UAT-dl2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Universal approximation theorem\n",
    "Neural networks are universal function approximators. They can be used to approximate ANY continuous function!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import dl2\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm\n",
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The classical form of the universal approximation theorem for arbitrary width is as follows: The following formulation, due to Allan Pinkus,[9] extends the classical results of George Cybenko and Kurt Hornik."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='uat.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This theorem extends straightforwardly to networks with any fixed number of hidden layers: the theorem implies that the first layer can approximate any desired function and that later layers can approximate the identity function. Thus any fixed-depth network may approximate any continuous function, and this version of the theorem applies to networks with bounded depth and arbitrary width."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'input_dim': 1, 'output_dim': 50, 'layer': 'dense', 'activation': 'sigmoid', 'use_bias': True, 'requires_wgrad': True}\n",
      "{'input_dim': 50, 'output_dim': 1, 'layer': 'dense', 'activation': 'none', 'use_bias': True, 'requires_wgrad': True}\n",
      "trainable parameters: 151\n"
     ]
    }
   ],
   "source": [
    "f = dl2.NN()\n",
    "f.add(dl2.dense(50, input_dim=(1), activation='sigmoid'))\n",
    "f.add(dl2.dense(1))\n",
    "f.init()\n",
    "f.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.reshape(np.arange(0, 10, 0.01), (1000, 1))\n",
    "y = x ** 2 + x - np.sqrt(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# function to approximate\n",
    "plt.plot(x, y, c='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NN approximation\n",
    "plt.plot(x, [f.forward(xi) for xi in x], c='blue')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "f.opt, f.loss_fn = dl2.GD(f.params(), 1e-4, 0), 'mse' # SGD and mean-squared-error loss\n",
    "f.tqdm_disable = True\n",
    "history = f.fit(x, y, epochs=2000, batch_size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# function to approximate\n",
    "plt.plot(x, y, c='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NN approximation\n",
    "plt.plot(x, [f.forward(xi) for xi in x], c='blue')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}