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@justinhou95
Created February 22, 2022 09:35
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{
"cells": [
{
"cell_type": "markdown",
"id": "4078fede",
"metadata": {},
"source": [
"# 1. ReLU Nerual Network on $\\mathbb{R}$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "94531e8e",
"metadata": {},
"outputs": [],
"source": [
"import time\n",
"from IPython.display import display, clear_output\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from importlib import reload\n",
"import solution1\n",
"\n",
"def plot_helper1(funcs):\n",
" x = np.linspace(-5,5,1001)\n",
" plot_nums = len(funcs)\n",
" fig, axs = plt.subplots(1,plot_nums,figsize = [plot_nums*3,2],sharey=True,sharex=True)\n",
" for ith, func in enumerate(funcs):\n",
" y = func(x)\n",
" axs[ith].plot(x,y)\n",
" axs[ith].grid()"
]
},
{
"cell_type": "markdown",
"id": "be27fef6",
"metadata": {},
"source": [
"## Variations of ReLU"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "3920ee2d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x144 with 4 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"r = lambda x: (x > 0) * x\n",
"r_inv = lambda x: r(-x)\n",
"t = lambda x: r(x-1)\n",
"t_inv = lambda x: r_inv(x-1)\n",
"funcs1 = [r,r_inv,t,t_inv]\n",
"plot_helper1(funcs1)"
]
},
{
"cell_type": "markdown",
"id": "99bd4db2",
"metadata": {},
"source": [
"## Hat function"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "0340c254",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x144 with 4 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"f1 = lambda x: r(x) + r_inv(x)\n",
"f2 = lambda x: r(1-f1(x))\n",
"x1, y1, width1 = 2, 10, 2\n",
"f3 = lambda x: f2((x-x1)/(width1/2))*y1\n",
"x2, y2, width2 = -1, 8, 4\n",
"f4 = lambda x: f2((x-x2)/(width2/2))*y2\n",
"funcs2 = [f1,f2,f3,f4]\n",
"plot_helper1(funcs2)"
]
},
{
"cell_type": "markdown",
"id": "9c13f676",
"metadata": {},
"source": [
"## Piecewise linear approximation by hat functions"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "8d53b4aa",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x216 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"func_obj = lambda x: np.sin(x**2) \n",
"grid_points = 33 # 33 = 2^5 + 1\n",
"x_grid = np.linspace(-5,5,grid_points)\n",
"y_grid = func_obj(x_grid)\n",
"\n",
"plt.figure(figsize = [5,3])\n",
"x = np.linspace(-5,5,1001)\n",
"plt.plot(x,func_obj(x),'r')\n",
"plt.scatter(x_grid,y_grid)\n",
"plt.legend(['objective', 'observation'])\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "e7959720",
"metadata": {},
"source": [
"## Q1: \n",
"Objective function:\n",
"$$\n",
"f(x) = \\sin(x^2),\\quad x \\in \\mathbb{R}.\n",
"$$\n",
"Construct a neural network $f_{nn}$ such that \n",
"$$\n",
"f_{nn}(x) = f(x),\\quad \\forall x \\in \\text{x_grid} \n",
"$$\n",
"(i.e. they match values on observation points). Actually $f_{nn}$ is a scaled Faber-Schauder\n",
"expansion of $f$.\n",
"\n",
"How should we select the width?"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "deb5fdd6",
"metadata": {},
"outputs": [],
"source": [
"def plot_helper2(func_obj, func):\n",
" x = np.linspace(-5,5,1001)\n",
" plt.figure(figsize = [6,3])\n",
" plt.plot(x,func_obj(x))\n",
" plt.plot(x,func(x))\n",
" plt.legend(['Objective function' , 'Approximation'])\n",
" plt.grid()\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "587e01a8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x216 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# piecewise interpolation \n",
"width = 10/(grid_points-1)\n",
"# Write your own func_nn here \n",
"func_nn = solution1.construct_func_nn(x_grid,y_grid,width,f2) # please comment this line while solving exercise \n",
"\n",
"plot_helper2(func_obj, func_nn)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "f6522f45",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x216 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# wrong width, not match on grid\n",
"width = 1\n",
"# Write your own func_nn here \n",
"func_nn = solution1.construct_func_nn(x_grid,y_grid,width,f2) # please comment this line while solving exercise \n",
"\n",
"plot_helper2(func_obj, func_nn)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "763d98df",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x216 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# overfitting \n",
"width = 0.1\n",
"# Write your own func_nn here \n",
"func_nn = solution1.construct_func_nn(x_grid,y_grid,width,f2) # please comment this line while solving exercise \n",
"\n",
"plot_helper2(func_obj, func_nn)"
]
},
{
"cell_type": "markdown",
"id": "7fe50332",
"metadata": {},
"source": [
"# 2. ReLU Nerual Network on $\\mathbb{R}^2$"
]
},
{
"cell_type": "markdown",
"id": "7b7d19c5",
"metadata": {},
"source": [
"## Q2:\n",
"Construct 4 neural networks correponding to the following figures."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "626c4f09",
"metadata": {},
"outputs": [],
"source": [
"from matplotlib import cm\n",
"def plot_helper3(funcs):\n",
" fig, ax = plt.subplots(1,4,subplot_kw={\"projection\": \"3d\"},figsize = [16,4], sharex = True, sharey = True)\n",
" for i,func in enumerate(funcs):\n",
" X = np.arange(-5, 5, 0.25)\n",
" Y = np.arange(-5, 5, 0.25)\n",
" X, Y = np.meshgrid(X, Y)\n",
" Z = func(X,Y)\n",
" surf = ax[i].plot_surface(X, Y, Z, cmap=cm.coolwarm)\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "b733de4b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1152x288 with 4 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Write your own func_nn here \n",
"funcs = solution1.construct_hat2d(r,f2) # please comment this line while solving exercise \n",
"plot_helper3(funcs)"
]
},
{
"cell_type": "markdown",
"id": "dc478192",
"metadata": {},
"source": [
"You might find this website with visualization on $\\mathbb{R}^2$ helpful: https://playground.tensorflow.org/"
]
},
{
"cell_type": "markdown",
"id": "54970ace",
"metadata": {},
"source": [
"# 3. ReLU Nerual Network from $\\mathbb{R}^m$ to $\\mathbb{R}^n$\n",
"In this section, we shortly introduce how to use keras to build neural networks. \n",
"\n",
"Nice tutorials:\n",
"- https://www.tensorflow.org/guide/keras/sequential_model\n",
"- https://www.tensorflow.org/guide/keras/functional"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "16fd6caf",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2.4.1\n"
]
}
],
"source": [
"import tensorflow as tf\n",
"from tensorflow import keras\n",
"from tensorflow.keras import layers\n",
"print(tf.__version__)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "24201fdd",
"metadata": {},
"outputs": [],
"source": [
"# Sequential \n",
"layer1 = layers.Dense(2, activation=\"relu\", name=\"layer1\")\n",
"layer2 = layers.Dense(3, activation=\"tanh\", name=\"layer2\")\n",
"layer3 = layers.Dense(4, name=\"layer3\")\n",
"model1 = keras.Sequential([layer1, layer2, layer3])\n",
"model1.build((None,2))\n",
"# model1.summary()"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "f58e5700",
"metadata": {},
"outputs": [],
"source": [
"# Functional\n",
"inputs = keras.Input(shape=(2,))\n",
"x = layer1(inputs)\n",
"x = layer2(x)\n",
"outputs = layer3(x)\n",
"model2 = keras.Model(inputs=inputs, outputs=outputs)\n",
"# model2.summary()"
]
},
{
"cell_type": "markdown",
"id": "e7177cba",
"metadata": {},
"source": [
"Construct a (ReLU) neural network : $\\mathbb{R}^2 \\to \\mathbb{R}$ with 2 hidden layers, each with 10 neurals. "
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "2a344d73",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Model: \"sequential_1\"\n",
"_________________________________________________________________\n",
"Layer (type) Output Shape Param # \n",
"=================================================================\n",
"layer1 (Dense) (None, 10) 30 \n",
"_________________________________________________________________\n",
"layer2 (Dense) (None, 10) 110 \n",
"_________________________________________________________________\n",
"layer3 (Dense) (None, 1) 11 \n",
"=================================================================\n",
"Total params: 151\n",
"Trainable params: 151\n",
"Non-trainable params: 0\n",
"_________________________________________________________________\n"
]
}
],
"source": [
"# write your own neural network below \n",
"func_nn = solution1.construct_nn()# please comment this line while solving exercise \n",
"func_nn.summary()"
]
},
{
"cell_type": "markdown",
"id": "9c3eb1ca",
"metadata": {},
"source": [
"b) Let $T = 10$ and \n",
"$$\n",
"S_{t+1} = S_t + \\text{func_nn}(S_t,t),\\quad t = 0, \\dots, 9.\n",
"$$\n",
"Construct a neural network such that\n",
"$$V_{nn} \\colon S_0 \\mapsto S_T$$"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "4ad7c34d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Model: \"model_1\"\n",
"__________________________________________________________________________________________________\n",
"Layer (type) Output Shape Param # Connected to \n",
"==================================================================================================\n",
"input_2 (InputLayer) [(None, 1)] 0 \n",
"__________________________________________________________________________________________________\n",
"tf.compat.v1.shape (TFOpLambda) (2,) 0 input_2[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.ones (TFOpLambda) (None, 1) 0 tf.compat.v1.shape[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.math.multiply (TFOpLambda) (None, 1) 0 tf.ones[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.concat (TFOpLambda) (None, 2) 0 input_2[0][0] \n",
" tf.math.multiply[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.compat.v1.shape_1 (TFOpLambd (2,) 0 input_2[0][0] \n",
"__________________________________________________________________________________________________\n",
"sequential_1 (Sequential) (None, 1) 151 tf.concat[0][0] \n",
" tf.concat_1[0][0] \n",
" tf.concat_2[0][0] \n",
" tf.concat_3[0][0] \n",
" tf.concat_4[0][0] \n",
" tf.concat_5[0][0] \n",
" tf.concat_6[0][0] \n",
" tf.concat_7[0][0] \n",
" tf.concat_8[0][0] \n",
" tf.concat_9[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.ones_1 (TFOpLambda) (None, 1) 0 tf.compat.v1.shape_1[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.__operators__.add (TFOpLambd (None, 1) 0 input_2[0][0] \n",
" sequential_1[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.math.multiply_1 (TFOpLambda) (None, 1) 0 tf.ones_1[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.concat_1 (TFOpLambda) (None, 2) 0 tf.__operators__.add[0][0] \n",
" tf.math.multiply_1[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.compat.v1.shape_2 (TFOpLambd (2,) 0 input_2[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.ones_2 (TFOpLambda) (None, 1) 0 tf.compat.v1.shape_2[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.__operators__.add_1 (TFOpLam (None, 1) 0 tf.__operators__.add[0][0] \n",
" sequential_1[1][0] \n",
"__________________________________________________________________________________________________\n",
"tf.math.multiply_2 (TFOpLambda) (None, 1) 0 tf.ones_2[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.concat_2 (TFOpLambda) (None, 2) 0 tf.__operators__.add_1[0][0] \n",
" tf.math.multiply_2[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.compat.v1.shape_3 (TFOpLambd (2,) 0 input_2[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.ones_3 (TFOpLambda) (None, 1) 0 tf.compat.v1.shape_3[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.__operators__.add_2 (TFOpLam (None, 1) 0 tf.__operators__.add_1[0][0] \n",
" sequential_1[2][0] \n",
"__________________________________________________________________________________________________\n",
"tf.math.multiply_3 (TFOpLambda) (None, 1) 0 tf.ones_3[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.concat_3 (TFOpLambda) (None, 2) 0 tf.__operators__.add_2[0][0] \n",
" tf.math.multiply_3[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.compat.v1.shape_4 (TFOpLambd (2,) 0 input_2[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.ones_4 (TFOpLambda) (None, 1) 0 tf.compat.v1.shape_4[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.__operators__.add_3 (TFOpLam (None, 1) 0 tf.__operators__.add_2[0][0] \n",
" sequential_1[3][0] \n",
"__________________________________________________________________________________________________\n",
"tf.math.multiply_4 (TFOpLambda) (None, 1) 0 tf.ones_4[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.concat_4 (TFOpLambda) (None, 2) 0 tf.__operators__.add_3[0][0] \n",
" tf.math.multiply_4[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.compat.v1.shape_5 (TFOpLambd (2,) 0 input_2[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.ones_5 (TFOpLambda) (None, 1) 0 tf.compat.v1.shape_5[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.__operators__.add_4 (TFOpLam (None, 1) 0 tf.__operators__.add_3[0][0] \n",
" sequential_1[4][0] \n",
"__________________________________________________________________________________________________\n",
"tf.math.multiply_5 (TFOpLambda) (None, 1) 0 tf.ones_5[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.concat_5 (TFOpLambda) (None, 2) 0 tf.__operators__.add_4[0][0] \n",
" tf.math.multiply_5[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.compat.v1.shape_6 (TFOpLambd (2,) 0 input_2[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.ones_6 (TFOpLambda) (None, 1) 0 tf.compat.v1.shape_6[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.__operators__.add_5 (TFOpLam (None, 1) 0 tf.__operators__.add_4[0][0] \n",
" sequential_1[5][0] \n",
"__________________________________________________________________________________________________\n",
"tf.math.multiply_6 (TFOpLambda) (None, 1) 0 tf.ones_6[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.concat_6 (TFOpLambda) (None, 2) 0 tf.__operators__.add_5[0][0] \n",
" tf.math.multiply_6[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.compat.v1.shape_7 (TFOpLambd (2,) 0 input_2[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.ones_7 (TFOpLambda) (None, 1) 0 tf.compat.v1.shape_7[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.__operators__.add_6 (TFOpLam (None, 1) 0 tf.__operators__.add_5[0][0] \n",
" sequential_1[6][0] \n",
"__________________________________________________________________________________________________\n",
"tf.math.multiply_7 (TFOpLambda) (None, 1) 0 tf.ones_7[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.concat_7 (TFOpLambda) (None, 2) 0 tf.__operators__.add_6[0][0] \n",
" tf.math.multiply_7[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.compat.v1.shape_8 (TFOpLambd (2,) 0 input_2[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.ones_8 (TFOpLambda) (None, 1) 0 tf.compat.v1.shape_8[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.__operators__.add_7 (TFOpLam (None, 1) 0 tf.__operators__.add_6[0][0] \n",
" sequential_1[7][0] \n",
"__________________________________________________________________________________________________\n",
"tf.math.multiply_8 (TFOpLambda) (None, 1) 0 tf.ones_8[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.concat_8 (TFOpLambda) (None, 2) 0 tf.__operators__.add_7[0][0] \n",
" tf.math.multiply_8[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.compat.v1.shape_9 (TFOpLambd (2,) 0 input_2[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.ones_9 (TFOpLambda) (None, 1) 0 tf.compat.v1.shape_9[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.__operators__.add_8 (TFOpLam (None, 1) 0 tf.__operators__.add_7[0][0] \n",
" sequential_1[8][0] \n",
"__________________________________________________________________________________________________\n",
"tf.math.multiply_9 (TFOpLambda) (None, 1) 0 tf.ones_9[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.concat_9 (TFOpLambda) (None, 2) 0 tf.__operators__.add_8[0][0] \n",
" tf.math.multiply_9[0][0] \n",
"__________________________________________________________________________________________________\n",
"tf.__operators__.add_9 (TFOpLam (None, 1) 0 tf.__operators__.add_8[0][0] \n",
" sequential_1[9][0] \n",
"==================================================================================================\n",
"Total params: 151\n",
"Trainable params: 151\n",
"Non-trainable params: 0\n",
"__________________________________________________________________________________________________\n"
]
}
],
"source": [
"# write your own neural network below \n",
"model = solution1.construct_Vnn(func_nn)# please comment this line while solving exercise \n",
"model.summary()"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "e1890f17",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<tf.Tensor: shape=(1, 1), dtype=float32, numpy=array([[9.0294485]], dtype=float32)>"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"S = tf.constant([[1]])\n",
"model(S)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.8.12 64-bit ('deep_hedge': conda)",
"language": "python",
"name": "python3812jvsc74a57bd0d42c10dd17494b873eaf240106df0a13a9aa441e372cea07a522242d1d1c2655"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.12"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
@justinhou95
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Please let me know if there is any mistake!

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