Machine Learning Kurs im Rahmen der Studierendentage im SS 2023
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# A simple neural network with one hidden layer in pure Python\n",
"\n",
"## Introduction\n",
"We consider a simple feed-forward neural network with one hidden layer:"
]
},
{
"attachments": {
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"image/png": 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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"![nn.png](attachment:48b1ed6e-8e2b-4883-82ac-a2bbed6e2885.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this example the input vector of the neural network has two features, i.e., the input is a two-dimensional vector:\n",
"\n",
"$$\n",
"\\mathbf x = (x_0, x_1).\n",
"$$\n",
"\n",
"We consider a set of $m$ vectors as training data. The training data can therefore be written as a $n \\times 2$ matrix where each row represents a feature vector:\n",
"\n",
"$$ \n",
"X = \n",
"\\begin{pmatrix}\n",
"x_{00} & x_{01} \\\\\n",
"x_{10} & x_{11} \\\\\n",
"\\vdots & \\vdots \\\\\n",
"x_{m-1\\,0} & x_{m-1\\,1} \n",
"\\end{pmatrix} $$\n",
"\n",
"The known labels (1 = 'signal', 0 = 'background') are stored in a $n$-dimensional column vector $\\mathbf y$.\n",
"\n",
"In the following, $n_1$ denotes the number of neurons in the hidden layer. The weights for the connections from the input layer (layer 0) to the hidden layer (layer 0) are given by the following matrix:\n",
"\n",
"$$\n",
"W^{(1)} = \n",
"\\begin{pmatrix}\n",
"w_{00}^{(1)} \\dots w_{0 \\, n_1-1}^{(1)} \\\\\n",
"w_{10}^{(1)} \\dots w_{1 \\, n_1-1}^{(1)} \n",
"\\end{pmatrix}\n",
"$$\n",
"\n",
"Each neuron in the hidden layer is assigned a bias $\\mathbf b^{(1)} = (b^{(1)}_0, \\ldots, b^{(1)}_{n_1-1})$. The neuron in the output layer has the bias $\\mathbf b^{(2)}$. With that, the output values of the network for the matrix $X$ of input feature vectors is given by\n",
"\n",
"$$\n",
"\\begin{align}\n",
"Z^{(1)} &= X W^{(1)} + \\mathbf b^{(1)} \\\\\n",
"A^{(1)} &= \\sigma(Z^{(1)}) \\\\\n",
"Z^{(2)} &= A^{(1)} W^{(2)} + \\mathbf b^{(2)} \\\\\n",
"A^{(2)} &= \\sigma(Z^{(2)})\n",
"\\end{align}\n",
"$$\n",
"\n",
"The loss function for a given set of weights is given by\n",
"\n",
"$$ L = \\sum_{k=0}^{m-1} (y_{\\mathrm{pred},k} - y_{\\mathrm{true},k})^2 $$\n",
"\n",
"We can know calculate the gradient of the loss function w.r.t. the wights. With the definition $\\hat L = (y_\\mathrm{pred} - y_\\mathrm{true})^2$, the gradients for the weights from the output layer to the hidden layer are given by: \n",
"\n",
"$$ \\frac{\\partial \\tilde L}{\\partial w_i^{(2)}} = \\frac{\\partial \\tilde L}{a_k^{(2)}} \\frac{a_k^{(2)}}{\\partial w_i^{(2)}} = \\frac{\\partial \\tilde L}{a_k^{(2)}} \\frac{a_k^{(2)}}{z_k^{(2)}} \\frac{z_k^{(2)}}{\\partial w_i^{(2)}} = 2 (a_k^{(2)} - y_k) a_k^{(2)} (1 - a_k^{(2)}) a_{k,i}^{(1)} \\equiv \\delta^{(2)}_k a_{k,i}^{(1)}$$\n",
"\n",
"Applying the chain rule further, we also obtain the gradient for the weights from the input layer to the hidden layer read: \n",
"\n",
"$$ \\frac{\\partial \\tilde L}{\\partial w_{ij}^{(1)}} = \\frac{\\partial \\tilde L}{\\partial a_k^{(2)}} \\frac{\\partial a_k^{(2)}}{\\partial z_k^{(2)}} \\frac{\\partial z_k^{(2)}}{\\partial a_{k,j}^{(1)}} \\frac{\\partial a_{k,j}^{(1)}}{\\partial z_{k,j}^{(1)}} \\frac{\\partial z_{k,j}^{(1)}}{\\partial w_{ij}^{(1)}} $$\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## A simple neural network class"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# A simple feed-forward neutral network with on hidden layer\n",
"# see also https://towardsdatascience.com/how-to-build-your-own-neural-network-from-scratch-in-python-68998a08e4f6\n",
"\n",
"import numpy as np\n",
"\n",
"class NeuralNetwork:\n",
" def __init__(self, x, y):\n",
" n1 = 3 # number of neurons in the hidden layer\n",
" self.input = x\n",
" self.weights1 = np.random.rand(self.input.shape[1],n1)\n",
" self.bias1 = np.random.rand(n1)\n",
" self.weights2 = np.random.rand(n1,1)\n",
" self.bias2 = np.random.rand(1) \n",
" self.y = y\n",
" self.output = np.zeros(y.shape)\n",
" self.learning_rate = 0.01\n",
" self.n_train = 0\n",
" self.loss_history = []\n",
"\n",
" def sigmoid(self, x):\n",
" return 1/(1+np.exp(-x))\n",
"\n",
" def sigmoid_derivative(self, x):\n",
" return x * (1 - x)\n",
"\n",
" def feedforward(self):\n",
" self.layer1 = self.sigmoid(self.input @ self.weights1 + self.bias1)\n",
" self.output = self.sigmoid(self.layer1 @ self.weights2 + self.bias2)\n",
"\n",
" def backprop(self):\n",
"\n",
" # delta2: [m, 1], m = number of training data\n",
" delta2 = 2 * (self.y - self.output) * self.sigmoid_derivative(self.output)\n",
"\n",
" # Gradient w.r.t. weights from hidden to output layer: [n1, 1] matrix, n1 = # neurons in hidden layer\n",
" # self.layer1.T: m x n1 matrix\n",
" d_weights2 = self.layer1.T @ delta2\n",
" d_bias2 = np.sum(delta2)\n",
"\n",
" print(self.layer1.shape) \n",
" \n",
" # shape of delta1: [m, n1], m = number of training data, n1 = # neurons in hidden layer\n",
" delta1 = (delta2 @ self.weights2.T) * self.sigmoid_derivative(self.layer1)\n",
" d_weights1 = self.input.T @ delta1\n",
" d_bias1 = np.ones(delta1.shape[0]) @ delta1 \n",
" \n",
" # update weights and biases\n",
" self.weights1 += self.learning_rate * d_weights1\n",
" self.weights2 += self.learning_rate * d_weights2\n",
"\n",
" self.bias1 += self.learning_rate * d_bias1\n",
" self.bias2 += self.learning_rate * d_bias2\n",
"\n",
" def train(self, X, y):\n",
" self.output = np.zeros(y.shape)\n",
" self.input = X\n",
" self.y = y\n",
" self.feedforward()\n",
" self.backprop()\n",
" self.n_train += 1\n",
" if (self.n_train %1000 == 0):\n",
" loss = np.sum((self.y - self.output)**2)\n",
" print(\"loss: \", loss)\n",
" self.loss_history.append(loss)\n",
" \n",
" def predict(self, X):\n",
" self.output = np.zeros(y.shape)\n",
" self.input = X\n",
" self.feedforward()\n",
" return self.output\n",
" \n",
" def loss_history(self):\n",
" return self.loss_history\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Create toy data\n",
"We create three toy data sets\n",
"1. two moon-like distributions\n",
"2. circles\n",
"3. linearly separable data sets"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# https://scikit-learn.org/stable/auto_examples/classification/plot_classifier_comparison.html#sphx-glr-auto-examples-classification-plot-classifier-comparison-py\n",
"import numpy as np\n",
"from sklearn.datasets import make_moons, make_circles, make_classification\n",
"from sklearn.model_selection import train_test_split\n",
"\n",
"X, y = make_classification(\n",
" n_features=2, n_redundant=0, n_informative=2, random_state=1, n_clusters_per_class=1\n",
")\n",
"rng = np.random.RandomState(2)\n",
"X += 2 * rng.uniform(size=X.shape)\n",
"linearly_separable = (X, y)\n",
"\n",
"datasets = [\n",
" make_moons(n_samples=200, noise=0.1, random_state=0),\n",
" make_circles(n_samples=200, noise=0.1, factor=0.5, random_state=1),\n",
" linearly_separable,\n",
"]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Create training and test data set"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# datasets: 0 = moons, 1 = circles, 2 = linearly separable\n",
"X, y = datasets[1]\n",
"X_train, X_test, y_train, y_test = train_test_split(\n",
" X, y, test_size=0.4, random_state=42\n",
")\n",
"\n",
"x_min, x_max = X[:, 0].min() - 0.5, X[:, 0].max() + 0.5\n",
"y_min, y_max = X[:, 1].min() - 0.5, X[:, 1].max() + 0.5\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Train the model"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
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"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 25.08801533764488\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 4.874964262015792\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 2.3410774657323574\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 1.673115701796859\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"loss: 1.3214647322223636\n",
"(120, 3)\n",
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"loss: 1.103942262974622\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.9554041072149319\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.8433686045059402\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"loss: 0.7523324840955374\n",
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"loss: 0.6751268935657366\n",
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"loss: 0.6088647998770811\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.5525408476488657\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"loss: 0.5052564062280487\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.4656732595638309\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.43230116918021555\n",
"(120, 3)\n",
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"loss: 0.40381664746435475\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.37917415441404057\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"loss: 0.35758784940801913\n",
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"loss: 0.3384741124092202\n",
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"loss: 0.3213960313670268\n",
"(120, 3)\n",
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"loss: 0.30602085675934976\n",
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"loss: 0.2920900227615915\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.2793986112572263\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.26778130230395514\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.2571026404339547\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.2472501596370228\n",
"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.23812942071467064\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"loss: 0.22966035047104455\n",
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"loss: 0.22177448581659043\n",
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"loss: 0.21441286071191368\n",
"(120, 3)\n",
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"loss: 0.20752435951517925\n",
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"loss: 0.20106441542465858\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.19499396883752154\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.18927862460012662\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"loss: 0.18388796360660056\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"loss: 0.17879497567581076\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.1739755887765731\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"loss: 0.16940827554827434\n",
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"loss: 0.16507372237672874\n",
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"loss: 0.16095454949610333\n",
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"loss: 0.15703507301048927\n",
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"loss: 0.1533011015783423\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.14973976193054134\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.1463393485052672\n",
"(120, 3)\n",
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"(120, 3)\n",
"loss: 0.14308919335741355\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.13997955319344332\n",
"(120, 3)\n",
"(120, 3)\n",
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"loss: 0.13700151093593088\n",
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"loss: 0.13414688966682914\n",
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"loss: 0.13140817715831843\n",
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"loss: 0.12877845949277106\n",
"(120, 3)\n",
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"loss: 0.12625136251277663\n",
"(120, 3)\n",
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"loss: 0.12382100003902233\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.12148192795639788\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
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"loss: 0.11922910340360132\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.11705784841391932\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.11496381744891089\n",
"(120, 3)\n",
"(120, 3)\n",
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"loss: 0.11294296834566157\n",
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"loss: 0.11099153626486678\n",
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"loss: 0.1091060102832438\n",
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"loss: 0.10728311232156516\n",
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"loss: 0.10551977814023127\n",
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"loss: 0.10381314016900359\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.10216051196722928\n",
"(120, 3)\n",
"(120, 3)\n",
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"loss: 0.10055937413641874\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.09900736152894789\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.0975022516156561\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"loss: 0.0960419538914768\n",
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"loss: 0.09462450021247272\n",
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"loss: 0.09324803596998887\n",
"(120, 3)\n",
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"loss: 0.09191081201844312\n",
"(120, 3)\n",
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"loss: 0.09061117728261675\n",
"(120, 3)\n",
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"loss: 0.08934757197858895\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.08811852138963955\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"loss: 0.08692263014476885\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.08575857695309241\n",
"(120, 3)\n",
"(120, 3)\n",
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"loss: 0.08462510975223628\n",
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"loss: 0.08352104123323299\n",
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"loss: 0.08244524470824319\n",
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"loss: 0.0813966502908232\n",
"(120, 3)\n",
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"loss: 0.08037424136149476\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.07937705129404021\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"loss: 0.07840416042035353\n",
"(120, 3)\n",
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"loss: 0.07745469321379238\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.0765278156728971\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.07562273288903286\n",
"(120, 3)\n",
"(120, 3)\n",
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"loss: 0.07473868678303591\n",
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"loss: 0.073874953997321\n",
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"loss: 0.07303084393113003\n",
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"loss: 0.07220569690770146\n",
"(120, 3)\n",
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"loss: 0.07139888246313986\n",
"(120, 3)\n",
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"(120, 3)\n",
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"loss: 0.07060979774766113\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.06983786603069106\n",
"(120, 3)\n",
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"loss: 0.06908253530203273\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.06834327696197065\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.067619584593793\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
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"loss: 0.06691097281272669\n",
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"loss: 0.06621697618580996\n",
"(120, 3)\n",
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"loss: 0.06553714821764274\n",
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"loss: 0.06487106039737628\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
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"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"(120, 3)\n",
"loss: 0.06421830130267316\n"
]
}
],
"source": [
"y_train = y_train.reshape(-1, 1)\n",
"\n",
"nn = NeuralNetwork(X_train, y_train)\n",
"\n",
"for i in range(100000):\n",
" nn.train(X_train, y_train)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot the loss vs. the number of epochs"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'loss')"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"plt.plot(nn.loss_history)\n",
"plt.xlabel(\"# epochs / 1000\")\n",
"plt.ylabel(\"loss\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": []
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.colorbar.Colorbar at 0x15e0c9360>"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 900x700 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"from matplotlib.colors import ListedColormap\n",
"\n",
"cm = plt.cm.RdBu\n",
"cm_bright = ListedColormap([\"#FF0000\", \"#0000FF\"])\n",
"\n",
"xv = np.linspace(x_min, x_max, 10)\n",
"yv = np.linspace(y_min, y_max, 10)\n",
"Xv, Yv = np.meshgrid(xv, yv)\n",
"XYpairs = np.vstack([ Xv.reshape(-1), Yv.reshape(-1)])\n",
"zv = nn.predict(XYpairs.T)\n",
"Zv = zv.reshape(Xv.shape)\n",
"\n",
"fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(9, 7))\n",
"ax.set_aspect(1)\n",
"cn = ax.contourf(Xv, Yv, Zv, cmap=\"coolwarm_r\", alpha=0.4)\n",
"\n",
"ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright, edgecolors=\"k\")\n",
"\n",
"# Plot the testing points\n",
"ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.4, edgecolors=\"k\")\n",
"\n",
"ax.set_xlim(x_min, x_max)\n",
"ax.set_ylim(y_min, y_max)\n",
"# ax.set_xticks(())\n",
"# ax.set_yticks(())\n",
"\n",
"fig.colorbar(cn)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
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"nbformat": 4,
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}