/O4/2Mi6htMCu9O0RERD9bDFhaoVU33u7aZBIU3BMiIqKfNwYsrVCrVVBZY5YGMwMWIiIipTBgcULMspgYsBARESmGAYsTGmvA0mBmDQsREZFSGLA4oVVbDhEzLERERMphwOJEY4aFAQsREZFSGLA4wRoWIiIi5TFgcULKsLCtmYiISDEMWJxghoWIiEh5DFic0GjYJURERKQ0BixOsEuIiIhIeQxYnGCXEBERkfIYsDjBGhYiIiLlMWBxghkWIiIi5TFgcaIxw8KiWyIiIqUwYHGCc1iIiIiUx4DFCXYJERERKY8BixOsYSEiIlIeAxYntBp2CRERESmNAYsTzLAQEREpjwGLE+wSIiIiUh4DFieYYSEiIlIeAxYn2CVERESkPAYsTnAOCxERkfLaFLCsXLkSUVFR0Ov1SEhIwN69e1vc9ujRo7j//vsRFRUFlUqF5cuXt/s53UkrLQmxhoWIiEgpsgOWdevWITU1FYsXL8aBAwcQExOD5ORkFBQUONy+qqoKffv2xZIlSxAaGtohz+lOrGEhIiJSnuyAZdmyZXj88ccxe/ZsDBkyBKtWrYK3tzdWr17tcPvRo0fjtddew4MPPgidTtchz+lO0hwWLgkREREpRlbAUldXh8zMTCQlJTU+gVqNpKQkZGRktGkH2vKctbW1KCsrs/voLMywEBERKU9WwFJUVASTyYSQkBC7x0NCQmA0Gtu0A215zrS0NBgMBukjMjKyTd/bFewSIiIiUt512SW0YMEClJaWSh+5ubmd9r2YYSEiIlKeVs7GQUFB0Gg0yM/Pt3s8Pz+/xYLaznhOnU7XYj1MR+OkWyIiIuXJyrB4enoiLi4O6enp0mNmsxnp6elITExs0w50xnN2JLHolhkWIiIi5cjKsABAamoqZs2ahfj4eIwZMwbLly9HZWUlZs+eDQCYOXMmIiIikJaWBsBSVHvs2DHp35cvX8bBgwfh6+uL/v37u/ScStKwhoWIiEhxsgOWadOmobCwEIsWLYLRaERsbCw2b94sFc3m5ORArW5M3Fy5cgUjR46U/v/666/j9ddfx/jx47Ft2zaXnlNJWtawEBERKU4lCMJ1fyYuKyuDwWBAaWkp/P39O/S5V/5wBq99exLT4iPx6i9HdOhzExER/ZzJOX9fl11C7sQMCxERkfIYsDihYZcQERGR4hiwOMEMCxERkfIYsDih0bBLiIiISGkMWJxghoWIiEh5DFicaKxhYcBCRESkFAYsTjDDQkREpDwGLE6wS4iIiEh5DFic0Fqn9jaYmGEhIiJSCgMWJ1jDQkREpDwGLE6whoWIiEh5DFic0GiYYSEiIlIaAxYnmGEhIiJSHgMWJ9glREREpDwGLE5IXULMsBARESmGAYsT7BIiIiJSHgMWJ6QaFs5hISIiUgwDFieYYSEiIlIeAxYntBp2CRERESmNAYsTWnYJERERKY4BixMadgkREREpjgGLE1rWsBARESmOAYsTGk66JSIiUhwDFieYYSEiIlIeAxYnbNuaBYFBCxERkRIYsDghjuYHmGUhIiJSCgMWJzTWOSwA61iIiIiUwoDFCbGGBWCGhYiISCkMWJzQ2AQsvJ8QERGRMhiwOKFR2S4JcdotERGREhiwOKFWqyAmWbgkREREpAwGLC7Qcjw/ERGRohiwuEDD4XFERESKYsDiAi3H8xMRESmKAYsLxFksJhbdEhERKaJNAcvKlSsRFRUFvV6PhIQE7N27t9Xt169fj+joaOj1egwfPhybNm2y+3x+fj4eeeQRhIeHw9vbG5MmTcLp06fbsmudghkWIiIiZckOWNatW4fU1FQsXrwYBw4cQExMDJKTk1FQUOBw+127dmH69OmYM2cOsrKykJKSgpSUFGRnZwMABEFASkoKzp07hy+++AJZWVno3bs3kpKSUFlZ2b5X10GkolvOYSEiIlKESpB5R7+EhASMHj0aK1asAACYzWZERkbi6aefxnPPPdds+2nTpqGyshIbN26UHhs7dixiY2OxatUqnDp1CoMGDUJ2djaGDh0qPWdoaCj+9re/4bHHHnO6T2VlZTAYDCgtLYW/v7+cl+OSm5ZsxeWSanwx9ybERAZ0+PMTERH9HMk5f8vKsNTV1SEzMxNJSUmNT6BWIykpCRkZGQ6/JiMjw257AEhOTpa2r62tBQDo9Xq759TpdNi5c6ec3es0Wg2XhIiIiJQkK2ApKiqCyWRCSEiI3eMhISEwGo0Ov8ZoNLa6fXR0NHr16oUFCxbg2rVrqKurw6uvvopLly4hLy/P4XPW1tairKzM7qMzsa2ZiIhIWYp3CXl4eOCzzz7DqVOn0L17d3h7e+OHH37A5MmToVY73r20tDQYDAbpIzIyslP3sbHoll1CRERESpAVsAQFBUGj0SA/P9/u8fz8fISGhjr8mtDQUKfbx8XF4eDBgygpKUFeXh42b96Mq1evom/fvg6fc8GCBSgtLZU+cnNz5bwM2TTWwIkZFiIiImXIClg8PT0RFxeH9PR06TGz2Yz09HQkJiY6/JrExES77QFgy5YtDrc3GAzo0aMHTp8+jf3792Pq1KkOn1On08Hf39/uozOxrZmIiEhZWrlfkJqailmzZiE+Ph5jxozB8uXLUVlZidmzZwMAZs6ciYiICKSlpQEA5s2bh/Hjx2Pp0qWYMmUK1q5di/379+Ott96SnnP9+vXo0aMHevXqhSNHjmDevHlISUnBxIkTO+hlto9Uw8K2ZiIiIkXIDlimTZuGwsJCLFq0CEajEbGxsdi8ebNUWJuTk2NXezJu3DisWbMGL7zwAhYuXIgBAwZgw4YNGDZsmLRNXl4eUlNTkZ+fj7CwMMycORMvvvhiB7y8jsEMCxERkbJkz2Hpijp7Dsu0/8vAnvPFWPnrUZgyIqzDn5+IiOjnqNPmsPxcNc5hYZcQERGREhiwuIBdQkRERMpiwOIC1rAQEREpiwGLCzjploiISFkMWFzADAsREZGyGLC4oHEOC4tuiYiIlMCAxQXMsBARESmLAYsL2CVERESkLAYsLmCGhYiISFkMWFyg0bBLiIiISEkMWFzADAsREZGyGLC4oHEOC7uEiIiIlMCAxQXMsBARESmLAYsLpC4hEwMWIiIiJTBgcQEzLERERMpiwOIC3kuIiIhIWQxYXMAMCxERkbIYsLigcQ4Lu4SIiIiUwIDFBcywEBERKYsBiwt4LyEiIiJlMWBxATMsREREymLA4gKxS6jBxBoWIiIiJTBgcYGWbc1ERESKYsDiAg2XhIiIiBTFgMUFWg0zLEREREpiwOICsUuogfcSIiIiUgQDFhewhoWIiEhZDFhc0FjDwi4hIiIiJTBgcQEzLERERMpiwOICdgkREREpiwGLCzw0HM1PRESkJAYsLmCGhYiISFkMWFzAGhYiIiJlMWBxAbuEiIiIlMWAxQVa6+A4EwfHERERKYIBiwtYw0JERKSsNgUsK1euRFRUFPR6PRISErB3795Wt1+/fj2io6Oh1+sxfPhwbNq0ye7zFRUVeOqpp9CzZ094eXlhyJAhWLVqVVt2rVPwXkJERETKkh2wrFu3DqmpqVi8eDEOHDiAmJgYJCcno6CgwOH2u3btwvTp0zFnzhxkZWUhJSUFKSkpyM7OlrZJTU3F5s2b8dFHH+H48eN49tln8dRTT+HLL79s+yvrQMywEBERKUt2wLJs2TI8/vjjmD17tpQJ8fb2xurVqx1u/8Ybb2DSpEmYP38+Bg8ejJdffhmjRo3CihUrpG127dqFWbNm4bbbbkNUVBR+85vfICYmxmnmxl3YJURERKQsWQFLXV0dMjMzkZSU1PgEajWSkpKQkZHh8GsyMjLstgeA5ORku+3HjRuHL7/8EpcvX4YgCPjhhx9w6tQpTJw40eFz1tbWoqyszO6jM7FLiIiISFmyApaioiKYTCaEhITYPR4SEgKj0ejwa4xGo9Pt//Wvf2HIkCHo2bMnPD09MWnSJKxcuRK33nqrw+dMS0uDwWCQPiIjI+W8DNmkLiFmWIiIiBTRJbqE/vWvf2H37t348ssvkZmZiaVLl2Lu3Ln4/vvvHW6/YMEClJaWSh+5ubmdun+sYSEiIlKWVs7GQUFB0Gg0yM/Pt3s8Pz8foaGhDr8mNDS01e2rq6uxcOFCfP7555gyZQoAYMSIETh48CBef/31ZstJAKDT6aDT6eTseruINSyCAJjNAtTW/xMREZF7yMqweHp6Ii4uDunp6dJjZrMZ6enpSExMdPg1iYmJdtsDwJYtW6Tt6+vrUV9fD7Xaflc0Gg3MXaRmRKNpDFCYZSEiInI/WRkWwNKCPGvWLMTHx2PMmDFYvnw5KisrMXv2bADAzJkzERERgbS0NADAvHnzMH78eCxduhRTpkzB2rVrsX//frz11lsAAH9/f4wfPx7z58+Hl5cXevfuje3bt+ODDz7AsmXLOvCltp3WJqPCOhYiIiL3kx2wTJs2DYWFhVi0aBGMRiNiY2OxefNmqbA2JyfHLlsybtw4rFmzBi+88AIWLlyIAQMGYMOGDRg2bJi0zdq1a7FgwQLMmDEDxcXF6N27N1555RU88cQTHfAS20+jts2wmAFolNsZIiKinyGVIAjXfcqgrKwMBoMBpaWl8Pf37/DnN5kF9Ftomc57cNEdCPD27PDvQURE9HMj5/zdJbqEujrbGlvWsBAREbkfAxYXqFQqTrslIiJSEAMWF3EWCxERkXIYsLhIyrCYGLAQERG5GwMWF/F+QkRERMphwOIirYb3EyIiIlIKAxYXsYaFiIhIOQxYXMQuISIiIuUwYHERMyxERETKYcDiosYMC4tuiYiI3I0Bi4ukDAvbmomIiNyOAYuLtGp2CRERESmFAYuLWMNCRESkHAYsLtJqODiOiIhIKQxYXMQaFiIiIuUwYHER57AQEREphwGLi1jDQkREpBwGLC5ilxAREZFyGLC4iBkWIiIi5TBgcREn3RIRESmHAYuLmGEhIiJSDgMWF4lzWFjDQkRE5H4MWFyksRbdcg4LERGR+zFgcZEH57AQEREphgGLi1jDQkREpBwGLC5qrGFhlxAREZG7MWBxETMsREREymHA4iJOuiUiIlIOAxYXMcNCRESkHAYsLuLdmomIiJTDgMVFUoaFc1iIiIjcjgGLi3gvISIiIuUwYHGRNOmWS0JERERux4DFRbyXEBERkXIYsLiIXUJERETKaVPAsnLlSkRFRUGv1yMhIQF79+5tdfv169cjOjoaer0ew4cPx6ZNm+w+r1KpHH689tprbdm9TsEuISIiIuXIDljWrVuH1NRULF68GAcOHEBMTAySk5NRUFDgcPtdu3Zh+vTpmDNnDrKyspCSkoKUlBRkZ2dL2+Tl5dl9rF69GiqVCvfff3/bX1kHY4aFiIhIOSpBEGSdgRMSEjB69GisWLECAGA2mxEZGYmnn34azz33XLPtp02bhsrKSmzcuFF6bOzYsYiNjcWqVascfo+UlBSUl5cjPT3dpX0qKyuDwWBAaWkp/P395bwcl32YcQEvfnEUdw4PxZsz4jrlexAREf2cyDl/y8qw1NXVITMzE0lJSY1PoFYjKSkJGRkZDr8mIyPDbnsASE5ObnH7/Px8fP3115gzZ06L+1FbW4uysjK7j84mdQlxDgsREZHbyQpYioqKYDKZEBISYvd4SEgIjEajw68xGo2ytn///ffh5+eH++67r8X9SEtLg8FgkD4iIyPlvIw2YQ0LERGRcrpcl9Dq1asxY8YM6PX6FrdZsGABSktLpY/c3NxO3y/WsBARESlHK2fjoKAgaDQa5Ofn2z2en5+P0NBQh18TGhrq8vY7duzAyZMnsW7dulb3Q6fTQafTydn1duMcFiIiIuXIyrB4enoiLi7OrhjWbDYjPT0diYmJDr8mMTGxWfHsli1bHG7/zjvvIC4uDjExMXJ2yy0aMywczU9ERORusjIsAJCamopZs2YhPj4eY8aMwfLly1FZWYnZs2cDAGbOnImIiAikpaUBAObNm4fx48dj6dKlmDJlCtauXYv9+/fjrbfesnvesrIyrF+/HkuXLu2Al9XxWMNCRESkHNkBy7Rp01BYWIhFixbBaDQiNjYWmzdvlgprc3JyoFY3Jm7GjRuHNWvW4IUXXsDChQsxYMAAbNiwAcOGDbN73rVr10IQBEyfPr2dL6lz8F5CREREypE9h6Urcscclh9OFGD2e/swoqcBXz51c6d8DyIiop+TTpvD8nMm1bBwDgsREZHbMWBxEWtYiIiIlMOAxUXsEiIiIlIOAxYXcQ4LERGRchiwuIhdQkRERMphwOIiLYtuiYiIFMOAxUW8lxAREZFyGLC4qLFLiEW3RERE7saAxUXMsBARESmHAYuLtNaiW3YJERERuR8DFhdpNMywEBERKYUBi4s46ZaIiEg5DFhcpLEJWG6A+0USERFdVxiwuEjMsADMshAREbkbAxYXaWwCFtaxEBERuRcDFheJXUIAMyxERETuxoDFRcywEBERKYcBi4tYw0JERKQcBiwuUqtVEGOWBo7nJyIicisGLDJw2i0REZEyGLDIIN1PyMSAhYiIyJ0YsMjAabdERETKYMAiA+8nREREpAwGLDIww0JERKQMBiwySDUs7BIiIiJyKwYsMrBLiIiISBkMWGRozLAwYCEiInInBiwysIaFiIhIGQxYZOAcFiIiImUwYJFBwwwLERGRIhiwyKDVsEuIiIhICQxYZNCwS4iIiEgRDFhk0LJLiIiISBEMWGRgDQsREZEyGLDIwAwLERGRMtoUsKxcuRJRUVHQ6/VISEjA3r17W91+/fr1iI6Ohl6vx/Dhw7Fp06Zm2xw/fhz33HMPDAYDfHx8MHr0aOTk5LRl9zpNY4aFRbdERETuJDtgWbduHVJTU7F48WIcOHAAMTExSE5ORkFBgcPtd+3ahenTp2POnDnIyspCSkoKUlJSkJ2dLW1z9uxZ3HzzzYiOjsa2bdtw+PBhvPjii9Dr9W1/ZZ1AyzksREREilAJgiDr7JuQkIDRo0djxYoVAACz2YzIyEg8/fTTeO6555ptP23aNFRWVmLjxo3SY2PHjkVsbCxWrVoFAHjwwQfh4eGBDz/8sE0voqysDAaDAaWlpfD392/Tc7jisff34/vj+Vhy33A8OKZXp30fIiKinwM5529ZGZa6ujpkZmYiKSmp8QnUaiQlJSEjI8Ph12RkZNhtDwDJycnS9mazGV9//TUGDhyI5ORkBAcHIyEhARs2bGhxP2pra1FWVmb34Q6sYSEiIlKGrIClqKgIJpMJISEhdo+HhITAaDQ6/Bqj0djq9gUFBaioqMCSJUswadIkfPfdd7j33ntx3333Yfv27Q6fMy0tDQaDQfqIjIyU8zLaTKNhlxAREZESFO8SMlsLWKdOnYrf//73iI2NxXPPPYe77rpLWjJqasGCBSgtLZU+cnNz3bKvzLAQEREpQytn46CgIGg0GuTn59s9np+fj9DQUIdfExoa2ur2QUFB0Gq1GDJkiN02gwcPxs6dOx0+p06ng06nk7PrHYJdQkRERMqQlWHx9PREXFwc0tPTpcfMZjPS09ORmJjo8GsSExPttgeALVu2SNt7enpi9OjROHnypN02p06dQu/eveXsXqdjhoWIiEgZsjIsAJCamopZs2YhPj4eY8aMwfLly1FZWYnZs2cDAGbOnImIiAikpaUBAObNm4fx48dj6dKlmDJlCtauXYv9+/fjrbfekp5z/vz5mDZtGm699Vbcfvvt2Lx5M7766its27atY15lB5HuJcS2ZiIiIreSHbBMmzYNhYWFWLRoEYxGI2JjY7F582apsDYnJwdqdWPiZty4cVizZg1eeOEFLFy4EAMGDMCGDRswbNgwaZt7770Xq1atQlpaGp555hkMGjQI//vf/3DzzTd3wEvsOGKGpZ4ZFiIiIreSPYelK3LXHJaXvjyK93ZdwNzb+2F+cnSnfR8iIqKfg06bw/JzxxoWIiIiZTBgkUGaw8IaFiIiIrdiwCIDMyxERETKYMAig9QlxICFiIjIrRiwyMAMCxERkTIYsMjASbdERETKYMAiAzMsREREymDAIkNjhoUBCxERkTsxYJGBGRYiIiJlMGCRQaPhvYSIiIiUwIBFBg9mWIiIiBTBgEUGdgkREREpgwGLDFoNMyxERERKYMAiAyfdEhERKYMBiwzsEiIiIlIGAxYZOIeFiIhIGQxYZGCGhYiISBkMWGRglxAREZEyGLDIoLUW3TZwcBwREZFbMWCRgTUsREREymDAIoM4h4UBCxERkXsxYJFBw6JbIiIiRTBgkUHLJSEiIiJFMGCRoTHDwi4hIiIid2LAIoOWo/mJiIgUwYBFBtawEBERKYMBiwxSDQvnsBAREbkVAxYZmGEhIiJSBgMWGTiHhYiISBkMWGRglxAREZEyGLDIIHYJmQXAzCwLERGR2zBgkUHMsACASWDAQkRE5C4MWGTQ2gYszLAQERG5DQMWGWwzLOwUIiIich8GLDLYZVg4i4WIiMht2hSwrFy5ElFRUdDr9UhISMDevXtb3X79+vWIjo6GXq/H8OHDsWnTJrvPP/LII1CpVHYfkyZNasuudSr7DAs7hYiIiNxFdsCybt06pKamYvHixThw4ABiYmKQnJyMgoICh9vv2rUL06dPx5w5c5CVlYWUlBSkpKQgOzvbbrtJkyYhLy9P+vjkk0/a9oo6kUqlkoIW1rAQERG5j+yAZdmyZXj88ccxe/ZsDBkyBKtWrYK3tzdWr17tcPs33ngDkyZNwvz58zF48GC8/PLLGDVqFFasWGG3nU6nQ2hoqPTRrVu3tr2iTiYGLPUMWIiIiNxGVsBSV1eHzMxMJCUlNT6BWo2kpCRkZGQ4/JqMjAy77QEgOTm52fbbtm1DcHAwBg0ahCeffBJXr15tcT9qa2tRVlZm9+EuvJ8QERGR+8kKWIqKimAymRASEmL3eEhICIxGo8OvMRqNTrefNGkSPvjgA6Snp+PVV1/F9u3bMXnyZJhMJofPmZaWBoPBIH1ERkbKeRntwmm3RERE7qdVegcA4MEHH5T+PXz4cIwYMQL9+vXDtm3bMGHChGbbL1iwAKmpqdL/y8rK3Ba0aFnDQkRE5HayMixBQUHQaDTIz8+3ezw/Px+hoaEOvyY0NFTW9gDQt29fBAUF4cyZMw4/r9Pp4O/vb/fhLhrreH7OYSEiInIfWQGLp6cn4uLikJ6eLj1mNpuRnp6OxMREh1+TmJhotz0AbNmypcXtAeDSpUu4evUqwsLC5OyeWzDDQkRE5H6yu4RSU1Px9ttv4/3338fx48fx5JNPorKyErNnzwYAzJw5EwsWLJC2nzdvHjZv3oylS5fixIkTeOmll7B//3489dRTAICKigrMnz8fu3fvxoULF5Ceno6pU6eif//+SE5O7qCX2XEaa1gYsBAREbmL7BqWadOmobCwEIsWLYLRaERsbCw2b94sFdbm5ORArW6Mg8aNG4c1a9bghRdewMKFCzFgwABs2LABw4YNAwBoNBocPnwY77//PkpKShAeHo6JEyfi5Zdfhk6n66CX2XG0GjHDwqJbIiIid1EJwvV/2+GysjIYDAaUlpZ2ej3LL5Zuw7nCSqz7zVgk9A3s1O9FRER0I5Nz/ua9hGRiDQsREZH7MWCRiV1CRERE7seARSZmWIiIiNyPAYtM7BIiIiJyPwYsMnmwS4iIiMjtGLDIxAwLERGR+zFgkUlrLbplDQsREZH7MGCRScqwmBiwEBERuQsDFpnYJUREROR+DFhkYg0LERGR+zFgkYn3EiIiInI/BiwycdItERGR+zFgkYk1LERERO7HgEUm1rAQERG5HwMWmZhhISIicj8GLDJxDgsREZH7MWCRqTHDwi4hIiIid2HAIhO7hIiIiNyPAYtMjXNYGLAQERG5CwMWmdglRERE5H4MWGRilxAREZH7MWCRqTHDwqJbIiIid2HAIhMzLERERO7HgEUmL08tAKCsukHhPSEiIvr5YMAiU5hBDwAwltUovCdERD9vucVVKK2qV3o3yE0YsMgUKgYspQxYyLHT+eX4+nCe0rtBdEM7V1iBCUu346F39kAQuET/c8CARSYxw5JfVsM6FnIo9dNDmLvmAHadLVJ6V4huWJuPGlFnMuPI5VIculSq9O6QGzBgkamHrw5qlWUOy9WKWqV3R3Fms4AXNhzBqu1nld6VLsFkFnDSWA4A2HGaAQtRZ9l2olD692cHLim4J+QuDFhk0mrUCPazZFnyuCyE48YyfLQ7B0u+OYEfThYovTuKu1JSjTqTpeU94+xVhfeG6MZUWlWPzJxr0v+/PHQFdQ0cNXGjY8DSBmIdCwMW4EpJ4zF44fNsVNb+vLunzhdVSv8+crkUFT/z40HUGXacKYTJLKBvDx8E++lQUlXPC6afAQYsbSB1CpVWK7wnyrtS0ngMLpdUY9mWU536/S5ercTWE/md+j3a48LVxoDFZBaw70KxgntDHe2EsQw19Sald+Nn7wfrclDS4BCkjIwAwGWhnwMGLG0gZVi6SGvzsu9O4u+bTyjyva9Yg7boUD8AwLs/ncfhSyWd9v1+9/EBPPrefhzK7bzv0R62GRYA2H2Oy0I3io2Hr2DS8h1Y8o0yf2tkYTYL2H7Kkk25bVAP3DfKErBsPVGAkqo6JXeNOhkDljYI60KtzVcravHPrWfw5razKCh3//6IS0L3j+qJqbHhMAvAc/87gnpTx68nF1XU4uiVMgDAyfzyDn/+jnDBGrDE9+4GANjNOpYbxrp9uQCAnWdYTN0eucVV+PXbu9ucKc2+Uoqiijr46rSI790d0aH+GBLmj3qTgK86cZzAS18exaTlP+JyCTPrSmHA0gYh/l2nhsX2iv5CUZXbv3+e9Y83LECPF+8aggBvDxzLK8M7O893+Pfab7O8cvla13zTuHDV8jN4cEwvAJY6lvKa62OwVV2DGWa26jt0taIWu6zB57nCClTXcVmorT7Zm4NdZ6/iD+sPo6wNfxtbT1iyKzf3D4Kn1nIKE7MsnbUsVG8yY82eHJwwluOZT7I65YKMnGPA0gZhBi8AllksSjtXaBuwVLayZecQa1jCA7wQ5KvD83cOBgD8Y8sp/H3zCXyYcQHfHTXi8KWSdr/J7zlvE7B0waucBpMZucWWgGVcv0D0DvSGWYDTOpaK2ga899N53PnGDsxff6jDg4bK2gb8M/00TreSlbpQVImYP3+Hp9dm3TBDuOoazNh6Ih+p6w4iadl2PPrePvx98wl8eegKTueXy5qj9E22UdreLFhqWaht9l+wdPcUV9bhzR/kj0P44aSlfuX26B7SY/fEhkOjViErpwTnCis6ZkdtnC2skLr/Mi9ew9LvOrdWjxxrU8CycuVKREVFQa/XIyEhAXv37m11+/Xr1yM6Ohp6vR7Dhw/Hpk2bWtz2iSeegEqlwvLly9uya24RZtMlpPSb+zmbIOX8VfcGLA0mM/LLLbNoIgIsQdwv43ripv6BqG0w481tZ/HiF0fxmw8zcc+Kn5C0bHu7Chb3nu/aGZZL16rRYBag06oR6q/H2D6BAIDd5xwHLDlXq/CXr44h8W/peOmrYziWV4b1mZfwbxkzbUqr6/H2j+dQWN7yTKC/bz6BZVtO4c9fHWtxm2+PGlFdb8LXh/Pw3bGuW9Tsin0XijF//SHE/3ULHn1vPz7LuowzBRXYeqIAb247i2c+ycId//gR9775k8t/vxsPX7H7v7g0SfLUNphw0KbGbfVP53HpmuuZ4aKKWqlG7rZBwdLjwX563DogCADwedblDtlXW0cvW37e3bw9AACrtp9lV5ICZAcs69atQ2pqKhYvXowDBw4gJiYGycnJKChw/MPbtWsXpk+fjjlz5iArKwspKSlISUlBdnZ2s20///xz7N69G+Hh4fJfiRsF++sAWK7gril8Hwvbqwl3Z1gKymthMgvQqlUI8rUcE5VKhf97OB4vTBmMmYm9MXFICGJ6GqD3UONySTW+PWps0/cqq6nHsbzGk0RnZFjyy2pQ0I6smRgwRgX6QK1WIbGfGLA0r2P5v+1nMf71H7D6p/Mor21A3x4+mG5dRlr63UmXp+R+sOsCXtl0HE98lOkwM3OhqBIf78kBYDmR1zY4Dhhts1d/+erYdbvkcaGoEg+sysD6zEsoq2lADz8dHhkXhf/MjMfLU4fi1wm9ENe7G1Qq4PClUlxxYVm3oLxGOj53x1jem2x/F91FEATklVYrfpHUHtmXS1HXYEagjycS+wairsGM17496fLX/3iqEIIADAnzl5bmRfeN6gkA+OzA5Q7PUooB6tTYCMxK7A0A+H+fHuoSdYw/J7IDlmXLluHxxx/H7NmzMWTIEKxatQre3t5YvXq1w+3feOMNTJo0CfPnz8fgwYPx8ssvY9SoUVixYoXddpcvX8bTTz+Njz/+GB4eHm17NW6i02oQ5OsJAMhTuLXZLsPi5oBFfO2hBj00apX0uK9Oi8du6Yu/TB2Gt2bG44unbsYT4/sBANbuzW3T98q8cA2CAPjptdL37sg3pZp6E6b8cwcmLv+xzcXLYsAYFeQNABjb1xKwZF8utVurP5Vfjte+PQlBAMYP7IH3Zo/G978fj7T7huOXcT1hFoBnPjno0n6cKrAErJkXr2Hd/ubH9rXvTqLBepxqG8w4mFPSbBuTWcA+6wnZx1ODyyXV+Pe2MzJeedch1pn0D/bFJ4+Pxe4FE/DSPUORNCQEDydG4W/3Dsf/nhyHQSGWrraTLiztfHPECEEAYiMDMHFICABlMizr9uUiMW0rPrIGoNcjcTkornc3PD9lMFQq4IuDV3DQxa4/R8tBojuGhMBPp8Xlkmos/PwIdpwu7LBhckevWEb/Dw33x8IpgzEswh/FlXV45pMsNChUz7LrbBHi//o91u3rnN+HrljPJitgqaurQ2ZmJpKSkhqfQK1GUlISMjIyHH5NRkaG3fYAkJycbLe92WzGww8/jPnz52Po0KFydkkxXeEmiCazgIs2y0AXr1a59errsrVDKNxa09OaB+IjoVIBGeeutikTJF7hThwSCo1ahXqTgIJWlkHkOmEsR1FFHUqq6rGsjevTjQGLDwDL70ifIB9LHYt1/wVBwIsbstFgFjBxSAjef3QMbhsUDLU14Ht56jAMCvFDUUWtS2+Gtj//Jd+cQJHN7SIO5Zbg68N5UKksb7SA4+Wp43llKK9tgJ9OiyX3jwAArPrxnN1zXy/Ewuw7h4UisV+gXSBta5C1Df94nvNuM3E56K4RYdJxPJFX1uYTlSAIeH/XBew4Xeh8Yxv/sxaUftfGLGVXsM8asIyO6o5hEQbcN9KSFXnl62NO37saTGb8eMoasNgsB4n0Hhr8eqwlS7l2Xy4efmcvRr28BU9+lGlXsC+XIAhSRm1ouAE6rQYrpo+Cr06LvReKsfz7021+7raqazDj+c+zUVRR2ykNDv/ZcQ7DXvoWu7pYR5ysgKWoqAgmkwkhISF2j4eEhMBodPxHZDQanW7/6quvQqvV4plnnnFpP2pra1FWVmb34W6h/paTtJKdQpeuVaHeJMBTq4ZGrUJ1vQn5Ze67v1GeVHCrd7Klpcbl1gGWq6JPHWQCnNl73nLlPK5fIEKtqeDLJR3XFXXM5op53f5cu//byi+rabF49by1Q6hPoI/02Ni+3QE0jun/4uAV7DlfDL2HGovuHtLsObw8NXjzoVHw8dRg97li/OP71oOni9bvGeSrQ2l1PV75+jgAy5ts2jeWf983sqe03ORoeUoMBuOjuuGuEWG4uX8Q6hrM+EsrNS9yfH04Dze/uhXfHGl/y2lFbUOrV377LoqvpXurzxMdagk8xPs+tSSvtFo6yU4ZEYaoQB94e2pQ22Buc0Yz+3IZFn95FI+9v18q0namtLoeB6zZsUO5JV1iWaiuwYx73/wJD7+zx6WrcbNZQObFxt81APhD8kDoPdTYd+Ga0+Xig7klKK2uh8HLA7GRAQ63+VNyNN6eGY8HR0eih58OFbUN+CbbiBn/2WMXzMtx6Vo1ymsa4KFRoX+wLwDLRcmS+4cDAFZuO2NXX+cO7++6IP3+ncqvQM5Vx79HNfUmvLr5BLafkhccbzqSh6o6E/6y8ViXyrQo3iWUmZmJN954A++99x5UKsdXQ02lpaXBYDBIH5GRkZ28l811xiyWitqGVjs5mhKXg/oE+qBnN0sAdcGNV8VXpJZm5xkWAHhwtOXntD7zkqyr0+o6Ew5b78Y6pk93qcD3UguFt+U19ciyuc+IK8SUr1atgiAAr2xqfsV3Kr8cdyzbjin/2ulwKbBphgVoXBbaff4qymrq8VdrQPH0LwagZzdvh/vSr4evlOlY+cNZ7Glh+FxJVR1Kqy1LTf+aPhIqlaXg8KczRdh2shC7zxXDU6tG6sSB0n5k5lxrVvgsPv+YPoFQqVR46Z6h8NCokH6iAOnH21eAu/N0EZ5dl4VL16rx/IZslLaj5mvH6ULEvbwFf/jvIYefN5bWILe4GmoVMLJXQKvPJQ46dNbts+mI5SQa37sbwgxeUKtVGBxmCXbauix03Po9axvM+OvXrgWFP50pkrqUymoapPZ5JR3LK0NWTgl2nC7CTy7UXJ0rqsC1qnrotGoMDTcAsHRcPn5LXwCWDGFrSzhikev4gT2g1Tg+danVKtwxJARL7h+BPQsm4Iu5NyE61A+1DZa25LYQ3xsGhvhJbdQAcNeIcDwQ1xOCAPx+3cE2tWi3RVFFLf6Zbsnq+OosS+Tft/B3+sneHPx721nMWr0Xad8cd+l9VxAEnM63LDWfMJbjqyYF50qSFbAEBQVBo9EgP9/+4OTn5yM0NNTh14SGhra6/Y4dO1BQUIBevXpBq9VCq9Xi4sWL+H//7/8hKirK4XMuWLAApaWl0kdubtvqItqjI+8ndKWkGn/bdByJf0vHHf/4ER/uvujS14ktzX17+CDKelXvzsJbaUnIxYBlwuAQBPl6orC8VlqLtlVR2+AwEMjKuYYGs4Bwgx49u3khwhqctVR4u/jLo7j3zV34z45zrr4UKeX7+zsGwlOjxk9nrkrzHgDLlfas1XtRVtOAugYzdpyyf4OuazBL3Q59bAKWRGugcPRKGV768iiKKmrRN8gHj93Sp9X9uTsmHPdYCzxbejMSsyvBfjok9gvEw2MtxYAvbMiWprHOHheFiAAv9Ovhgx5+OtQ1mO3qBcxmAXut6fIEazaof7AvHr3Zsn9//upYmzu7si+X4rcf7ke9SYBGrUJxZZ3TjFFLLl2rwjOfZKG2wYyNh/Ic3rNqv/XqfXCYP/z0rdfBiUtC5worWyxEBuyXg0TislBbC2/PFjQWyn97NN+lpaFtTTpSDubKC8g7w5HLpdK/P97tPBgQ61diIwPsTvy/Hd8PQb46XLhahbd+dNwhV1pVj0/3W5bEHNWvOKJWqxATGYAnb7PUz320+2KbalrEwFT8udtafM9Q9Orujcsl1Vj8xVHZz90WS787hfLaBgyPMODpX/QHAKS3MIRvg03H1P9tP4dfv73H6UV2flktym3+vv6x5VSXmTsjK2Dx9PREXFwc0tPTpcfMZjPS09ORmJjo8GsSExPttgeALVu2SNs//PDDOHz4MA4ePCh9hIeHY/78+fj2228dPqdOp4O/v7/dh7tJGZYy14puiypq8c2RPHx31IgfThZg15kibD9ViHlrs3Dr33/AWz+ek35JXvn6GM4UOJ8lcL7Isk2fIB/pJNnW1uZ6kxmZF4utVfiupQDF4CLc4HxJCAA8tWrcb63kb1oodjq/HLf+/Qfc/vq2Zssx4pLFmD7doVKppAxLS63NmRctb4x///akSxkrk1nACWstQ/LQUOlk/cqm46g3mVFaXY9HVu9DXmkNxCRg0yvK3GtVMAuAt6cGwX466fFgfz369vCBIFi6FwDgL1OHQafVON2vMX0sAURLvwsXrcsJvQMtmZo/JA9CsJ8O54sqcTK/HAYvD/zuNssbmkqlkrIstneRPl1QgZKqenh5aDA8wiA9/swvBiDUX4+c4iq8vFH+0lBucRUeeXcfKutMSOwbiP/MjAcAfLj7ouwZJrUNJsz9+IDUkVdnMjucNrvfpj7CmTCDHv56LRrMAs4WOP6buXStClk5JVCpgDuHNwYsQ6QMS6nDr3PmtPXnKS5tvvTl0VZPpIIgSCn9gSGWJYlDuW373h3pqE3AsuV4vtO5VPta+Pn46rR4YYplftM/t55xuNSW9s1xFJbXol8PH0weFtbs862ZPCwMwX46FJTX4pts+cuSx6401q805avT4h/TYqC2Zje/PCQ/G1FZ24Dn/ncYr3970ul779ErpVhrfe9cdPcQ3GEtAt9zrrhZhudcYQUOXSqFRq3CK/cOk2pupvxzR6tB8ukCy3thRIAXgnw9ceFqFf6b2TXu0yR7SSg1NRVvv/023n//fRw/fhxPPvkkKisrMXv2bADAzJkzsWDBAmn7efPmYfPmzVi6dClOnDiBl156Cfv378dTTz0FAAgMDMSwYcPsPjw8PBAaGopBgwZ10MvseHIyLCazgIf+swdPfnwAv/kwE7Pf3Ydf/2cPZq3eiy8OXkGDWUBi30C8MyseN/cPQk29GamfHnQa1TZmWHwRZT1pOcuw1JvMuFZZh9ziKhy+VIJ3dp7HnPf2YeRftuD+f2dg5uq9eHnjcZeCFtuhca76lXVZaOuJAinSv3i1EjP+swfFlXWoqTdj8ZfZdt9/rxSwWE64rWVYqutMyLGeyOsazEj99JDT43i+qBLV9SboPdToE+SDubf3Q6CPJ84VVuLdn87jtx/ux8n8cvTw0+G1X8YAAH46c9VuH8Xj3jvQp9nSphgoAJY6iJut8yKcEdfLz7QwCOuizfcEAH+9Bxbf3Vi0Pvf2fjB4N2YaxGyPbR3LHmttUFzvbvCwSbP76LRYcv9wqFTAx3tysF5G3dHVilrMXL0XRRW1iA71w//NjMPt0cGYPCwUJrOAxV8clVWD8ZevjuHQpVIYvDyQPNTyBr31ePMxCuKAPrE+ojUqlaqxjiXfcQD1tXXMe0Kf7gi2aaEVT1xHr5S1qZZEDED/PHUognw9cbawEu/vutDi9ieM5cgvq4WXhwaPWZdPXO2q6UxihkXvoYbJLODTfa3/juy/2PLPZ2psOG4ZYKmdWvjZEbvjuutsEdZan3vJ/SOg93Ae7Nvy1KrxkDX7+O5PF2R9LdB6hgUA4np3x1O/GAAAeOHzI3Y3hHWmpt6E336YibX7crHihzNY30pgIAgC/vLVMQiCJeM3Oqo7+vbwRd8ePmgwC1JBsmjDQUvwdMuAIMxI6I2vnr4Zg8P8cbWyDrNW722xfktcDhoW4Y+5t1sueN74/nSXuOmn7IBl2rRpeP3117Fo0SLExsbi4MGD2Lx5s1RYm5OTg7y8xih23LhxWLNmDd566y3ExMTgv//9LzZs2IBhw4Z13KtQgDjt1ujC8Lj/HbiEE8Zy+HhqMLJXAIZF+GNgiC/6BvngvpER2Pj0zfjkN2MxYXAIXntgBPz1Why+VIoVW1tvLbVbEgoSl4Qcr20v/PwIBr3wDQY8/w1GvrwFt/z9B9yz4ie8vPEY0k8UoKK2AQYvy8lt9U/n8fyG7FaLrarrTNIVrytdQqJ+PXwxJqo7zILluOSVVuPXb+9BQXkt+gf7wstDg30XrknDn+oazDhgrUcRMw6tZVjOFlZY2p91Whi8PHDksvPjKKb2o0P9oVGr4Kf3QOrEgQCAv206gd3niuGr0+K92aNxd0wY9B5qFFXU4lR+YyAhXhX2CWpelzLOOo/F21MjXUm6QgxYLl2rdjgXRcqwdG/8nncOD8WjN/XBncNDMTMxym57sQA4K6dEevPZY+0aSujTPCtx26BgPDvBchye35CN7MvOr+obTGY89sF+nC+qRESAF95/dAz8rcszz08ZDL2HGnvOF2Oji/d8+V/mJXy8JwcqFbD8wVg8PNbymtJPFNj9fpbX1OO49ecY39t5hgUAosOsdSwtdAp9bS0SnjLCfi7UgBBfaNUqlFTVy14Srqk3Ide6dDiyVwD+OCkaAPBG+ukWZwBtsy6fJvYLlH5Ox66UtbqU1dlqG0w4Zc1ePmU9qa3dl9vi9OCC8hpcvFoFlQoY1bt5wKJSqfBKynDoPdTIOHcV/7NmI2vqTVj42REAwENje7mUPXNk+phe8NSocTC3RFZ929WKWhjLLJnV6LCWM/lP/6I/YiIDUFbTgNRPD7pUqNpgMuOZT7Kw80yRlLn9y1fHWhyktznbiD3ni6HTqrHgzsb3kaTBlnNvuk0QLwiCtBx0r/Vu1n2CfPD578ZhdFQ3mAVIN5BsSswADgj2w68TeiHcoIexrAYfuViq0JnaVHT71FNP4eLFi6itrcWePXuQkJAgfW7btm1477337LZ/4IEHcPLkSdTW1iI7Oxt33nlnq89/4cIFPPvss23ZNbcR07lVdSaU1TRfTxfV1Jvwjy2Wdftnkwbi89/dhI1P34Lvfj8eW/9wG5ZNi8Uwm1R8mMELL6dYgrkVP5xp8UqqsrYBRusbXF+bJaELVyub/bGUVtXjk705qLVJO+s91Ajy1eHWgT2wYHI0Nj59M7JevAN//+UIqFXAmj05+MP6Qy0WaYl3afbx1MDfS9vi63dkmjXLsmZPDmb8Zw8ul1QjKtAbax5PwNMTLG9+f9t0AmU19ThyuQS11kFT/XpYXqNthqVpsCimMweH+dsdx9buIG07Y0Hax/hIKf2uVauw6qE4qaVRfNP8yWZZ4oLN0LimJg0NxZO39cO/H4qTAl1XBPp4opu3BwTBEog1JXYG9LapmVGpVFh09xC8OSOu2ZVonyAfBPvpUGeyBIGCIEjLbQk2WSBbT/+iPyZEB6OuwYzffpiJa5Wt3w33v5mXkJVTAn+9Fh/MGWM33KtnN288OV78+R5HVZ3jv5sGkxnG0hpsO1mA5zdYTlbP/GIAbh8UjDF9usNXp7VMPLUJoLJySmAWgMjuXlL205lBUuFt84CloKwGhy+VQqWy/Pxs6T00UjApt/D2XGElBAHw12vRw1eHX47qiZjIAFTUNmBJC3dct70zca/u3gjw9kCdydxioOUOJ43lqDcJ6Obtgcdu6QuDlwcul1Q3u8oXZVqXgwaF+EkBbFO9Ar0xzxogv/L1MRRX1uGN9NO4cLUKIf46Kbhrix5+Omno33sOslmCIDhclhN/vlGBPlKBqyMeGjWWT4uFt7W7z7b+zRGzWcAf/3sY3x3Lh6dWjQ8eHYNRvSy/B3/87+Fm7+FnCiqkSdW/vbWvdNEGABOiLS3eP5wskN6vD+SUIKe4Ct6eGmnZCLD87ooTgo9cdvy7Ky6jDwjxhU6rwbNJlp/Jm9vOosJB7Zg7Kd4ldL3y8tQgwJpub62I6d2fLiCvtAYRAV542Doh0ZmpsRG4OyYcJrOA1HUHHV5di1f03X08EeDtiYgAL2jVKtQ2mKVARrT/YjEEAYgK9MahRRNx+pXJOPHyZOx/IQkfPDoGvx3fD8MiDFCrVfhVfCSWPzgSGrUKn2VdxjNrsxz+IefZFNy62t0lunN4mDTg6VxhJcINenz0WAKC/fR47Oa+6Bvkg6KKWvxjy6lm9StAY4alqs6EkiZdJ2I6c0CIL+6JCceUEWGW4/jpoRZTmuIa9RCbgEWrUSPtvhEYGu6PNx4cabeMc1N/y79tp9GKmS3bDiHb5/rTpGiMH+hasaBIpWpso3QUsIhBkm2GxdnzNU7fLca5okoUVdTCU6vGiJ7N1+cBS+Hismmx6B1oKSx8Zm1Wi1fRVXUNWGYNzuclDUS/Hr7Ntvnt+L7o2c0LeaU1eOnLo3h/1wX8deMxPPFhJu761w7E//V7DHjhG4xNS8cj7+5DTb0Ztw7sgWcmWFLunlo1bh1oOf5bbYqRxTkbo13MrgCNrc2Oamp+PG352Q6PMKCHTU2SSPxdkVvHIi7vDQjxg0qlglqtwp/vsSzjfXbgcrN5IeU19VJtzviBPaBSqRDTMwAAcMhBEH62sAJTV+zEbz7Yjw8yLuBcYUWntECLy0HDIgzQe2jwyzhLbdrHexxfhbdUv9LUY7f0QXSoH65V1WPuxwfw1o+WwvmXpw5rMdBx1eybogBYlvps621+PFWIcUu2ImnZdqnrTnTUwXtDS/oE+Ug3YWztjt6CIGDxl0fxWdZlaNQqrPz1KNwyoAeW/ioWXh4a7Dp7FR/ZHMc9567i/n/vgrGsBn2DfPBb6xBOUVzvbjB4eaCkqrH1/YuDluxK8tBQeHvaB1pirZqjjKkgCHYZFsByY8m+QT4orqzDOzs6fuaLHAxY2iFUumuz4zXLkqo6vGmdGJp6x0BZa68vTx2KEH8dzhVVYol1noatxiUIywlSq1EjsrvjOhaxBmRs30AYvD3sahUcuScmHP+eMQqeGjU2HTFi8ZfNb6Mgt6XZlpenBlNHWq52gnx1+PjxsVKLr6dWjZesb+AfZFzE/6xrumNsliz0Ho2ThpvWsTT+sVlOln+dOgw9/HQ4U1CBpd81HwEuCEKLRXVxvbvh62duwZQR9kV+N1sDlt3niqUrmqY/j44i1bE0KbytrjNJg/PEoltXSG3WZ69Ky0EjIwNa/d00eHlg1UNx0HuoseN0EZZtcTxKffXO8ygor0Vkdy88ZB3g1ZTeQ4MX77LMn/l0/yUs/vIo/rPzPDYfNSL7chmKKmohCIBGrUKYQY9JQ0PxxrRYuwFwE6ItV4zf26TAxROis/krtsQMS35ZbbPMkZgpEGcHNSUW3rY0r6clZ6xXr/1tgrnYyABMi7dkHef/97DdBcpPZ66iwSygT5CPVKskziBxNLV41bazOHSpFN8dy8eiL47iF0u346YlW/HihuxW7zfVVIPJjE/35ba4fJJtvToXs8PinJ+tJwoc1nC0Vr9iy0OjRtp9w6UhkyazgDuHh2LiUMddqHIMizBgdFQ3NJgFfLz7ImrqTXjpy6OYuXov8kprkFNchbV77ZsBGgfGudbYMa5f84uZplb/dAEf7r4IlQpY9qsYKQPSJ8gHC+60ZJH+tuk4zhdV4ouDl/HwO3tRWl2Pkb0CsP6JRPg0yfRoNWrcPsjye/r98XzUm8zSkmuKdTnIlhiwnC+qbFaoW1hRi9LqeqhVllID8fnFJfK3d5xzmmXtTAxY2sHZLJaVP5xBeU0DokP9HP7itCbA21Mq8Px4T06zyF+qX7E5QYqFt007hWyzFK6aODQU/5w+EgDw1aG8ZlfV4pJQhAtD4xxJvWMQ5t7eD5/+dmyzk/ytA3tg0lBLgeZZ6+tsuu8tzWJpTGdaTkbdfDyx5D7LgKf3d11s9gdaUF6Lq5V1UKsgjWt3ZkiYPwK8PVBR24BDl0pRU2+SjoejJaH2ELMUTQMWsbDY4OWBAG9Pl59PLLw9mFsiLTW0tBxka3CYP161mQ3TdPjf1YparNpuuRr+w8RBrXZBTRwSgtk3RWFYhD+Sh4bgsZv74KW7h+A/M+Px9TM3Y9/zSTj918nIWDABqx6OQzcf+9d326AeUKksJ5O80mrUm8zIyhWv4J0X3Ip8dVpEdrf8HtkuC5nNgnSFfGsLWTHbwls5xAyLGIiKFt45GKH+epwvqsTfv21cGhK7g2yzc1LA0iTDUlnbINXdzEzsjXH9AuGpUeNKaQ0+3H0RScu2Y/3+XKcZl4KyGsz4zx788X+H8fgHmQ4zauLVuXjy6x/si7F9LbVpa5sU31bVNUjHyZWAcmSvbphpLZL112ulC5iOMPsmSwfgR3tyMOWfO6TlIfH35t2fLthllBuXix1nIJsSLwhO5Ve0GCB+Yg2KFkyOxtRY+/PCQwm9cVP/QNTUm/Hrt3dj3tqDqDOZMXlYKD55fCwCfZtn+wAgaYgYxFva5Isr6xDkq8NN/Zr/bXfz8ZTmdjXNspyxZqh7dfe2u4i5c1gY4np3w4yEXtJUbiUwYGmH1jqFLl2rwvu7LGm9P02ObnFEeGtuHdgDA0N80WAWsLVJn73U0tzDJmCRCm8bA5bK2gbpl1JOwAI03pujorahWdpcyrDIqMmw1d3HE/OTo9HXwbIBALx49xDoPSy/nn56rZS+FznqFKqpb+wQGhDS+Ly/iA5Gvx4+qDOZ8X2TOxGLV8j9evjCy9O1DJharZJO/LvOFCG3uAqCYDkBipmfjtJShkVaDpKRXRG3D/XXo85klu7K7Kjg1pGpsRGYe7slHb3wsyN20zP/tfUMKqyzIe5uUqTalEqlwuK7h2Lj07dYbpR51xA8clMfJA0JwdBwyxJMa2+Kgb46jOplOcGkHy/A0StlqKk3I8Dbw+EyVGsGhYgTbxt/v7OvlKK4sg6+Om2LA+jEJYLLJdWyhuGJP8emAYvB20OanPruTxeQcdbShbZdHJY2qDFgibEGLOcKK+0uZL7JNqKqzoSoQG/8+Z6hWPP4WBxaPBHvzh6NoeH+KK2ux/z/HsZD7+xp8bYLGWev4s5/7pQucooqapstU9U1mKUOE9tW+F8nWIKMdfty7GrfDuaUwGSdoxThYkb2T5Oj8dvxffF/D8cj2K9tF0WOTBwSgnCDHsWVdThbWIlgPx3ef3SMdUlaB2NZjTR7p7K2QcqcDmml4NZWdx9PaSiho6nSF69W4kxBBbRqFaaNbp6FVKtV+PsvY+Cr00rnlcdv6YOVvx7Vahb01oE9oFWrcK6wEm+kW7L6d8eEtThgT/y5HblkH7CcanLBZ7tf63+biAV3DpaaM5TAgKUdxPH8juYPLNtyCnUmMxL7BuI2mbULtiZZZw58c8R+bLU45bZvUOMbnzSLxaZT6IB16FpEgFeLk1VbolGrEGt9wxbX0UXiH5OclmY5IgK88LS1VfDm/kHNAj5HnULnCithFixZhx42VyIqlQp3WU+iXzfpThGvoFxZo7Y1zrostPNMkfSmFhXkLbuexxnxxHbhaqXdSUAsuO3lYv2KyLaORRAsBcXiyd8Vf5g4CPeOjECDWcDvPspE9uVSXCiqlDoIFkyOdssV2C+shYZbTxRIJ9T43t1kf+9oB4W34nLQuH6BLS6fGrw8pKvUo3mu1bE0mBrH+TcNWABLV5a4tDL/v4eQlVuCK6U10GnVUoAMWE6K4s/dtpj8v5mWzMYv43pKv4denhrcPigYX8y9CQsmR0OntQxFTF7+I57+JAtvfH8aXx/OwwljGd7cdgYz/rMbRRW1GBTiJy19fnvUPsg/lV+OOpPZ7hgAQPLQEHT38UR+WS3++vVxnDBa2r7bslzn7anFgsmDpd/VjqLVqKUi0juHh+LbZ2/F+IE9oNNq8Ii1xuWtH89BEATr/lsGMzqqY2qJuCyU4SBgETt5Rkd1b/HEHxHghdcfGIGoQG+8PHUonp8yxOnvtb/eQxr8eMjaqHFvK1l9cSnvSJMMS9MldVtKZlakfVB6B65nYS1kWE4ay6W23OcmR7frJCZ2KGw/VSh1VQiCIC0J9bPNsIjTbm2unva2YTnIllgkt/+ifcAiZjZcHRrXFk+O74d3ZsVL3T62pIDF5n5CYofQwBDfZsdcnFT64+lCuyticY3a1SsokfhmnpVTIt1Ar6OXgwBLy7iXhwb1JkFqYwZa70pyRmxvBoARPQ0uZ5YAS8Dz6v0jMK5fICrrTHj0vX148QvLzRzHD+whBXKdbcJgS8Dy05kiqUBWzglRJLU22wUslue7xcmFhjTx1sVloZxiy72/9B7qFjMNz08ZjJ7dvHDpWjV++2EmAMuSXdOrazHLIp6ccoursPtcMVQq4D7rcEZbWo0avx3fD9/9/lZpyeGrQ1fwj+9PYe6aA5i0fAf+vvkkzAJw/6ie2DD3Jml2yXfHjHbLSNlSwa2/3d+ZTquRvua9XRcwafkO3Pb6Nmn5UM5yXWf61ehIHP/LJLw5w365ccaY3vD21OCEsRw7ThfZ1LbJvJjp13xAo0jsHhJ/f1syaVgYts2/HQ83GU3QGrG2C7DUn9hmv5oSi+ybLglJAUuIvEyluzBgaYeW7tj8yd4cCILliiOmhZt0uWpwmB96B3qjtsEszWMorKhFRW0D1CpLK6BIzLDkXK2S1p3bUr9iK946MyHTJi0sCIJdl1BnUatV1nH+za9uIqzZItslIbFDqH9w81qUASF+GBTih3qTgO+ONWarWpti2ZqoQG+EGyxLK+JddDu64BawHIN+wZbntV0WEpe+eslcEgLsB9m5Ur/SlKdWjVUPx2FQiB8Kymux47RljsRzk9vedirXoBA/RAR4obah8Q6+bTkhihmWU/nlMJsFlNfUS3N/xrdQcCsSf2eaBiwFZTUOZ6SIP79+PXxbvFr11Wml2jWxBsJRhlaqY7FOvBV/B2/uH9Tq32TvQB98NCcBH81JwHOTo/FAXE+M6hUAf71lbtGr9w/H6w+MgJenBuMH9oDeQ41L16rtbkNg2yHU1LMTBuD1B2IwIToYnlo1Ll6tkv5G42R0cHU2R0G6wdtDGrnw9o5zNgPj5L03jOnbHWqVpajVtiGjvKZeGtQoZgg7kjiPBQBSYiNavVAeZn1NF65W2S0rnmnSIdTVMGBph8YMS+MvZYPJLK2Bir/87aFSqaQsy+Zsy4lWzK707OZtV9wYHuAFT40adSYz8kqrUVNvkua4uFqn0FRsrwBo1CpcKa2R6lZKqupRbW0RdnXmRUcTr1CvlDQGi2KGxVE6E4DU7SNW0JfX1Es3kZO7JKRSqaRsghg8dEaGBWjsKLENWMT7CLna0myrV3dvKZU/ro0pd3+9B96dPVrqlLtvZE/ppoDuoFKp7K5SPbVqhydQZ6ICfeCpVaOqzjLQbddZS1dOVKC302BwiM1NEGsbTPg86xLuffMnjPlbOv6w/nCz7U+3UL/SVGK/QKkFF7AUGTcVG2l5rQdzS2A2C9LodLG9uDUqlQo3DwjCE+P74bUHYvDZ727CocUTkfXiHZg2upfdcpLYJWW7LNS04NaWWq3CL+N64p1HRuPAi3fgzRmjcN/ICPx2fF8MDuuaJ0Fbj97UBxq1CjtOF0n38JKbYfHXe0jHxjbLsvN0EepNlo6vlmr32qNXoDcS+wbCT6+V2qtbYlt4K95ioaiiFsWVdVCpILsWzF0YsLSDeLIuq2mQbsa280wRiirq0N3HE7c4uUJzVfIwS8Cy9UQBahtMLbbQatQqqevhQlEVDl8qRV2DGUG+ujZf/Xt7aqU3ZnFZSOyICfL1lD0mu6OIRbfFlXXSUpmYYRnYQrePGLD8dKYI1yrrpGWAMIMe3X3kF8ve1N/+ZO9oBktHkGaxWE949SazdNXalu+pUllmP6TdN1xa2mqL8AAvfPKbsZg3YQAWWVuV3WmCzRVlbM8Al+7P1JRWo5YC3ON55dI9VlrqDrI1NMLyd3G6oBzj0rbi9+sOIcvaarzpSF6z9k/x59ffhZPBH5OjcdugHrhvZITDv92h4QZo1SoUVdTi86zLuHStGn46LSYOaVv7rzgTpimxnfi7o5aLpXqTGccdFNw64qvT4s7hYVg2LRYLJg/u8PquzhDZ3Vu6b1RRheXnJ/diBgASpfbmxoAl3boc1BnZFdG7s0dj559+4VK9orgsJA5gFN8/I7t5y1omdicGLO3gp/eQph+Kw9q+ONh4d1dn805cFdszAKH+elTUNuCnM0U4Z22N7Nuj+RuZ7U0Q91iLvhJshq61hTg7QSxuFLMabe0Q6ggGLw/4WY/9lZJq1DaYpLqOltZf+/XwxeAwfzSYBXx71Ng4MK6NmYGb+tmf7DtjSQhoXOISr9AvX6uGyWyphQiWUQxoKyYyANPH9Gr3SaRPkA9+f8dAu3sWuUtCn+7wtr6xunL/oJZI9xQylkv1Ky3NX7EV6m8JdM0CcLWyDmEGPf7fHQMxINgXJrOALU3ust04NM55wOLlqcF7s8dg2bRYhz8jvYdGqr8RJ+TeFRPW4SeapMHB0KhVOGEsx8WrlZaC2wYz/PRa2QXf14vHbe6k7qfTIlJmswIAqVhY7PYymwX84GL9SnvoPTQud/E0Lbw94yRD3RUwYGkn2zqWqroGfGu9EmnaX98earVKuunb5myjlGFxlFYUh0tdKKrE3gvtq18RifdmETuFpLs0t3EGS0cRsyyXrlVLHUL+em2rJ3Gx+PbrI3kOR/LLEeyvl/64/fVadOukk7bttFuzubH4tlf3ju9Kup7oPTS4d2QENGoVJg1r+2AxsY7l26NG5BRXwUOjcqk7RaVS4cW7BuOuEWFY9VAcdvzxdjw9YQDusY6A/+ZIY0eaIAiNGZYOOiGIE2/FWhdXloPkCvD2lJaTvzuaj6PiwLhwww37uzeiZ4BUmD443L9N3TGjo7pBq1bhckk1courcehSCa5W1sFPp23z/ZA62oiIAACNS3yNBbddd+mOAUs72XYKbTmWj6o6E3p198aoFuY3tJXY3rzlWL50072+Dq7oxSWCMwUVyLxof9PAthKvXk8Yy1BR2yAtRyiZYQFsO4Wq7f7YWnsjFQOWXWevSm2HbUn5isQx/X2Cmt+luaP0DvSGVq1CVZ0JeWU10gyN3p1UM3M9+fM9Q3HghTswwnrybgsxUyEWlsb17tZsmmhL7h3ZEyt+PQqThoVKMy8mD7cETzvPFEkFjXmlNaisM0GrVnXYzy3WpqC/b5CPrPZ0OZKty0LfHjVKV+PDW7iVw41ifnI0Qv31eKCNQaC3Z+MMn11ni6R25lsH9eiwzHt7DbMuaV68WoXSqvrGGSzMsNy4xKJDY2m11MqcEhve4Sev0VHd0N3HE9eq6qUiT4dLQtY3w11ni1BVZ4LBy8PlCa4tCfHXo2c3L5gFICvnmrQk5OoQqM4iDY+7Vi2NPHf2x9Y70NLuZzILyC22BF5Dwtr+5nv/qJ7w8tBIAWVn8NCo7QLR9hTc3mi0GnW7l6PEEf0iV+pXWtM/2A8Dgn1RbxKQbl0WEgPq3oHeHbdUbBOw3G8ze6WjiaPjM3Ou4UdrjU9bCpyvJ3G9u2H3wgl4IL7tjRPi7JyMc1el+pUJnVi/IleAt6dU85h9pbSxQ6iLtjQDDFjaTcywZF8uww7rPIipMsfwu0KrUeMOmyJDLw8NQhxMgIwKspzE6k2WtubRUd07ZOCP2N68/8I15IkzWJQOWGwyLKfyXU9n2t4byM9mPHtbDO9pwLG/JOPJ2/o537gdbDuFpIClDS3N1FwPX51d0bUr9SvOTLYWbn5j7exracJte/Tr4YuIAC94e2qcdoW0R3iAF0b0NEAQGrvTnBXcUmPh7dbjBTieVwaVCtKdkrsKcVnox1OFUpFxR/6OdjQGLO0Ual0W+e6YESazgJiehk5rCZs0vHGdvk+Qj8NAJNzgBU9t44+1re3MTcVLA+SKbW582DVqWC5fq3ba0mxryvDGgGVwuH+7r0zdsZZvO6KfS0IdS6VSSXUsQb6ebS7CtnXn8MaBjxW1DZ0y30KtVuF/T47DN/Nu6fTl2WSbmw/66bTM7rlgZK8A6LRqlFs7SEf16tambsTOJGbKNljv7tyzm1ezuzt3JQxY2knMsIj3B+vIYtumxvULlDpj+jhYDgIsb2K2bybtrV8RiXUsWTklyLcW+Sm+JGT9/heuVkrzVFxJZ0Z295YG+rW14NbdGgOWcmlJkBmWjiMGKbcM6NEhGclBIX7oG+SDugYztp4o6PCCW1GoQe+WwHXikMbs7pA2FqL+3Og9NIjr3VhX1JntzG0ltjbnl1ne07ty/QrAgKXdbAenadQq3B3T+o3f2kOn1UjryYNDW75SE+sdvD01HXZCHhjsBz+9FlV1JpjMArRqlcMJtO4kZliKKupgMgvw02mlmiJn/jBxIEb0NOBBBzcg64rEE93B3BLUNpihUasUX5K7kfxmfF/MubkP/jhpUIc8n0rV2Ln0zZG8Fu/SfL3oH+wrFflzOch1toMZO7Odua2GNZni25U7hAAGLO0WZhOw3NQ/SNZNstrixbuG4IUpg/HITX1a3EacBxLXu1uLd+uUS93kJnmhBn2b7kDdkYJ8dHbLX/0d3EOoJbcM6IEvn7q5WcFlVyUWWIu1ST27eXWZboMbQbCfHi/eNaRDl1bEAWTpxwtQbB0i56hQ/nqgUqnw5G39EOynQ0on1OjdqMSalT5BPu1ufugMBm8Pu3k6XT3D0nUXq64TBi8P6D3UqKk3496RnZddEXXz8cRjt/RtdZtfxffE3vPFeHJ8xxaCjo7qhu3W+7aEK9zSDFiCqIgAL2kuzcAuev+LjuDtqZVuigfIv0szud/QcH9EdveSutG6en2AMw/ER7ara+bnaFiEAWseT0BEgFeXnVszvKdBWmZmhuUGp1Kp8MT4frhjSAgmd2Jrqxz9g/2wYe5NHX7nXNublyk9NE5kW0fTldvxOoLtckJn3beIOo5KpcKdNu8J1+tyELXPuH5BXbpA3naJr6v/jjJg6QDPJg3E2zPjFbuvjrvERgZAa10GCusi9RO2gVNX/2NrL9t70LDg9vow2aYjzZV7CBG520hrA0Kv7t7SrWa6qq69d9SleHlqMDTCgEO5JYp3CIkiAhpP3C3d9PBGYRuQcUno+hDT04Bwgx5XSmtu+ICark9j+nTHyynDpNb+rowBC8nyp0mD8Om+XNwT2/n1Oq4QO4V8PDV2BdA3IrsloU660SJ1LJVKhb9MHYYvDl3BXZ3YQUjUViqVCg+P7a30briEAQvJMq5fEMb169jamPYQ11/jo9p3R+rrwYBgP2jVKqjVqjbdQZaUkTQkBEk2c0yIqG0YsNB1bVCoH75PHW83D+dGZfD2wP89HAeNWgUvzxu7XoqIqCkGLHTd+znVBkwYzCt1Ivp5YpcQERERdXkMWIiIiKjLY8BCREREXR4DFiIiIuryGLAQERFRl8eAhYiIiLo8BixERETU5TFgISIioi6PAQsRERF1eQxYiIiIqMtrU8CycuVKREVFQa/XIyEhAXv37m11+/Xr1yM6Ohp6vR7Dhw/Hpk2b7D7/0ksvITo6Gj4+PujWrRuSkpKwZ8+etuwaERER3YBkByzr1q1DamoqFi9ejAMHDiAmJgbJyckoKChwuP2uXbswffp0zJkzB1lZWUhJSUFKSgqys7OlbQYOHIgVK1bgyJEj2LlzJ6KiojBx4kQUFha2/ZURERHRDUMlCIIg5wsSEhIwevRorFixAgBgNpsRGRmJp59+Gs8991yz7adNm4bKykps3LhRemzs2LGIjY3FqlWrHH6PsrIyGAwGfP/995gwYYLTfRK3Ly0thb+/v5yXQ0RERAqRc/6Wdbfmuro6ZGZmYsGCBdJjarUaSUlJyMjIcPg1GRkZSE1NtXssOTkZGzZsaPF7vPXWWzAYDIiJiXG4TW1tLWpra6X/l5aWArC8cCIiIro+iOdtV3InsgKWoqIimEwmhITY3+I+JCQEJ06ccPg1RqPR4fZGo9HusY0bN+LBBx9EVVUVwsLCsGXLFgQFBTl8zrS0NPz5z39u9nhkZKScl0NERERdQHl5OQwGQ6vbyApYOtPtt9+OgwcPoqioCG+//TZ+9atfYc+ePQgODm627YIFC+yyNmazGcXFxQgMDIRKperQ/SorK0NkZCRyc3O53NTJeKzdh8fafXis3YfH2n066lgLgoDy8nKEh4c73VZWwBIUFASNRoP8/Hy7x/Pz8xEaGurwa0JDQ13a3sfHB/3790f//v0xduxYDBgwAO+8847d8pNIp9NBp9PZPRYQECDnpcjm7+/PPwA34bF2Hx5r9+Gxdh8ea/fpiGPtLLMiktUl5Onpibi4OKSnp0uPmc1mpKenIzEx0eHXJCYm2m0PAFu2bGlxe9vnta1TISIiop8v2UtCqampmDVrFuLj4zFmzBgsX74clZWVmD17NgBg5syZiIiIQFpaGgBg3rx5GD9+PJYuXYopU6Zg7dq12L9/P9566y0AQGVlJV555RXcc889CAsLQ1FREVauXInLly/jgQce6MCXSkRERNcr2QHLtGnTUFhYiEWLFsFoNCI2NhabN2+WCmtzcnKgVjcmbsaNG4c1a9bghRdewMKFCzFgwABs2LABw4YNAwBoNBqcOHEC77//PoqKihAYGIjRo0djx44dGDp0aAe9zLbT6XRYvHhxsyUo6ng81u7DY+0+PNbuw2PtPkoca9lzWIiIiIjcjfcSIiIioi6PAQsRERF1eQxYiIiIqMtjwEJERERdHgMWJ1auXImoqCjo9XokJCRg7969Su/SdS0tLQ2jR4+Gn58fgoODkZKSgpMnT9ptU1NTg7lz5yIwMBC+vr64//77mw0fJPmWLFkClUqFZ599VnqMx7rjXL58GQ899BACAwPh5eWF4cOHY//+/dLnBUHAokWLEBYWBi8vLyQlJeH06dMK7vH1y2Qy4cUXX0SfPn3g5eWFfv364eWXX7a7Hw2Pd9v8+OOPuPvuuxEeHg6VStXsvn+uHNfi4mLMmDED/v7+CAgIwJw5c1BRUdH+nROoRWvXrhU8PT2F1atXC0ePHhUef/xxISAgQMjPz1d6165bycnJwrvvvitkZ2cLBw8eFO68806hV69eQkVFhbTNE088IURGRgrp6enC/v37hbFjxwrjxo1TcK+vf3v37hWioqKEESNGCPPmzZMe57HuGMXFxULv3r2FRx55RNizZ49w7tw54dtvvxXOnDkjbbNkyRLBYDAIGzZsEA4dOiTcc889Qp8+fYTq6moF9/z69MorrwiBgYHCxo0bhfPnzwvr168XfH19hTfeeEPahse7bTZt2iQ8//zzwmeffSYAED7//HO7z7tyXCdNmiTExMQIu3fvFnbs2CH0799fmD59erv3jQFLK8aMGSPMnTtX+r/JZBLCw8OFtLQ0BffqxlJQUCAAELZv3y4IgiCUlJQIHh4ewvr166Vtjh8/LgAQMjIylNrN61p5ebkwYMAAYcuWLcL48eOlgIXHuuP86U9/Em6++eYWP282m4XQ0FDhtddekx4rKSkRdDqd8Mknn7hjF28oU6ZMER599FG7x+677z5hxowZgiDweHeUpgGLK8f12LFjAgBh37590jbffPONoFKphMuXL7drf7gk1IK6ujpkZmYiKSlJekytViMpKQkZGRkK7tmNpbS0FADQvXt3AEBmZibq6+vtjnt0dDR69erF495Gc+fOxZQpU+yOKcBj3ZG+/PJLxMfH44EHHkBwcDBGjhyJt99+W/r8+fPnYTQa7Y61wWBAQkICj3UbjBs3Dunp6Th16hQA4NChQ9i5cycmT54MgMe7s7hyXDMyMhAQEID4+Hhpm6SkJKjVauzZs6dd37/L3K25qykqKoLJZJIm+IpCQkJw4sQJhfbqxmI2m/Hss8/ipptukiYfG41GeHp6NruZZUhICIxGowJ7eX1bu3YtDhw4gH379jX7HI91xzl37hz+/e9/IzU1FQsXLsS+ffvwzDPPwNPTE7NmzZKOp6P3Ex5r+Z577jmUlZUhOjoaGo0GJpMJr7zyCmbMmAEAPN6dxJXjajQaERwcbPd5rVaL7t27t/vYM2AhxcydOxfZ2dnYuXOn0rtyQ8rNzcW8efOwZcsW6PV6pXfnhmY2mxEfH4+//e1vAICRI0ciOzsbq1atwqxZsxTeuxvPp59+io8//hhr1qzB0KFDcfDgQTz77LMIDw/n8b6BcUmoBUFBQdBoNM06JvLz8xEaGqrQXt04nnrqKWzcuBE//PADevbsKT0eGhqKuro6lJSU2G3P4y5fZmYmCgoKMGrUKGi1Wmi1Wmzfvh3//Oc/odVqERISwmPdQcLCwjBkyBC7xwYPHoycnBwAkI4n3086xvz58/Hcc8/hwQcfxPDhw/Hwww/j97//vXTTXR7vzuHKcQ0NDUVBQYHd5xsaGlBcXNzuY8+ApQWenp6Ii4tDenq69JjZbEZ6ejoSExMV3LPrmyAIeOqpp/D5559j69at6NOnj93n4+Li4OHhYXfcT548iZycHB53mSZMmIAjR47g4MGD0kd8fDxmzJgh/ZvHumPcdNNNzdrzT506hd69ewMA+vTpg9DQULtjXVZWhj179vBYt0FVVZXdTXYBy410zWYzAB7vzuLKcU1MTERJSQkyMzOlbbZu3Qqz2YyEhIT27UC7SnZvcGvXrhV0Op3w3nvvCceOHRN+85vfCAEBAYLRaFR6165bTz75pGAwGIRt27YJeXl50kdVVZW0zRNPPCH06tVL2Lp1q7B//34hMTFRSExMVHCvbxy2XUKCwGPdUfbu3StotVrhlVdeEU6fPi18/PHHgre3t/DRRx9J2yxZskQICAgQvvjiC+Hw4cPC1KlT2WbbRrNmzRIiIiKktubPPvtMCAoKEv74xz9K2/B4t015ebmQlZUlZGVlCQCEZcuWCVlZWcLFixcFQXDtuE6aNEkYOXKksGfPHmHnzp3CgAED2NbsDv/617+EXr16CZ6ensKYMWOE3bt3K71L1zUADj/effddaZvq6mrhd7/7ndCtWzfB29tbuPfee4W8vDzldvoG0jRg4bHuOF999ZUwbNgwQafTCdHR0cJbb71l93mz2Sy8+OKLQkhIiKDT6YQJEyYIJ0+eVGhvr29lZWXCvHnzhF69egl6vV7o27ev8Pzzzwu1tbXSNjzebfPDDz84fI+eNWuWIAiuHderV68K06dPF3x9fQV/f39h9uzZQnl5ebv3TSUINqMBiYiIiLog1rAQERFRl8eAhYiIiLo8BixERETU5TFgISIioi6PAQsRERF1eQxYiIiIqMtjwEJERERdHgMWIiIi6vIYsBAREVGXx4CFiIiIujwGLERERNTlMWAhIiKiLu//A81rOJs42s0UAAAAAElFTkSuQmCC\n"},"metadata":{}},{"name":"stdout","text":"MAE : 0.12\nRMSE : 0.16\nMAPE : 0.5928\nR2 : 0.874\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"
","image/png":"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\n"},"metadata":{}}],"execution_count":130},{"cell_type":"markdown","source":"### Boucle d’entraînement avec DataLoader\n\nUne epoch correspond à un passage complet sur `train_loader`.\nChaque minibatch entraîne une mise à jour des paramètres.\n\n```python\nepochs = 30\nloss_history = []\n\nfor _ in range(epochs):\n epoch_loss = 0.0\n nb_batches = 0\n\n for Xb, yb in train_loader:\n optimizer.zero_grad()\n\n y_pred = model(Xb)\n loss = criterion(y_pred, yb)\n\n loss.backward()\n optimizer.step()\n\n epoch_loss += loss.item()\n nb_batches += 1\n\n loss_history.append(epoch_loss / nb_batches)\n```\n\nInterprétation:\n\n* boucle externe: epochs\n* boucle interne: minibatchs\n* chaque minibatch → une mise à jour des paramètres\n* `loss_history` stocke la loss moyenne de l’epoch","metadata":{}},{"cell_type":"markdown","source":"> #### Exercice \n> Sur le dataset `abalone_mini`, prédire la variable cible `Weight`\n> à partir des autres variables explicatives, en utilisant PyTorch et un `DataLoader`.\n>\n> Convertir `X_train`, `y_train`, `X_test`, `y_test` en tenseurs PyTorch (`torch.tensor`)\n> avec le type `torch.float32`, et mettre $y$ au format `(n,1)` avec `.view(-1,1)`.\n>\n> Construire un `TensorDataset` puis un `DataLoader` avec `batch_size=32` et `shuffle=True`.\n>\n> Définir le modèle PyTorch (par exemple `nn.Linear(m, 1)`), la loss (`nn.MSELoss`)\n> et l’optimiseur (`torch.optim.SGD`).\n>\n> Entraîner le modèle pendant un nombre d’epochs fixé en itérant sur le `DataLoader`.\n> Stocker la loss moyenne de chaque epoch dans une liste `loss_history`.\n>\n> Indication (loss moyenne par epoch) \n> Pendant une epoch, le `DataLoader` fournit plusieurs minibatchs.\n> La loss calculée à chaque itération correspond donc à un minibatch, pas à toute l’epoch.\n> Pour obtenir une valeur représentative de l’epoch, on peut:\n> - additionner les losses de tous les minibatchs dans une variable `epoch_loss`\n> - compter le nombre de minibatchs dans `nb_batches`\n> - stocker la moyenne:\n> `loss_history.append(epoch_loss / nb_batches)`\n>\n> Évaluer le modèle sur le jeu de test avec MSE et/ou $R^2$.\n>\n> Tracer la courbe `loss_history` pour analyser la convergence.\n","metadata":{}},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"## Deux neurones en séquence\n\nJusqu’ici, nous avons utilisé un **seul neurone linéaire**,\nc’est à dire une transformation affine:\n\n$$\nu = X w + b\n$$\n\nEn PyTorch, cela correspond à une couche `nn.Linear`.\n\n\n### Chaîner deux neurones linéaires\n\nOn peut maintenant construire un modèle composé de **deux neurones successifs**.\n\nLe premier neurone calcule:\n\n$$\nh = X w_1 + b_1\n$$\n\nLe second neurone prend cette sortie comme entrée:\n\n$$\nu = h w_2 + b_2\n$$\n\nOn obtient donc un modèle à **deux couches**, sans non-linéarité.\n\n\n### Implémentation en PyTorch\n\nLa manière la plus simple de chaîner plusieurs couches est d’utiliser `nn.Sequential`.\n\n```python\nmodel = nn.Sequential(\n nn.Linear(m, k),\n nn.Linear(k, 1)\n)\n```\n\noù:\n\n* `m` est le nombre de variables d’entrée\n* `k` est le nombre de neurones du premier étage\n* `1` est la dimension de sortie\n\n\n","metadata":{}},{"cell_type":"markdown","source":"### 💡 Syntaxe à reprendre\n\n_Repère syntaxique pour aborder l'exercice ci-dessous._\n\n```python\nfrom torch.utils.data import TensorDataset, DataLoader\nscaler = StandardScaler()\nX_train = scaler.fit_transform(X_train)\nX_test = scaler.transform(X_test)\nX_train_t = torch.tensor(X_train, dtype=torch.float32)\ny_train_t = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)\nX_test_t = torch.tensor(X_test, dtype=torch.float32)\ny_test_t = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)\ntrain_dataset = TensorDataset(X_train_t, y_train_t)\nbatch_size = 32\ntrain_loader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)\nm = X_train_t.shape[1]\nmodel = nn.Sequential(nn.Linear(m, 10), nn.Linear(10, 1))\ncriterion = nn.MSELoss()\noptimizer = torch.optim.SGD(model.parameters(), lr=0.1)\nepochs = 100\nloss_history = []\nfor _ in range(epochs):\n nb = 0\n epoch_loss = 0\n for (Xb, yb) in train_loader:\n optimizer.zero_grad()\n u = model(Xb)\n loss = criterion(u, yb)\n loss.backward()\n optimizer.step()\n epoch_loss += loss.item()\n nb += 1\n loss_history.append(epoch_loss / nb)\nwith torch.no_grad():\n y_hat = model(X_test_t)\ny_hat = y_hat.cpu().numpy().reshape(-1)\n```\n","metadata":{}},{"cell_type":"markdown","source":"> #### Exercice \n> On considère maintenant un modèle composé de **deux neurones linéaires en séquence**,\n> sans fonction d’activation non linéaire entre les deux couches.\n>\n> Implémenter en PyTorch un modèle de la forme:\n>\n> $$\n X \\;\\xrightarrow{\\;\\text{Linear}\\;}\\; h \\;\\xrightarrow{\\;\\text{Linear}\\;}\\; \\hat{y}\n $$\n>\n> en utilisant `nn.Sequential` avec deux couches `nn.Linear`.\n>\n> Appliquer ce modèle à la prédiction de la variable cible `Weight`\n> à partir des autres variables explicatives du dataset `abalone_mini`,\n> en conservant exactement:\n> - le même découpage train / test\n> - la même normalisation des entrées\n> - la même fonction de coût\n> - le même optimiseur\n>\n> **Indications (reproductibilité)** \n> Pour garantir des résultats comparables d’une exécution à l’autre:\n> - utiliser `random_state=42` lors de l’appel à `train_test_split`\n> - fixer la graine du générateur aléatoire PyTorch avec `torch.manual_seed(0)`\n> avant l’initialisation du modèle\n>\n> Entraîner le modèle avec un `DataLoader` en minibatch,\n> puis évaluer les performances sur le jeu de test (MSE et/ou $R^2$).\n>\n> Comparer les résultats avec ceux obtenus précédemment\n> avec un **seul neurone linéaire**.\n>\n> Question \n> Observe-t-on une amélioration de la prédiction ?\n> Interpréter le résultat à la lumière du fait que\n> deux neurones purement linéaires en séquence\n> sont mathématiquement équivalents à un seul neurone linéaire.\n","metadata":{}},{"cell_type":"code","source":"df = pd.read_csv('/kaggle/input/datasets/pyim59/mini-datasets/abalone_mini.csv')\n\nX = df.drop(columns='Weight').to_numpy()\ny = df['Weight'].to_numpy()\n\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n\nscaler = StandardScaler()\nX_train = scaler.fit_transform(X_train)\nX_test = scaler.transform(X_test)\n\nX_train_t = torch.tensor(X_train, dtype=torch.float32)\ny_train_t = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)\n\nX_test_t = torch.tensor(X_test, dtype=torch.float32)\ny_test_t = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)\n\nprint(X_train.shape)\nprint(y_train.shape)\n\ntrain_dataset = TensorDataset(X_train_t, y_train_t)\n\nbatch_size = 32\n\ntrain_loader = DataLoader(\n train_dataset,\n batch_size=batch_size,\n shuffle=True\n)\n\nmodel = nn.Sequential(\n nn.Linear(X_train_t.shape[1], 3),\n nn.Linear(3, 1)\n )\n\ncriterion = nn.MSELoss()\noptimizer = torch.optim.SGD(model.parameters(), lr=0.1)\n\nepochs = 100\nloss_history = []\nfor _ in range(epochs):\n nb=0\n epoch_loss=0\n for Xb, yb in train_loader:\n optimizer.zero_grad()\n u = model(Xb)\n loss = criterion(u, yb)\n loss.backward()\n optimizer.step()\n epoch_loss += loss.item()\n nb += 1\n loss_history.append(epoch_loss/nb)\n\nplt.plot(loss_history)\nplt.show()\n\nwith torch.no_grad():\n y_hat = model(X_test_t)\n\ny_hat = y_hat.cpu().numpy().reshape(-1)\n\nprint(f\"MAE : {mean_absolute_error(y_test,y_hat):.2f}\")\nprint(f\"RMSE : {np.sqrt(mean_squared_error(y_test,y_hat)):.2f}\")\nprint(f\"MAPE : {mean_absolute_percentage_error(y_test,y_hat):.4f}\")\nprint(f\"R2 : {r2_score(y_test,y_hat):.3f}\")\n\nplt.scatter(X_test[:,1], y_test)\nplt.scatter(X_test[:,1], y_hat, c='red')\nplt.show()","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T02:33:58.345770Z","iopub.execute_input":"2026-05-13T02:33:58.346488Z","iopub.status.idle":"2026-05-13T02:34:06.408855Z","shell.execute_reply.started":"2026-05-13T02:33:58.346448Z","shell.execute_reply":"2026-05-13T02:34:06.407903Z"}},"outputs":[{"name":"stdout","text":"(3341, 4)\n(3341,)\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"
","image/png":"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\n"},"metadata":{}},{"name":"stdout","text":"MAE : 0.13\nRMSE : 0.18\nMAPE : 0.4117\nR2 : 0.864\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"
","image/png":"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\n"},"metadata":{}}],"execution_count":131},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"> #### Exercice \n> Montrer qu'un modèle composé de **deux neurones linéaires en séquence**,\n> est équivalent à une neurone linéaire","metadata":{}},{"cell_type":"markdown","source":"![LinearNeuron2Neurons.png](attachment:08c300f2-15c3-457d-b4ca-fcb83cf9dfde.png)","metadata":{},"attachments":{"08c300f2-15c3-457d-b4ca-fcb83cf9dfde.png":{"image/jpeg":"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"}}},{"cell_type":"markdown","source":"## Fonctions d’activation non linéaires\n\nJusqu’ici, nous avons vu que **composer des neurones purement linéaires**\nne permet pas d’augmenter la capacité du modèle:\nle résultat reste équivalent à un seul neurone linéaire.\n\nPour dépasser cette limitation, on introduit une **fonction d’activation non linéaire**\nentre les couches.\n\n\n\n### Qu’est-ce qu’une fonction d’activation ?\n\nUne fonction d’activation est une fonction appliquée **après le calcul linéaire**\nd’un neurone.\n\nPour une couche linéaire:\n\n$$\nz = X w + b\n$$\n\non applique une activation:\n\n$$\nh = \\phi(z)\n$$\n\noù $\\phi$ est une fonction **non linéaire**.\n\nCette non-linéarité est la clé qui permet aux réseaux de neurones\nde modéliser des relations complexes.\n\n\n\n### Pourquoi la non-linéarité est indispensable\n\n\n\nSans activation non linéaire:\n\n* empiler des couches linéaires ne change rien\n* le modèle reste globalement linéaire\n\nAvec une activation non linéaire:\n\n* les couches ne se simplifient plus\n* chaque couche transforme l’espace des données\n* le réseau devient **expressif**\n\nMessage clé:\n\n> La profondeur n’a de sens que si l’on introduit de la non-linéarité.\n\n\n\n### Fonctions d’activation courantes\n\nIl existe plusieurs fonctions d’activation classiques,\nchacune avec ses propriétés.\n\n\n\n#### Sigmoid\n\n$$\n\\phi(z) = \\frac{1}{1 + e^{-z}}\n$$\n\nCaractéristiques:\n\n* sortie bornée entre 0 et 1\n* historiquement utilisée\n* gradients très faibles pour $|z|$ grand (saturation)\n\nUtilisation:\n\n* sorties probabilistes\n* rarement utilisée dans les couches cachées modernes\n\n\n\n#### Tanh\n\n$$\n\\phi(z) = \\tanh(z)\n$$\n\nCaractéristiques:\n\n* sortie bornée entre -1 et 1\n* centrée autour de 0\n* saturation pour $|z|$ grand\n\nUtilisation:\n\n* parfois utilisée à la place de sigmoid\n* encore présente dans certains modèles (RNN)\n\n\n\n#### ReLU (Rectified Linear Unit)\n\n$$\n\\phi(z) = \\max(0, z)\n$$\n\nCaractéristiques:\n\n* très simple\n* non saturante pour $z > 0$\n* gradients constants dans la région active\n\nC’est aujourd’hui l’activation **par défaut** dans la majorité des réseaux profonds.\n\n![LinearNeuronReLu.png](attachment:c0b48092-7e77-489a-98bf-426e5f8efcb1.png)\n\n### Pourquoi ReLU est utilisée en général\n\nReLU est privilégiée pour plusieurs raisons pratiques:\n\n1. **Stabilité du gradient**\n Pas de saturation pour les valeurs positives,\n ce qui facilite l’apprentissage profond.\n\n2. **Convergence plus rapide**\n Les gradients restent significatifs,\n contrairement à sigmoid ou tanh.\n\n3. **Simplicité de calcul**\n Très peu coûteuse numériquement.\n\n4. **Comportement parcimonieux**\n De nombreux neurones sont à zéro,\n ce qui agit comme une forme de régularisation.\n\n\n### Comparaison\n\n* sigmoid / tanh\n - gradients qui disparaissent\n - apprentissage lent ou bloqué\n\n* ReLU\n - gradients simples et stables\n - réseaux profonds entraînables\n\n","metadata":{},"attachments":{"c0b48092-7e77-489a-98bf-426e5f8efcb1.png":{"image/jpeg":"/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAcFBQYFBAcGBgYIBwcICxILCwoKCxYPEA0SGhYbGhkWGRgcICgiHB4mHhgZIzAkJiorLS4tGyIyNTEsNSgsLSz/2wBDAQcICAsJCxULCxUsHRkdLCwsLCwsLCwsLCwsLCwsLCwsLCwsLCwsLCwsLCwsLCwsLCwsLCwsLCwsLCwsLCwsLCz/wAARCAFkA4QDASIAAhEBAxEB/8QAHAABAQADAQEBAQAAAAAAAAAAAAYDBAUHAgEI/8QAUBAAAQQBAgIECwQGBQoGAgMAAAECAwQFBhEhMQcSFEETF1FTVWFxgZKi0RUiMpE3QlJiobEkc3R1sggWIyY2Q4LBwtI0RFRWY3IllDOj4v/EABQBAQAAAAAAAAAAAAAAAAAAAAD/xAAUEQEAAAAAAAAAAAAAAAAAAAAA/9oADAMBAAIRAxEAPwD+kQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA4eU1di8Tl2YudbMlx8XhmxQVnyqrd1Tf7qL5AO4DDUssuVIrDGSMbI3rI2ViscntavFF9pm3AA5OZ1LjcA+P7Sklgjem/hvAPdG3jt95yIqN950q9iG3XjsV5WSwyNRzHsXdrkXkqKBkAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAc7N5/Gadx63cpaZWh36qKu6q5fIiJxVT4wGpMXqbHuuYuz4aJruo/dqtc13PZUXlwA6hAW/wBPVH+6Xf4lKHGa0wWZzsuJx9ztNmJrnOVjHKzZFRF2dtsvFSet/p6o/wB0v/xKBV52LNT14ocLYq1XvftLPMxXrGzbmxvJXb+XgQvRvHah17quvcvTX5a7o4lnmX7zkRzu7knsTgenLyPN9BuRek/Wuyov+mb/AInAeg3khXH2EsNR0Pg3ddF4ordl3/gRnQ+sq9Hdfrqvg/DS+CRe5nW4J+e5aXHxx0p3zM68TY3K9u2+6bcUIfonitO06tyOykeInkkWpQVOu6unXXfeTmvfw27wL4AAAAAAAAAAAAAAAEVNnM9f6Rchp/H2qVSCpVZYa+WssrlVdt04PTylXPchxuO7RkrUMTImJ4WZ6+DZvtxXivD2bkZiv0653+7Yv5tKvJYDF5e3VsZCmy0+oqrEkm6saq7ceryVeHDdOAGtpzVuL1U659lvkljqPSN0jmdVr1VN9278dvaiHN1vkc/gMNfzVG7S7NWY1za8tVznKu6Iv30eneu/I4fRIxsd3VLGNRrW5FURETZETd3A7vSj+jLM/wBU3/G0ChxVmS7hqVqXqpJPAyR3VTZN1airt+ZtnO0//szjP7LF/gQ6IAAAAAAAAAGllMxjsJTW3krkNSBP1pHbb+pE5qvqQnm60v5Pjp/TN+9Ev4bFlUqxO9aK77yp7gK4EklrX8idZMbgYUX9V9mVyp70bsfn21rOlu65pirdjTmtC6nW9zXom/5gVwJzGa5w+QuNozumxeQXglW/GsL1X93fg73KUYAAAAAAAAAAAAAAAAAAAAAAAAAGKzagp1n2LM0cEMabukkcjWtT1qpLrr2O+9Wadw9/ObLt4aJngoN/6x+yL7twK0Ekl7Xs69aPD4Wo3ubNcfI75W7D7S11VXrTYDF3WpzSrdcx35Pbt/ECtBK19f4+Owytm6tvA2Hrs1L0fVjcv7sibtX80Klj2yMR7HI5rk3RUXdFQD9AAAAAAAAAAAAAAABxtX5Wxg9I5HJVEYs9aFXsSRN277pzQwaXmzV3HVsjkr1SWG1WbK2KGssasVyIvFyvXfZN05GDpH/Rzm/7Ov8ANDf0lx0Zhv7FD/gQDjp0kY2yk78ZjctlYK67STVau7G+9ypv7kOrhtR09WYKW3g7SNfxj3mjVViftw6zd035ovPj5THlMhhdB6bkmbBFVrsVfBV4Wo1ZZF49VqeVVOP0X6bu4PBWbWQZ4G1k5u0LB5pvci+vivDu4IB943PZuLpGXTmRsU7MPYlteEhrrEu/W2ROLl9ZaEAn6e1/uj/rL8AAAAAAAAAAT2W1th8XdWg2SW/kP/R0o1ml96Jwb71QChBI/bmsbyItLS0FNi8nZC6iO97WIu35n6tnX7E6y47Ayp+w2zK1fzVuwFaCRXWWTxnHPaXvVIk/FYqOS3GnrXq/eRPcd/E5vGZ2p2nGXYbcW+yrG7dWr5FTmi+pQN8AAAAAAAAAAAAAAAAAAAAAAAAAAAABoW8Lj7uUrZGzXbNZqNc2FzlVUZ1tt16vLfhz5njuKx2Th1vqLRmLlSpXvT9eWZF2dDAm6r1U8qtejS41B0jw1cpb0/h6k1zOte2GFnVTwavcm/WVd+Td+O+35cSNt016OukjBZLI23zsuQu7bafuqOkcqpIvsTdi7eRAPVMNpXC4B7JMbj4q8rYUgWRqfecxF34r3rvx3JLKWq9Tp1oy2Z4oI0xTk60j0an4nd6lbp7UMWpK9i1UrytpMlWOCd6bNsIicXtTn1d90489jdtYvH3pEkt0a1h6JsjpYmvVE8m6oBgyGPp6hxrI3zyuruckjX1bDo+tz/WYqbpx9hwIOi/TVWd01aO7BK7feSO9K1y+9HblbDDFXhbDDGyKNibNYxqNRqeREQ+wORmc3idO4tzsjdiha2JeqySTd8iIm2yIvFynD6Kcbaxugq7bcT4XzSSTNjemytY5eG6d3Dj7ytlpVZ52Ty1opJY02Y9zEVzfYvcZgAAAAAAAAAAAHF1TqihpPDuv3lV269SKJn4pXeRP+a9x2jyfU2+ounPE4ef71WgxsisXkq9VZF/PZie4Dufb2ulwcubdiMTBWZGs6VJZJPDrGib8V5Iu3dsb2gNX3NZVL96enFVrRTJFAjXK5y/dRXdZV5805Ihl6RsxHhtCZGRXo2WxGtaJPK5/D+Cbr7jD0W437N6PMcit6r7KOsO/4l3T5dgNHFfp1zv92xfzaVeZzlbBwRy2YrUqSKqNbWrvmXdE34o1F295MS4vO4zpLyWeqYpt+raqRwNRLLI3IqbKq7L7C2hc+SCN8sfgpHNRXM62/VXbim6cwPJujvOJhb+bXI4zK10yFvw8S9hlcmyqvBdm8F4oWHSj+jLM/wBU3/G0rCO15WzmbwWQwmPw6Sx2Y2tbZdaYxN90Vfurx7tgKDT/APszjP7LF/gQ6Jp4ivJUwlGtMiNlhrxxvRF32VGoim4AAAAAACd1JqZ+NsQ4rF10vZu2m8NffZsbe+SRf1WJ/Hkhv6izcOnsDZyUzVk8E3Zkac5HquzWp61VUQ0NJYCbGVZchk3JNmsiqS25f2V7o2+RrU4IgGLD6MihuJlc5OuYzC8fDTJ/o4f3Ymcmp6+ZTmOxZgqV32LM0cEMadZ8kjka1qeVVXghyF1rpZq7O1JiEX13Yv8AuA7YOH/ntpX/ANy4f/8Aei/7jq0r1TI1ksUrUNqByqiSQyI9qqnPinADBlcNjs5SdUyVOK1Cv6r277etF5ovrQlXTZPo/ci2p58pprfZZX/fsUfJ1l/Xj9fNC4PmSNksbo5GNex6K1zXJuiovNFQD8iljnhZNE9skcjUc1zV3RyLyVFPsjMF19I6pXTT1VcXea6fGOVd/BKnGSD2Jv1m+rdCzAAAAAAAAAAAAAAAAAAAAcnUWoqunMe2edr555neDr1ok3knkXk1qfzXuOlYniq1pJ5npHFE1XvcvJqIm6qSWkqkueyD9YZJio+w1WY6F6f+Hr9ztv2n81XybIApaTtZyxHk9YSNtSoqPhxrF/o1b2p/vHeteHkK9jGxsRjGo1rU2RETZEQ+jynpy1pqLSFTT7NO3Y6c2RuLXe98LZeGybcHIveoHqwPEcfrbXukelzD6S1ZkcdnK+Yb9yWtAkT4t+siLsiJ3t5Ki7pxReBZ6h6ZtE6YzcmKyGWd2uBUSdsED5UhXyOVqKiL6uYFraqV7tZ9e1BHPC9NnRyNRzV9ykfNhMlopy3NOJLdxSL1p8S93WVid7oFXkv7q8FK3HZGnl8bXyGPsR2alliSRSxru17V70NkDSw+XpZ3FQ5ChMkteZN0XkqL3oqdypyVDdIrIR/5l6rjytdOphsvM2G9GnBsM68GTJ5Ecv3Xe5S1AAAAAAAAAAHG1fk5MNo/KX4l2lhruVi+Ry8EX81QDg3tc3sjqWXA6Uow3rFf/wATasPVsEPHZU4cVXfh7fLspys7r7VOm8rXw93GYye7cVnZ5oHv8GqK7qru1eO+/rN3ocxjKeh0u7bzXpnyPevNUavVRP4KvvOPkJ49TdPlCtGqPgxEe71TinXbu5fyc5qe4Cw6Rv0cZrf/ANMv80N7Sz0j0RiHu32bRiVdk3X8Cdx8ayxlrM6MyePpNa+zYhVkbXO6qKu6d5i0muXrY2pjchiOyMqVmR+GSyyRHuaiJyTim/FQPOYdTS3dXyZ7OabzltK69XHVo6qrHA39tUXbd6+Xu/Lb0DSGp7+pbOSfYxU+NqwOjbXbYjcyR+6L1lXfgvFE5FOYrUksNSWSCDtErWqrIusjeuvcm68EAhU/T2v90f8AWX5D4zE5u10mrqG7jG0a3YVrdVbDZHdbrb9xcAAAAAAA+XvZFG6SRyMY1FVznLsiJ5VU+iN1I6TVGoo9KQPcyjExLGUkYuyqxV+5Ci9yu23X1AYluZPXs748ZZlxunGOVjrkf3Zru3NI1/VZ3dbmvcU+HwWNwFNKuNqR1o+a9VPvOXyudzVfWpuwwx14GQwxtjjjajWsamyNROSIhqZDOYnEvYzI5OnSc9Os1LE7I1cnlTrKgG8Dh/57aV/9zYf/APei/wC4yQ6v01ZmZFBqHFSyPVGtYy5G5XKvBEREdzA7BNZnRla5bXKYmZ2HzDU+7arpsknqkZyent4lKAJvTupZ7l2XC5qu2lm67eu6Nq/6OdnLwka97fKnNCkOBqzTzs1QjnpvSvlqLvDUrG3Fr0/VX913JUNjTGdbqHAQXvBrDMu8c8K84pWrs9q+xU/LYDrgAAAAAAAAAAAAAAAAAAAAAAAAADWjx1KG5Jbip147Mn45WxtR7va7bdT9t0KeQjbHcqwWWNXrI2aNHoi+XZTYAH4xjY2NYxqNa1NkRE2REP0AAD8e9sbHPcuzWpuq+RCY8ZWkPT1b5voBUAl/GTpD07W+b6Dxk6Q9O1vm+gFQCX8ZOkPTtb5voPGTpD07W+b6AVAJfxk6Q9O1vm+g8ZOkPTtb5voBUAl/GTpD07W+b6Dxk6Q9O1vm+gFQCX8ZOkPTtb5voPGTpD07W+b6AVB5pqvTWoaPSLW1Zp+mzIKrEZLCr0aqKjVavNU4K3binJUKPxk6Q9O1vm+g8ZOkPTtb5voBK6r0fqjVun57+QZC3Is6qVMdDJuyFm/31Vy8HSOTv5IibJzKLSFfVLuxvy0cOLo06yV2Uo1SR0zkRE673fq7bcET17mx4ydIena3zfQeMnSHp2t830AqAS/jJ0h6drfN9B4ydIena3zfQCoBL+MnSHp2t830HjJ0h6drfN9AKgEv4ydIena3zfQeMnSHp2t830AqAS/jJ0h6drfN9B4ydIena3zfQCoBL+MnSHp2t830I+n00w187crZCuljHpO9ILdZPveD3XqqrV58NuKbL6gKnNp9s9ImGxK/erY6J2TnbvwV+/UiRfYquX3FeROkMjTz2udR5WlOliv4GpDFIiKm7eq5y8+PNVLYDBeo1snQno3YGWK1hixSxPTdr2qmyoqew8F05jKHRP0ku0fqHH07enM1IsmIv2a7HuieuyLE9yp7E9vVXh1l2/oEmdf6Ix+v9JWcNfRGOd9+vOibuglT8L0/kqd6KqAbztJacexWuwGLc1ybKi041RU8n4TT0LpGLROnn4evK19dLU80KNb1eox8iuaznx6qKib9+xPdDWo83l9O3sPqGJXZPT9pcdLba7rMsdVOCo7vcibIvuXmqnooAAAS/SDSkm0rLfrJ/TcU9t+Byc0WNd3J729ZPeUNG3Hfx9e5Cu8diNsrfY5N0/mftyFtijPC9N2yRuYvsVFQgNE6905j9E4qnkMxBDarwJE+N3W3b1VVE7vIiAeigl/GTpD07W+b6Dxk6Q9O1vm+gFQCX8ZOkPTtb5voPGTpD07W+b6AVAJfxk6Q9O1vm+g8ZOkPTtb5voBUAl/GTpD07W+b6Dxk6Q9O1vm+gFQCX8ZOkPTtb5voPGTpD07W+b6AVAJfxk6Q9O1vm+g8ZOkPTtb5voBUAl/GTpD07W+b6EnlemOHG6qdFVZFlMO6Nio+FVbI13HrbKvBe7gu3tAp+kB77lDH4CJytdmrbK8m3NIU+/J8rdveVccbIomxxtRjGIjWtRNkRE5IefUtTY3V/SHgJ8bOssVWpakcxzVa6N69RuyovfsqnoYA8K/ymom2KukYHOVrZckrFVq7KiKjU3RfLxPdTUv4nHZTwP2hQq3PAP8ACReHhbJ1HeVu6LsvrQD+e8ZhKvRJ/lFY6vec7I4/NReDp37q9eaB7l6u3X8vW2aq/svQldKunqXdZYTK62x+lp7VqWO7DkKDZnWWqrkVUe5U25rwTyoqcz+rb2HxmTlgkv46pcfXd14XTwtkWN3Di1VTgvBOXkNXJaU0/mbSWsng8denbsiS2KzJHbJyTdU3A4HRDiqeG6L8XUx2YbmqaeFdFbbEsTXosjlVEavFERd04lqY69eGpXZXrQxwQxp1WRxtRrWp5EROCGQDQzmKhzmCuYydEWO1E6Pdf1VVOC+5dl9xztD5SXLaOozWV3txNWvPvz8JGqsdv7dt/eUB53p/VeD03lNR4/J5GGo5MrLLGx+/Frkau/BPLuB6ICX8ZOkPTtb5voPGTpD07W+b6AVAJfxk6Q9O1vm+g8ZOkPTtb5voBUAl/GTpD07W+b6Dxk6Q9O1vm+gFQcvUuH+39NX8X10jdahVjXLya7mir70Q5fjJ0h6drfN9B4ydIena3zfQCU0tQ6QMbhE02yhVowsc5EyMkqPWJrlVV6rUX7y8V2329Zr0tI6m0jrm7PgMXDcrWYEhhs2Z0RI9+qqvf3qvWRVVNuO5Z+MnSHp2t830HjJ0h6drfN9AO5ia1upia8F+4t60xu0k6sRnXd7E5G4S/jJ0h6drfN9B4ydIena3zfQCoBL+MnSHp2t830HjJ0h6drfN9AKgEv4ydIena3zfQeMnSHp2t830AqAS/jJ0h6drfN9B4ydIena3zfQCoBL+MnSHp2t830ONqrpTxVPCLPgMnUuXmys2hc1yo5u/3vJ3AXs8zK1eSeV3Vjjar3L5ERN1Jjo8gfJp6TNWG/0rNTvuyKvNGuXaNvsRiJ+ZJ3elnGZzRGWrPY/H5N9ORrInfea9Vbt91ye3v2PScLA2tgaEDE2bFXjYnsRqIBvEB0t9G8XSBplOyoyLN49VmoTuRPxc1jdv+q7ZPYuy+UvwB5Z0U5fT+uNPyQZHT2Mq6hxbuz5Gq6nG1zXpw66J1eCO2Xh3Kip5Ch1R0aYTO16C1KFHH26N6C5FPFWa1ydSRHOb93ZdnNRU9uy9xGdLGEt6I1DX6U9NoxliurYMtVV3VbchcqNRfW7knwr+rx9fqT9qpQ2Fikh8Kxr/AAcibOZum+yp3KneBmAAAkMen2L0nZCi3ZtbM10vRt7kmYvUk29aorVUryK1rfq4bVelsrbmbBBFNPFJI7kjXRd/vRALUEv4ydIena3zfQeMnSHp2t830AqAS/jJ0h6drfN9B4ydIena3zfQCoBL+MnSHp2t830HjJ0h6drfN9AKgEv4ydIena3zfQeMnSHp2t830AqAS/jJ0h6drfN9B4ydIena3zfQCoBL+MnSHp2t830HjJ0h6drfN9AKgEv4ydIena3zfQ0c10m6eiwd2TGZqrLeZC50DFa5es/bgm23lAtgea6Z6ZcXklZXzUX2bYdwSVN3QuX282+/8z0lrkc1HNXdF4ooH6AAAAAAAAAAHMx9mh81H8KGQAY+zQ+aj+FB2aHzUfwoZABj7ND5qP4UHZofNR/ChkAGPs0Pmo/hQdmh81H8KGQAY+zQ+aj+FB2aHzUfwoZABj7ND5qP4UHZofNR/ChkAGPs0Pmo/hQdmh81H8KGQAY+zQ+aj+FB2aHzUfwoZABj7ND5qP4UHZofNR/ChkAGPs0Pmo/hQdmh81H8KGQAY+zQ+aj+FB2aHzUfwoZABj7ND5qP4UHZofNR/ChkAGPs0Pmo/hQkKfRfgo87by16NchPYnfM2OVESKPdd9kb37evf2FmAJHDolHpQz1RGoxtunWsxoibJs3rRrt7OBXEfrBfsTPYbVCIvgK71p3VTuhlVERy+pr0avvLBF3TdABF671DfbPV0npyRG6gy7VVsu26Ua6cH2Hezk1O923kKTPZR+FwFzIxUbOQkrxK9lasxXySu7mtRPKv5czw7SOu9SYObIZTJ9Gmp8hncpL4S1aSu5rWtThHFGit3axreSd67qoHtum9PUNLafq4jGxqyvXbtu5d3PcvFz3L3ucu6qvlU6h5IvTPqHbh0U6o3/ql/wCwoeiWxnr2lLmR1FVuU7t7I2LCVrfWR0EauTqsRHcUaiJwAugABqZa22hhrlt6ojYIHyKq+RGqpxdB45tXQOGjmib4RarHu3am+7vvf8zW19M67Tp6Zru/pOamSF23NkDfvSu+FNveVkUbIYmRxtRrGIjWoncicgPns0Pmo/hQdmh81H8KGQAY+zQ+aj+FB2aHzUfwoZABj7ND5qP4UHZofNR/ChkAGPs0Pmo/hQdmh81H8KGQAY+zQ+aj+FB2aHzUfwoZABj7ND5qP4UHZofNR/ChkAGPs0Pmo/hQk8r0bYjOapdmMkr5meDZG2q37jPu78XKnFefLgWAAjMjTrYbpA0staCOtWkhs00ZG1Gtaqta9qbJ5eqpZkzryhYs6cS7SarruKmZfganNys4ub729ZDuYvI18viq2Qqv68FmNsjF9SpuBtE9qvXGD0X2D7asSQ/aE3gIOpE5+7uHPblzQoTw3/KU5aM/vX/tA9W1bq/EaJwS5fNTPhqJI2LrMjV69Z2+3BPYplyup8ZhtKS6iuTPbjYoWzukbGrl6jttl6qce9Dzf/KZ49D0n9th/wCo3+kZyL/k1XV3TZcVBt//AFgeg4PNUtRYOpl8dI6SpcjSWJzmq1VavqXihvkV0Pfoe0z/AGJn81LUASGhIo7bM7kVY17bmWndG5Wou7W7MT/Cp1NX5v7B0zatxp1rLkSGsxOb5n/dYie9d/cZtMYdMBpihjN+s6vEiPd+09eLl97lUDo9mh81H8KDs0Pmo/hQyADH2aHzUfwoOzQ+aj+FDIAMfZofNR/Cg7ND5qP4UMgAx9mh81H8KDs0Pmo/hQyADH2aHzUfwoOzQ+aj+FDIAMfZofNR/Cg7ND5qP4UMgAx9mh81H8KDs0Pmo/hQyADH2aHzUfwoOzQ+aj+FDIAMfZofNR/Cg7ND5qP4UMgAx9mh81H8KHG1TpWtqfCrjZJOysdIx7nxsRXbNXfZPJud0AReQ0Lh8RoTMUsVSayaalK1ZXfelevVXbdy8eack4FBpm6zI6Vxdti7pNVjf7+qm/8AE6aojkVFTdF7iR0NIuLlyWlZlVJMXMr6+/69aRVcxU9m6tX2AV4VURFVeCIDy3poz2egx9TAYbA5nIQZBd8hYx0LnOZX32dGxyIqI9/FN15J7QNrHIvSdq9mYkTr6Uwc6pj2L+G/aauy2F8rGLujPKu69x6QeOY/pYy2Lx1ehR6I9TV6taNIoomQqjWNRNkRPumjqLpH1lqmjWwuN0DqXDOt24GzXXse3wUaStV2ytam26Jsq78lUD3EBAAJHUSNudIWl6fB3ge025E232RGIxP4uK4j9MO+3dYZnUSL1qse2Npu7nNYu8jk9Sv4f8IFX2aHzUfwofvZofNR/ChkAGPs0Pmo/hQdmh81H8KGQAY+zQ+aj+FB2aHzUfwoZABj7ND5qP4UHZofNR/ChkAGPs0Pmo/hQdmh81H8KGQAY+zQ+aj+FB2aHzUfwoZABj7ND5qP4UNHM4aHL4O7j06kHaoXReESNFVnWTbfY6QAmNNdH2B0x1Za1XtFtOdmfZz9/V3N9xTgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGvfo18nj56VuJJa9hixyMXkqKmykvpfJWMJeTSWZlV08Lf6BafwS3CnJN/22pwVPebWuNT3tLYRblLFSX15Ofv/o4fW/bjt7PeqHnWh0tdJGaysuobM0yQwMWB0bup2Z6v3R0e34VTq8+/v3A9rBFx5zN6S/0Goq8uSxzODMrVj6zmt/8AmjTii/vJuhS4vOYvNQJNjb9e2xe+KRHKntTmgG+AfjntY1XOcjWpxVV4IgH6aOYzFLBYubIX5khrxJuq81Ve5ETvVe5DjZDXmMhsuo4psmbyXJK1JOvsv77/AMLE9aqYsbpm/k8nDmdVSxT2YV61WhFxgqr5eP43/vLy7gPrSuNuXMhY1RmIVhvXG+Dr1nc6tdF3Rv8A9nfid+RVAAAAAAAAAAAAAAAAAAAAAVN0IipL/mFn3ULC9TT2SlV9SZfw1JnLusTl7muXi1fLuhbmvfoVcpQmpXYGWK0zeo+N6bo5ANg896Weje50iUsSyjlIsdPjrCztfJEsiKqoiJyVOKKiKbsbM/ojaOOKfUGBbwajV61uq3ybf7xqfmd7Darwmeb/APj8hDLKn4oXL1JWL5FYuyp+QECzou1Rn8DlsNrfWP2zUuRM7P4Kq2N1eVruskieXltt3puT7uhTXeRw1fTOW6QGy6bgVqJDHXXwisav3W7r3JsmyKqomycOB7qANPEYqrg8NTxdGPwdWnC2CJqruqNamybr3qbM00deB800jY442q5z3LsjUTmqqcPL61weHlSvJb7TddwZUqp4aZy+Tqt5e/Y5SYbMaylZNqKP7OxDXI5mKY7d823FFncnd+4nvA/MSkmtdRxZ+Vj2YXHqv2ax6bdokXgs6p5E4o38y1PljGRRtjjajGNREa1qbIiJ3Ih9AAAAAAAAAAAAAAAAAAAAAAAAAAAAJfVuJuts1dRYaPwmUxyKjoeXaoV/FF7e9vr9pUHjXSJ0k6gp5CbEVacuGY3f/TP2WWVv7TVTgietN19aAerYXNUs/ior9GTrxP4Kips5jk5tcnc5O9DfPPcPpTI4/A4zM6etpBk5akT7dedVWG6vV3VX96P4/jT3nZoa8x62G0c3FJgcjy8Dc+6x6+Vkn4XJ7wKkHyyRkjEexyOavFFau6KfQAGlksxjsPXWfI3oKkSJv1pXo3f2b8yZk1FmNVL2fS9Z9Sk7g/LW41a1E/8AijXi9fWuyAZtU5izfuJpbByL9pWW/wBJnbxSlCvN6r+0qcGp69yixeMrYfFVsfTj8HXrMSNjfUnl9feaun9O0tO0XQVevJLK7wk9iVetLO9ebnO71/kdUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAcPVefdgcSi1o+0ZG29K9Ov3ySry9yc1XyIByNQPfqzUbdL13KmPq9WfKyNXbrJzZAi+V226+pDvYnTWKwV25ZxtVtZ13qrKxnBm7d9lRvJOfcY9LYBunsK2u+TtFyZyzWrC85pXcXO/5J6kQ7IAn8lobTmVnWefFxMsL/AL+BVhk+JiopQACTTo/rxp1Yc/qGFncxuRcqJ+e4To4wUrkdkH5DKKndduySJ8O6J/ArABrUMbSxdZK9GpDVhTkyJiMT8kNkAAAAAAAAAAAAAAAAAAAAAAAAAAcjL6UwWdcj8ji69iROUqt6sif8SbL/ABOuAJNvR7Rh4VMxnabO5kORf1U9ztwvR1i5l/p1/MZFn7FnISK38kVCsAHOxOn8Tg4vB4zHV6iLzWJiIq+1eanRAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAANXJ5KtiMXYyFyRIq9diyPd5ET/mR+K0lDquhcy+qKfhLGVangoXLxpwJ+BrV/Vdx6yqneplu/666uTHN+9hMLKj7S/q2LKcWxetrOa+vZC1Ax14GVq0UEaKjImIxu/kRNkMd2hUyNZ1e7Vhswu5slYj2/kpsACTd0b4Fj1fQ7bi3L/wChuSRJ8O+38AugK702l1BqKVn7Lsi5EX8kRSsAE7jtB6bxthLEWMjmsp/vrLlnf+b1UokRETZE2AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD4mmjrwPmle2OONquc5y7I1E4qqkhpeGTUuak1dcY5sGzocVC9PwQ7/AHpVT9p/8j81JI/VWeZpOq5UpxI2fKyt7mb7thRfK/bdfUWMcbIYmxxtRjGIjWtamyIickQD6AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACb1hmrNGtXxeK2dmMo5Yayc/BJ+vKvqanH27HbyF+ti8dPeuSpFXrsWSR69yITmkKFm/bsarykSx3Mg1G1oXc61ZOLW/8A2d+JfagHbwGEraewtfG1d1ZEn3nu/FI5eLnu8qqu6nRAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHE1Xn/sDD+Egj7RfsPSCnXTnLK78KexOa+pDsyyshifLI9rGMRXOc5dkRE5qpHabjfqnPP1Zaa5KcSOgxUTu5nJ0yp5X8k/dA7OlcB9gYdIpZO0XrD1nt2F5yyu/Evs7k9SHaAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAATur85YxtODH4xEkzOSf4CoxeTV/Wkd+61OP5AczI/wCumrfslv3sLiHtkur+rYsJxZD60b+J3r2QtUTZDmaewdfTuEgx9dVf1N3SSu/FK9eLnu9arxOmAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAONqjPt0/h1nZGti5M5IKldOc0ruDW+zvX1IoHG1PLJqbOR6RqPclZEbPlZWLt1Yt/uxb/tPX+BXwxRwQshiY2OONqNa1qbI1E4IiHG0pgHYHFOSzJ2jI23rYuT98kq8/cnJE8iHcAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAMF67Xx1Ce5albFBAxZJHu5NRE3VSY0hSsZS7Pq3JxOZYvN6lOF/OtW5tT1Od+JfcYMsq6z1T9hRr1sPi3tlyLk5Ty82QetE/E73IWqIiIiImyIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAH497Y2Oe9yNa1N1VV2RE8pG6eY7Vmon6qsNXsFbrQYqN3e3k+fbyu22T1IfWqbEuosxHpCjI5kb2pNlJmLxig7o0Xuc/l7NytrwRVa0deCNscUTUYxjU2RqImyIgGQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAJ/V+dnxOPiqY5qS5fIv7PTjX9peb1/danFfcdq5bgoUprdqVsUEDFkke5eDWom6qS2kqk+ZyM2rslE6OS0zwdCB6ca9bmi7dzn/iX1bIB29OYKDTuDhx8Llkc3d8szvxTSLxc9fWqnUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHI1Pno9O4SS2saz2HqkVaBv4ppXcGsT3/wRTrOc1jVc5Ua1E3VVXZEIzBNdq/Ui6mnav2ZTV0OLjcnB68nz7evk31AdfSWBkwmKe65Ik+UuvWxdm/bkXuT91qcE9h3QAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHA1bnpsPjo4KDEmy19/Z6US9715uX91qcVA5WacusNUN07Eqrise5s2TenKR/NkH/U71bIWaIjWoiIiInJEOVprAxadwkdJj1mlVVlnnd+KaV3Fz19q/wANjrAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADk6lz0WncJLdexZpVVI4IG/imldwaxPav8NwOLqy1NncpDpDHyOYthqS5GZi8Ya+/wCHfuc/knq3Uq61aGnVirV42xQwsRjGNTg1qJsiIcXSWBlw2OknvvSbLX39ouzeV68mp+61OCHfAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAMVmzDTqy2bEjYoYmq973LsjWom6qpKaUrTZ7KzavvxuYk7fA42F6cYa/7e3c5/P2bGPOudq/UiaZhVfsykrZ8o9q8HrzZB79t3epCza1rGI1rUa1qbIiJsiIB+gAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD8cqNaqqqIicVVSMwyLrHVC6hlTfE45zoca1U4Sv5Pn/6W+9TLq23PmcjBpHHSujkts8LfmYvGCtyVPU5/4U9W5U06kFClDUrRNighYjI2NTg1qJsiAZgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA4WrM+/B4tjakaT5O69K9KD9uRe9f3U5qvkQ7M88VWvJPPI2OKJqve9y7I1ETdVUktKwS6iy8ur7zHNje1YcZC9P/AOKDfjIqftP5+zYDs6YwLNO4VlVZFnsyOWazOvOaV3Fzl9/L1Ih2AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABy9R52DTuEmvzNWRzdmRQt/FNIvBrE9aqdRVRE3UisUn+eWqlzkn3sPi3uixzV5TS8nz+tE/C33qB1NIYKfFUZrmRckuXyT+0XJE5I7uYn7rU4J7yhAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAcPVmfdgcQi1o/D5G09K9ODvkldy9yc19SAcjUT3as1A3StZy9gr9WfKyN/Z5sgRfK7bdfUhYsY2KNrGNRrGoiI1E2RE8hyNLYBunsM2u+RZ7kzlmtWF5zSu4ucv8k9SIdkAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAczUOcr6dwk+RsIr0jTZkbfxSvXg1ietV4AcXV16xk7sGksXK6Ozeb17k7Odatycv8A9nfhT3lLQo18bQgpVImw14GJHGxvJEROBxdH4OxjaU1/JqkmYyT/AA9t6fqr+rGn7rU4fmUQAAAASfSXl72E0TYu46w6vZZJG1HoiKqIrkReaKh18PSnoVnT28vavJIxrv6T4NEj4bqqdVqeXv8AIB1QRV3pQw8eeo4rHtfkZLVhsCzRrtEzdyIqo79ZU35J+ZW3q0lyk+CK3NTe7baaHq9dvHu6yKn8ANgEPpbIZNOkPPYW3k571WlFE6JZmsRyK5N1/C1PKXAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAfE00deB80r2xxxtVznOXZGonFVUkNMwyanzj9W3GObWajocVC9PwxfrTKn7T+790/NSyP1Tn49J1XKlSNGz5WRq8o9/uw7+V+3H1IWMcbIYmRRsaxjERrWtTZEROSIB9AAAAQTrWWy3SllsKzNW6NOrUimjbXbHujlRu/FzV8oF6CXzurVwGSx+Er4+1lsncj3jY1zWI5G8Fc5y8E8q8NjUi15Zp6mqYTP4N+MlvLtXlZYbNG9d9kRVRE248PegFmCR143I4/T+RzVHNXKr60HWZAxsax7p3ru1V7/ACnc05Zmu6Xxlqw9ZJpqscj3qm3WcrUVV4AdIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABeCEVj99a6r+1n/ewmIkdHST9WxOnB03rRvJvr3U2NYX7N+zX0pi5VZdyLVdYmbzrVk4Pf7V/CnrUpMfQrYvHQUakSRV67EjjYnciAbIAA8pyrLq9NmOxVLLZFazuraswutPVibdZytRN+DVRGpt6z1Y8WxWYuXuljP2sVAy3kplWrVWTfwULGqjXSvVO5EYnDmqu2OnZz+q9Ha8xdLM5aPKUsk5rV6sKRo3d3VXZE4oqKqLz4oB3emD9HNr+ui/xoWMMUc+NZFKxr45Ika5rk3RyK3ZUVCO6YP0c2v66L/GhZ1l2oxKiKu0acE9gHnfSDXhqao0LXrRMhhjvdVkbGo1rU60fBETkelHlerv85c/n8Heq6TvRxYqfw6pLLEjpPvNXZNnLt+H+J6JiMjZyVV8tnF2sa9rur4OwrFVeHNOqqpsBI6c/TLqv+og/wAKF8QOnP0y6r/qIP8AChfAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADi6qz/2BiPCwxdovWHpBTrpzlld+FPYnNfUh2JJGRRukkcjGMRXOc5dkRE5qpHabjfqrUD9WWWr2KFHV8VG5P1N9nzbeV3JPUgHY0rgPsDEdSeXtF+y9Z7lhecsrua+xOSepDtgAcjVUTJNMXnyWrNVIInTeEryrE9Oq1V5p3eoluh92Qs6TmyORuWbT7U6oxZ5HP2a1EThuvDj1jd6WMj9n9Hl1rV+/aVldv/Eu6/KinA05X1RlNF06+nLcWIx9WBGxzSRdaW5Jze5N/wADOsqoi815gepEFiP06ag/u+H/AKT76LdW39T4a3Hk3JJcoyox0iNRvXaqcN0ThuioqcD4xH6dNQf3fD/0gXMvgYkWxL1GJG1VWR2ydVvNePch5zXif0ia7qZmJjo8DhXr4CVybLalRUVVb+7uicfV6+G10lw6jyjqmLxmJnuYx20tzwUrY/DIi8It1XdE4brw70MEGX1u77Px1LSLcNUZNEySRszJEZCjk6yI3u4d/MCg6R/0c5r+zr/NDoaS/wBjMN/Y4f8AAhz+kf8ARzm/7Ov80OhpL/YzDf2OH/AgHXAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADnZ/N1tPYWfI2t1ZEn3WN/FI5eDWN9arwOiRVT/XTV/b1+9hMLIrKyfq2LKcHSetrOSevdQOjpDCWaVexlcrs7M5NyS2V5+CT9SJvqanD27lIAANLM324vCXb7lRErQPl4+pqqbpw9Y4a3qDStvF0pooJbKNYr5d9kb1kV3L1IBIdCmLbFpu3l5G72bs6tVy8+q3/AP0rlNLV6f5x9NGDxVf77cejZZ1T9X73hHfwRvxHYw+ldY6Yxb8TiMriZqiuV0ctmB6SRqvFdkRVRePHidrSOi4NMrZtzWX5DK3F61i3Imyu477Incm/5/kBk1xp2xqnSs2LrTRwSyPY9HyIqtTqu3Xkb2GZmo2OZlUodVrWpH2VX7+vfre7kdQANjWv9t7FJ9npB2rh1PD9bqc+O/V48tzZAElpzTWVoavy2dyc1Nz8hHGzwdbr7NVvD9b1IVoAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAOPqjPs09hXWWxrPalckNWu3nNK7g1qfzX1IoHF1PNJqXNM0jTe5tfqpNlZmL+CHuiRf2n/wAivhhjrwRwwsbHFG1GMa1NkaicERDjaTwDsFiV7VJ4fJW3rYuz+cldz9yck9SHcAAADyzpfeuUy+nNOxuVHW7HXenqVUYi/wAXHoOQtVdOabnsIjYq1GuqtbyREa37rU/ghI6n0Dl87rNuerZWvVdTZF2Nro1f95qq5ety2TdV5bmXJ6S1NqtYquosrSr4xjkfJXxzHo6ZU5dZzuQHP6E8bNBpu7kpmq3t9jdu/e1qbb/ErvyOzPpvO1deZDUOLmxzm3K7IPB2fCIreqicfu+tCsp069CnDUqxNhghajI2NTg1E5IZgPiLwngWeG6nheqnX6n4d9uO2/cfYAExq/EZ7PY65i6b8dHStReDV83hPCNXv5cDs4Si/GYGhRle18laBkTnN5KrWoiqn5G8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGhnMzVwGGsZK45Uigbvsn4nryRqeVVXZEA4esMlasz19L4mRY8hkmqsszf/ACtdOD5Pav4W+tShxmNq4jGV8fSjSKvXYkbGp3In/M4ejsNarxWM1lmp9sZRySzJz8Cz9SFPU1Ofr3KYAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA/HvbGxz3uRrWpuqquyIhGafY7VuoXapsNX7PrdaHFRu705Pn28rttk9SH3qqxLqDLRaQoyOa2VqTZOZi7eCr7/AIN/2n8vZuVtevFUrR14I2xxRNRjGNTZGoibIiAZAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIqD/XXV62V+9g8JKrYU5ts2k5v9bWck9Zuaxylp7q+m8RJ1cplEVFkT/y0CcHyr/JPWvqO7icXVwuJrY6lH4OvXYjGJ3+1fWvNfWoG4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHI1Pno9O4SS34NZ7D3JFWgT8U0ruDWJ7/AOCKdZzkY1XOVEaibqq8EQjMG12sNTLqSZFXF0VdDi2KnCR3J8/v/C31bgdbSeAkwmMe+5Ik+Uuv7Rdn/bkXuT91qcET1HeAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADnVMHTp5q7lY2vdbuo1sj3u63Va1Nka3yJ37eU6IAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABqZXGw5jE2cdYfKyGyxY3rE/qO2Xnspmq1oaVSKtWjbFDC1GMY1Nka1E2REAAygAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD//2Q=="}}},{"cell_type":"markdown","source":"## Implémenter une activation non linéaire en PyTorch\n\nDans PyTorch, une fonction d’activation est implémentée comme une **couche à part entière**,\nplacée entre deux couches linéaires.\n\nElle ne contient **aucun paramètre à apprendre**,\nmais elle modifie la sortie de la couche précédente de manière non linéaire.\n\n\n### Structure générale d’un réseau avec activation\n\nUn réseau simple avec une couche cachée s’écrit conceptuellement:\n\n$$\nX ;\\xrightarrow{;\\text{Linear};}; h\n;\\xrightarrow{;\\phi;};\n\\tilde{h}\n;\\xrightarrow{;\\text{Linear};}; \\hat{y}\n$$\n\noù:\n\n* la première couche `Linear` calcule une transformation affine\n* $\\phi$ est une fonction d’activation non linéaire (par exemple ReLU)\n* la seconde couche `Linear` produit la sortie finale\n\n\n\n### Implémentation avec `nn.Sequential`\n\nLa manière la plus simple de chaîner des couches en PyTorch\nest d’utiliser `nn.Sequential`.\n\n```python\nmodel = nn.Sequential(\n nn.Linear(m, k),\n nn.ReLU(),\n nn.Linear(k, 1)\n)\n```\n\nInterprétation ligne par ligne:\n\n* `nn.Linear(m, k)`\n première couche linéaire\n transforme un vecteur d’entrée de dimension `m`\n en une représentation intermédiaire de dimension `k`\n\n* `nn.ReLU()`\n applique la fonction d’activation ReLU:\n $$\n \\text{ReLU}(z) = \\max(0, z)\n $$\n\n* `nn.Linear(k, 1)`\n seconde couche linéaire\n transforme la représentation activée en prédiction finale\n\n\n### Ce que fait réellement PyTorch\n\nLorsqu’on écrit:\n\n```python\ny_hat = model(X)\n```\n\nPyTorch effectue automatiquement les opérations suivantes:\n\n```python\nh = X @ W1 + b1\nh_relu = relu(h)\ny_hat = h_relu @ W2 + b2\n```\n\nsans que l’on ait besoin d’écrire explicitement ces étapes.\n\n\n\n### Rôle de l’activation dans l’apprentissage\n\nL’activation non linéaire agit à deux niveaux:\n\n* **représentation**\n elle transforme l’espace des données après chaque couche\n\n* **optimisation**\n elle modifie la forme de la fonction de coût\n et permet à la descente de gradient d’explorer des solutions\n inaccessibles avec un modèle purement linéaire\n\nSans cette activation:\n\n* le réseau se simplifie algébriquement\n* la profondeur n’apporte aucun gain\n\n\n\n### Choix de la dimension intermédiaire `k`\n\nLe paramètre `k` correspond au nombre de neurones dans la couche cachée.\n\n* petit `k` → modèle peu complexe\n* grand `k` → modèle plus expressif, mais risque de surapprentissage\n\nDans les exercices, on peut commencer par une valeur modeste\n(par exemple `k = 8` ou `k = 16`).\n","metadata":{}},{"cell_type":"markdown","source":"### 💡 Syntaxe à reprendre\n\n_Repère syntaxique pour aborder l'exercice ci-dessous._\n\n```python\nfrom torch.utils.data import TensorDataset, DataLoader\nscaler = StandardScaler()\nX_train = scaler.fit_transform(X_train)\nX_test = scaler.transform(X_test)\nX_train_t = torch.tensor(X_train, dtype=torch.float32)\ny_train_t = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)\nX_test_t = torch.tensor(X_test, dtype=torch.float32)\ny_test_t = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)\ntrain_dataset = TensorDataset(X_train_t, y_train_t)\nbatch_size = 32\ntrain_loader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)\nm = X_train_t.shape[1]\nmodel = nn.Sequential(nn.Linear(m, 10), nn.ReLU(), nn.Linear(10, 1))\ncriterion = nn.MSELoss()\noptimizer = torch.optim.SGD(model.parameters(), lr=0.1)\nepochs = 100\nloss_history = []\nfor _ in range(epochs):\n nb = 0\n epoch_loss = 0\n for (Xb, yb) in train_loader:\n optimizer.zero_grad()\n u = model(Xb)\n loss = criterion(u, yb)\n loss.backward()\n optimizer.step()\n epoch_loss += loss.item()\n nb += 1\n loss_history.append(epoch_loss / nb)\nwith torch.no_grad():\n y_hat = model(X_test_t)\ny_hat = y_hat.cpu().numpy().reshape(-1)\n```\n","metadata":{}},{"cell_type":"markdown","source":"> #### Exercice \n> On reprend le dataset `abalone_mini` et la prédiction de la variable cible `Weight`.\n>\n> L’objectif est maintenant d’introduire une **fonction d’activation non linéaire**\n> dans le modèle, afin d’augmenter sa capacité de représentation.\n>\n> Implémenter en PyTorch un réseau composé de:\n>\n> $$\n X \\;\\xrightarrow{\\;\\text{Linear}\\;}\\; h\n \\;\\xrightarrow{\\;\\text{ReLU}\\;}\\;\n \\tilde{h}\n \\;\\xrightarrow{\\;\\text{Linear}\\;}\\; \\hat{y}\n $$\n>\n> en utilisant `nn.Sequential` avec:\n> - une première couche `nn.Linear(m, k)`\n> - une activation `nn.ReLU()`\n> - une seconde couche `nn.Linear(k, 1)`\n>\n> où $m$ est le nombre de variables d’entrée\n> et $k$ la dimension de la couche cachée (par exemple $k=8$ ou $k=16$).\n>\n> Conserver exactement le même protocole expérimental que précédemment:\n> - même séparation train / test\n> - même normalisation des entrées\n> - même fonction de coût (MSE)\n> - même optimiseur et learning rate\n> - entraînement en minibatch avec `DataLoader`\n>\n> Entraîner le modèle pendant un nombre d’epochs fixé,\n> puis évaluer les performances sur le jeu de test (MSE et/ou $R^2$).\n>\n> Comparer les résultats obtenus avec:\n> - un seul neurone linéaire\n> - deux neurones linéaires sans activation\n> - deux neurones avec une activation ReLU intermédiaire\n>\n> Question \n> Observe-t-on une amélioration de la prédiction lorsque l’on introduit\n> une activation non linéaire ?\n> Comment expliquer ce résultat en termes de capacité du modèle\n> et de rôle des fonctions d’activation dans les réseaux de neurones ?\n","metadata":{}},{"cell_type":"code","source":"df = pd.read_csv('/kaggle/input/datasets/pyim59/mini-datasets/abalone_mini.csv')\n\nX = df.drop(columns='Weight').to_numpy()\ny = df['Weight'].to_numpy()\n\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n\nscaler = StandardScaler()\nX_train = scaler.fit_transform(X_train)\nX_test = scaler.transform(X_test)\n\nX_train_t = torch.tensor(X_train, dtype=torch.float32)\ny_train_t = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)\n\nX_test_t = torch.tensor(X_test, dtype=torch.float32)\ny_test_t = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)\n\nprint(X_train.shape)\nprint(y_train.shape)\n\ntrain_dataset = TensorDataset(X_train_t, y_train_t)\n\nbatch_size = 32\n\ntrain_loader = DataLoader(\n train_dataset,\n batch_size=batch_size,\n shuffle=True\n)\n\nmodel = nn.Sequential(\n nn.Linear(X_train_t.shape[1], 3),\n nn.ReLU(),\n nn.Linear(3, 1)\n )\n\ncriterion = nn.MSELoss()\noptimizer = torch.optim.SGD(model.parameters(), lr=0.1)\n\nepochs = 100\nloss_history = []\nfor _ in range(epochs):\n nb=0\n epoch_loss=0\n for Xb, yb in train_loader:\n optimizer.zero_grad()\n u = model(Xb)\n loss = criterion(u, yb)\n loss.backward()\n optimizer.step()\n epoch_loss += loss.item()\n nb += 1\n loss_history.append(epoch_loss/nb)\n\nplt.plot(loss_history)\nplt.show()\n\nwith torch.no_grad():\n y_hat = model(X_test_t)\n\ny_hat = y_hat.cpu().numpy().reshape(-1)\n\nprint(f\"MAE : {mean_absolute_error(y_test,y_hat):.2f}\")\nprint(f\"RMSE : {np.sqrt(mean_squared_error(y_test,y_hat)):.2f}\")\nprint(f\"MAPE : {mean_absolute_percentage_error(y_test,y_hat):.4f}\")\nprint(f\"R2 : {r2_score(y_test,y_hat):.3f}\")\n\nplt.scatter(X_test[:,1], y_test)\nplt.scatter(X_test[:,1], y_hat, c='red')\nplt.show()","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T02:45:10.477325Z","iopub.execute_input":"2026-05-13T02:45:10.477728Z","iopub.status.idle":"2026-05-13T02:45:18.566681Z","shell.execute_reply.started":"2026-05-13T02:45:10.477695Z","shell.execute_reply":"2026-05-13T02:45:18.565875Z"}},"outputs":[{"name":"stdout","text":"(3341, 4)\n(3341,)\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"
","image/png":"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\n"},"metadata":{}},{"name":"stdout","text":"MAE : 0.09\nRMSE : 0.12\nMAPE : 0.1902\nR2 : 0.942\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"
","image/png":"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\n"},"metadata":{}}],"execution_count":132},{"cell_type":"markdown","source":"## Couches cachées à plusieurs neurones\n\nJusqu’ici, nous avons considéré:\n\n* soit un seul neurone linéaire\n* soit deux neurones en séquence\n\nEn pratique, une **couche cachée** contient généralement **plusieurs neurones**.\n\n\n### Une couche cachée à $k$ neurones\n\nUne couche cachée de taille $k$ correspond à une transformation:\n\n$$\nh = \\phi(X W + b)\n$$\n\noù:\n\n* $X \\in \\mathbb{R}^{n \\times m}$ est l’entrée\n* $W \\in \\mathbb{R}^{m \\times k}$ est la matrice de poids\n* $b \\in \\mathbb{R}^{k}$ est le biais\n* $h \\in \\mathbb{R}^{n \\times k}$ est la représentation cachée\n* $\\phi$ est une fonction d’activation (ReLU par exemple)\n\n\n### Implémentation PyTorch (une couche cachée)\n\n```python\nk = 16\n\nmodel = nn.Sequential(\n nn.Linear(m, k),\n nn.ReLU(),\n nn.Linear(k, 1)\n)\n```\n\nInterprétation:\n\n* la première couche projette les données dans un espace de dimension $k$\n* chaque neurone apprend une combinaison différente des variables d’entrée\n* ReLU introduit la non-linéarité\n* la dernière couche produit la prédiction\n\n\n\n## Empiler plusieurs couches cachées\n\nOn peut empiler plusieurs couches cachées pour construire un réseau plus profond.\n\nExemple avec **deux couches cachées**:\n\n$$\nX \\rightarrow h_1 \\rightarrow h_2 \\rightarrow \\hat{y}\n$$\n\n\n### Implémentation PyTorch (plusieurs couches)\n\n```python\nmodel = nn.Sequential(\n nn.Linear(m, 32),\n nn.ReLU(),\n nn.Linear(32, 16),\n nn.ReLU(),\n nn.Linear(16, 1)\n)\n```\n\nIci:\n\n* première couche cachée: 32 neurones\n* seconde couche cachée: 16 neurones\n* chaque couche affine puis non linéairement l’espace des données\n\n\n\n## Pourquoi réduire le nombre de neurones à chaque couche ?\n\nIl est fréquent de voir des architectures du type:\n\n$$\nm \\rightarrow 32 \\rightarrow 16 \\rightarrow 8 \\rightarrow 1\n$$\n\nCe n’est **pas une règle absolue**, mais une **heuristique raisonnable**.\n\n\n\n### Intuition principale\n\nChaque couche cachée apprend une **représentation plus abstraite** que la précédente.\n\n* premières couches\n → combinent directement les variables d’entrée\n → capturent des motifs locaux ou simples\n\n* couches plus profondes\n → combinent des motifs déjà abstraits\n → nécessitent souvent **moins de dimensions**\n\n\n### Raisons pratiques\n\n1. **Réduction de la complexité**\n Diminuer progressivement la taille limite le nombre total de paramètres.\n\n2. **Régularisation implicite**\n Forcer le réseau à “compresser” l’information réduit le sur-apprentissage.\n\n3. **Stabilité de l’optimisation**\n Des couches trop larges partout rendent l’entraînement plus instable,\n surtout sur de petits datasets.\n","metadata":{}},{"cell_type":"markdown","source":"### 💡 Syntaxe à reprendre\n\n_Repère syntaxique pour aborder l'exercice ci-dessous._\n\n```python\nfrom torch.utils.data import TensorDataset, DataLoader\nscaler = StandardScaler()\nX_train = scaler.fit_transform(X_train)\nX_test = scaler.transform(X_test)\nX_train_t = torch.tensor(X_train, dtype=torch.float32)\ny_train_t = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)\nX_test_t = torch.tensor(X_test, dtype=torch.float32)\ny_test_t = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)\ntrain_dataset = TensorDataset(X_train_t, y_train_t)\nbatch_size = 32\ntrain_loader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)\nm = X_train_t.shape[1]\nmodel = nn.Sequential(nn.Linear(m, 32), nn.ReLU(), nn.Linear(32, 16), nn.ReLU(), nn.Linear(16, 1))\ncriterion = nn.MSELoss()\noptimizer = torch.optim.SGD(model.parameters(), lr=0.1)\nepochs = 100\nloss_history = []\nfor _ in range(epochs):\n nb = 0\n epoch_loss = 0\n for (Xb, yb) in train_loader:\n optimizer.zero_grad()\n u = model(Xb)\n loss = criterion(u, yb)\n loss.backward()\n optimizer.step()\n epoch_loss += loss.item()\n nb += 1\n loss_history.append(epoch_loss / nb)\nwith torch.no_grad():\n y_hat = model(X_test_t)\ny_hat = y_hat.cpu().numpy().reshape(-1)\n```\n","metadata":{}},{"cell_type":"markdown","source":"> #### Exercice \n> On reprend le dataset `abalone_mini` et la prédiction de la variable cible `Weight`.\n>\n> L’objectif est d’étudier l’impact de la **largeur** et de la **profondeur**\n> d’un réseau de neurones entièrement connecté.\n>\n> 1. Implémenter en PyTorch un réseau avec **une seule couche cachée**\n> de $k$ neurones, suivie d’une activation ReLU:\n>\n> $$\n X \\;\\xrightarrow{\\;\\text{Linear}(m,k)\\;}\\;\n h \\;\\xrightarrow{\\;\\text{ReLU}\\;}\\;\n \\hat{y}\n $$\n>\n> Tester plusieurs valeurs de $k$ (par exemple $k=8$, $16$, $32$).\n>\n> 2. Implémenter ensuite un réseau avec **deux couches cachées**,\n> en réduisant progressivement le nombre de neurones:\n>\n> $$\n X \\;\\xrightarrow{\\;\\text{Linear}(m,2k)\\;}\\;\n h_1 \\;\\xrightarrow{\\;\\text{ReLU}\\;}\\;\n h_2 \\;\\xrightarrow{\\;\\text{Linear}(2k,k)\\;}\\;\n \\tilde{h}\n \\;\\xrightarrow{\\;\\text{ReLU}\\;}\\;\n \\hat{y}\n $$\n>\n> (par exemple $32 \\rightarrow 16 \\rightarrow 1$).\n>\n> 3. Pour chaque architecture:\n> - utiliser le même découpage train / test (`random_state=42`)\n> - appliquer la même normalisation des entrées\n> - utiliser la même fonction de coût (MSE)\n> - utiliser le même optimiseur et les mêmes hyperparamètres\n> - entraîner en minibatch avec un `DataLoader`\n>\n> 4. Tracer la courbe de loss d’apprentissage pour chaque modèle.\n>\n> 5. Évaluer les performances sur le jeu de test (MSE et/ou $R^2$).\n>\n> Comparer les résultats obtenus:\n> - réseau peu profond vs plus profond\n> - couche cachée large vs couche cachée plus étroite\n>\n> Question \n> Observe-t-on une amélioration systématique des performances\n> lorsque l’on augmente le nombre de neurones ou de couches ?\n> Comment interpréter ces résultats en termes de capacité du modèle\n> et de risque de sur-apprentissage sur un petit dataset ?\n","metadata":{}},{"cell_type":"code","source":"df = pd.read_csv('/kaggle/input/datasets/pyim59/mini-datasets/abalone_mini.csv')\n\nX = df.drop(columns='Weight').to_numpy()\ny = df['Weight'].to_numpy()\n\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n\nscaler = StandardScaler()\nX_train = scaler.fit_transform(X_train)\nX_test = scaler.transform(X_test)\n\nX_train_t = torch.tensor(X_train, dtype=torch.float32)\ny_train_t = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)\n\nX_test_t = torch.tensor(X_test, dtype=torch.float32)\ny_test_t = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)\n\nprint(X_train.shape)\nprint(y_train.shape)\n\ntrain_dataset = TensorDataset(X_train_t, y_train_t)\n\nbatch_size = 32\n\ntrain_loader = DataLoader(\n train_dataset,\n batch_size=batch_size,\n shuffle=True\n)\n\nmodel = nn.Sequential(\n nn.Linear(X_train_t.shape[1], 32),\n nn.ReLU(),\n nn.Linear(32, 16),\n nn.ReLU(),\n nn.Linear(16, 8),\n nn.ReLU(),\n nn.Linear(8, 1)\n )\n\ncriterion = nn.MSELoss()\noptimizer = torch.optim.SGD(model.parameters(), lr=0.1)\n\nepochs = 100\nloss_history = []\nfor _ in range(epochs):\n nb=0\n epoch_loss=0\n for Xb, yb in train_loader:\n optimizer.zero_grad()\n u = model(Xb)\n loss = criterion(u, yb)\n loss.backward()\n optimizer.step()\n epoch_loss += loss.item()\n nb += 1\n loss_history.append(epoch_loss/nb)\n\nplt.plot(loss_history)\nplt.show()\n\nwith torch.no_grad():\n y_hat = model(X_test_t)\n\ny_hat = y_hat.cpu().numpy().reshape(-1)\n\nprint(f\"MAE : {mean_absolute_error(y_test,y_hat):.2f}\")\nprint(f\"RMSE : {np.sqrt(mean_squared_error(y_test,y_hat)):.2f}\")\nprint(f\"MAPE : {mean_absolute_percentage_error(y_test,y_hat):.4f}\")\nprint(f\"R2 : {r2_score(y_test,y_hat):.3f}\")\n\nplt.scatter(X_test[:,1], y_test)\nplt.scatter(X_test[:,1], y_hat, c='red')\nplt.show()","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-05-13T02:54:02.405188Z","iopub.execute_input":"2026-05-13T02:54:02.406165Z","iopub.status.idle":"2026-05-13T02:54:12.746370Z","shell.execute_reply.started":"2026-05-13T02:54:02.406114Z","shell.execute_reply":"2026-05-13T02:54:12.745682Z"}},"outputs":[{"name":"stdout","text":"(3341, 4)\n(3341,)\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"
","image/png":"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\n"},"metadata":{}},{"name":"stdout","text":"MAE : 0.07\nRMSE : 0.11\nMAPE : 0.1034\nR2 : 0.947\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"
","image/png":"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\n"},"metadata":{}}],"execution_count":134},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"## Récapitulatif\n\nCe notebook a introduit les bases du **deep learning** à partir du cas le plus simple:\nle **neurone linéaire**.\n\n* Un neurone linéaire calcule\n $u = Xw + b$\n et correspond à une **régression linéaire**.\n\n* L’apprentissage repose sur la **descente de gradient**:\n learning rate, epochs, batch, minibatch.\n\n* Le neurone a été implémenté *from scratch* pour comprendre:\n calcul des gradients, mise à jour des paramètres, historique de loss.\n\n* La **normalisation des données** est essentielle pour la stabilité\n et la vitesse de convergence (StandardScaler, MinMaxScaler, RobustScaler).\n Les statistiques doivent être calculées **uniquement sur le train**.\n\n* En régression, normaliser la **cible `y`** améliore souvent la convergence.\n\n* PyTorch automatise ces mécanismes:\n tenseurs, autograd, optimiseurs, `nn.Linear`.\n\n* Conventions de formes importantes:\n entrées `(n, m)`, sorties `(n, 1)`,\n avec `view(-1, 1)` (équivalent à `reshape(-1, 1)` en NumPy).\n\n* Le `DataLoader` gère les minibatchs et le mélange des données.\n\n* Empiler des couches **linéaires** n’augmente pas la capacité du modèle.\n La **non-linéarité** (ReLU) est indispensable pour rendre le réseau expressif.\n\n* Ajouter des couches et des neurones augmente la capacité,\n mais n’améliore pas forcément la généralisation sur de petits jeux de données.\n","metadata":{}}]}