2. Neural Networks with PyTorch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "    <div style=\"width: 150px; float: left;\"> <img src=\"data/D4Sci_logo_ball.png\" alt=\"Data For Science, Inc\" align=\"left\" border=\"0\"> </div>\n",
    "    <div style=\"float: left; margin-left: 10px;\"> <h1>NLP with PyTorch</h1>\n",
    "<h1>Neural Networks with PyTorch</h1>\n",
    "        <p>Bruno Gonçalves<br/>\n",
    "        <a href=\"http://www.data4sci.com/\">www.data4sci.com</a><br/>\n",
    "            @bgoncalves, @data4sci</p></div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "from pprint import pprint\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "import seaborn as sns\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import torch.nn.functional as F\n",
    "\n",
    "from tqdm.notebook import tqdm\n",
    "\n",
    "import torchvision\n",
    "from torchvision import datasets, transforms\n",
    "from torch.utils.data import DataLoader, Dataset\n",
    "\n",
    "import watermark\n",
    "\n",
    "%load_ext watermark\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by print out the versions of the libraries we're using for future reference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.11.7\n",
      "IPython version      : 8.12.3\n",
      "\n",
      "Compiler    : Clang 14.0.6 \n",
      "OS          : Darwin\n",
      "Release     : 24.3.0\n",
      "Machine     : arm64\n",
      "Processor   : arm\n",
      "CPU cores   : 16\n",
      "Architecture: 64bit\n",
      "\n",
      "Git hash: f27953c25cb37eda249660943e02750136eeb23f\n",
      "\n",
      "numpy      : 1.26.4\n",
      "pandas     : 2.2.3\n",
      "matplotlib : 3.8.0\n",
      "torchvision: 0.21.0\n",
      "seaborn    : 0.13.2\n",
      "watermark  : 2.4.3\n",
      "torch      : 2.6.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%watermark -n -v -m -g -iv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load default figure style"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('d4sci.mplstyle')\n",
    "colors = plt.rcParams['axes.prop_cycle'].by_key()['color']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Activation Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by defining a simple utility function to plot out the activation function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_activation_function(activation_fn, x_range=(-6, 6), num_points=100):\n",
    "    x = torch.linspace(x_range[0], x_range[1], num_points)\n",
    "    x.requires_grad_(True)\n",
    "    y = activation_fn(x)\n",
    "    y.backward(torch.ones_like(x))\n",
    "    gradient = x.grad\n",
    "    \n",
    "    fig, ax = plt.subplots(1)\n",
    "    ax.plot(x.detach().numpy(), y.detach().numpy())\n",
    "    ax.plot(x.detach().numpy(), gradient.detach().numpy())\n",
    "    ax.set_xlabel('x')\n",
    "    ax.legend(['Activation function', 'Gradient'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And generate plots for a few examples:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Linear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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zo127dnHkkUfm4CsBACrb008/HX/+858rOwYAkCcPPfRQuQ5sKC4ujgMPPDAOP/zw2HvvvWPXXXeNVq1aRd26dWO77baLlStXftNH+OKLL2LGjBnfdBHef//9KCkpydFXBBUvlXGkCcA25YYbboirrrqqTNf06tUrzjnnnDjxxBOjuLi4XHvnzp0b48ePjyeffDJefPHFWL9+/TevTZgwIXr16lWu9wUAqpY333wzDjzwwK3+4cfQoUPjmmuuqZhQAEC53H333XHOOedknatdu3Ycf/zxcfzxx0evXr2iRYsWZd61cuXKGDlyZPz+97+PhQsXluna4447Lp566qky7wSA6mrmzJnRpUuX2LRpU9bZOnXqxIgRI+Kss84q855Vq1bFwIED4+GHH040f/DBB8fUqVMjlUqVeRcAUH4fffRRoocipFKpOPTQQ+Okk06KXr16xV577VXmXSUlJTFu3Li4+eab48033yzTtS1atIiZM2dG48aNy7wXAKi6Vq5cGXvttVcsWLBgq97n8MMPj8mTJ1dMKAAgZyZNmhS9evWKDRs2JL6mU6dOceGFF8bpp58eTZo0KdfeJUuWxIQJE2L8+PHxzDPPxJIlS755bciQITFs2LByvS/kSrqyAwBQcR555JEylTEPPvjgmDZtWkyYMCH69OlT7jJmRES7du3i4osvjmeeeSa+/PLLuOOOO6Jz587lfj8AoOrZuHFjDBw4cItlzO7du+cxEQCQSz179ow///nPsWjRohg3blwMGDCgXGXMiIj69evHz3/+85g7d25ccsklZSpyTJgwIe6///5y7QWA6ujiiy9OXMZ86qmnylXGjIioV69ePPTQQzF48OBE89OmTfNnMgBUQR06dIhbbrklFixYEC+++GL8/Oc/L1cZMyKioKAgTj/99HjjjTfivvvui3r16iW+9rPPPouf//zn5doLAFRdQ4YM2WIZ02cEAGDbMW/evDjllFMSlzFbtmwZY8aMiRkzZsT5559f7jJmRESTJk2iX79+8Ze//CUWLVoUjzzySBxzzDEeEkmVpZAJsI1YsGBBDBo0KNFsQUFB3HTTTfHSSy/FQQcdVOFZGjRoEBdeeGHMmDEjpkyZkuhpnQBA1Tds2LB45513Nvt6jx49Et+PAABVU926deOiiy6K9957LyZNmhRnnXVW1K9fv8Lev7i4OG699dZ48skno1GjRomv+9WvflWmJ3ACQHX117/+NfFpEWPGjInDDz98q3fedddd8d3vfjfR7JAhQ2LVqlVbvRMA2DqpVCp69+4dEydOjPfffz8uvfTSaNWqVYXu+OEPfxhvvvlmmcqd9957b7z//vsVmgMAqDx///vfY8SIEZt9vXHjxvG73/0uj4kAgFzZtGlTfP/734/ly5cnmj/jjDNi5syZccYZZ0Q6XbHVtMLCwjjllFPimWeeiY8++ihOOumkCn1/qAgKmQDbgNLS0ujXr18sXbo062zdunXjscceiyuuuCIKCgpynu2QQw6JXXfdNed7AIDceu+99+LXv/71Zl8vLi6OUaNGeSIVAFRTjRs3jquuuio+/vjjuP3226Njx4453Xf88cfHs88+m/ikjY8//jgeeOCBnGYCgKrg+uuvTzT305/+NE4++eQK2ZlKpeK//uu/onXr1llnv/jiixg9enSF7AUAyq6wsDB++MMfxnvvvRePPvpofOc738npvt133z0mT54cnTp1SjRfWloaN910U04zAQD5sXbt2hg0aFBkMpnNztxyyy2x00475TEVAJArV199dbz66quJZ8eMGVOmhzCXV7t27eKQQw7J+R4oK4VMgG3AqFGjYsqUKVnniouL47HHHosTTzwxD6kAgG1FaWlpDBgwYIunUv3iF7/IeXEDAKh4derUiV/84hcxb968uP7666Np06Z5273//vvHn//858Tz99xzTw7TAEDle+qpp+Ldd9/NOteqVau44YYbKnR348aNY/jw4Ylmhw8fHhs3bqzQ/QDAlqVSqTjjjDNi1qxZcd9990WHDh3ytrtp06bx+OOPJ/6Q5bhx42LFihW5DQUA5NzVV18dH3744WZfP+KII2LAgAF5TAQA5MrMmTPjt7/9baLZa6+9Nq699tocJ4KqTyEToJpbtmxZ/OpXv0o0O2rUqDjqqKNynAgA2Nb8/ve/3+LTrzp27BhXXnllHhMBABWhe/fuMWfOnLjhhhuiYcOGlZLhlFNOiX79+iWanTp1anz66ac5TgQAled3v/tdorkbb7wx6tSpU+H7+/btG4ceemjWuU8++SQefvjhCt8PAHy7pk2bxptvvhljxoyJXXfdtVIytGvXLm6++eZEs2vXro0nnngix4kAgFx64403tvjgpu222y5GjhyZx0QAQC799Kc/jZKSkqxz/fv3j6uvvjoPiaDqU8gEqOauvfba+Prrr7PO9evXL370ox/lIREAsC2ZO3fuFh/+kEqlYtSoUVFcXJzHVABARdhzzz2jWbNmlR0jbrjhhigqKko0O2nSpBynAYDK8cknn8QLL7yQda5169bx/e9/P2c5hgwZkmjuvvvuy1kGAOBfNW7cOLp06VLZMWLAgAGJT+ZMcl8DAFRNGzdujAEDBmyxlPGrX/0qdttttzymAgBy5W9/+1s8//zzWed23333uOOOO/KQCKoHhUyAauyrr76KESNGZJ3bfvvt3QABAGWWyWRi0KBBsWbNms3ODB48OHr06JHHVADAtmaXXXaJE044IdHs1KlTc5wGACrHX/7yl8hkMlnnLrrooigsLMxZjuOPPz523333rHMvvPBCfPHFFznLAQBUPel0Os4777xEs75/B4Dq68Ybb4x33313s6937tw5LrvssjwmAgBy6frrr08096c//Snq1q2b4zRQfShkAlRjt99+e6xbty7r3DXXXBONGjXKfSAAYJsyevToLZ5C1aJFixg2bFgeEwEA26o+ffokmps9e3aOkwBA5RgzZkzWmXQ6Hf369ctpjlQqFT/4wQ+yzpWUlMRDDz2U0ywAQNXTt2/fRHNz586NTZs25TgNAFDRZs6cGTfeeONmX0+n0zF69OgoKirKYyoAIFdeeOGFePPNN7POnXrqqQ5tgH+jkAlQTa1duzbuvPPOrHOtWrWKwYMH5yERALAt+fTTT7M+1fL222+Phg0b5ikRALAtO+SQQxLNzZkzJ8dJACD/Pvvss3jnnXeyzvXo0SNatmyZ8zzf//73E81NmDAhx0kAgKqmVatW0bp166xzGzdujE8++SQPiQCAilJSUhIDBw6MDRs2bHbmwgsvjAMPPDCPqQCAXLrllluyzqRSqbjuuuvykAaqF4VMgGrqsccei8WLF2edu/jii6OwsDAPiQCAbcn5558fK1as2OzrvXv3TnySFQBANm3atIni4uKsc8uXL89DGgDIr4kTJyaaO+GEE3Kc5J/at28fu+22W9a5v//977F+/fo8JAIAqpLdd9890Zzv4QGgehk+fHi89tprm329devWccMNN+QxEQCQSwsXLoxnnnkm61yvXr2iY8eOeUgE1YtCJkA1NWbMmKwzRUVFMWjQoDykAQC2JQ8++GA8+eSTm329QYMGcccdd+QxEQCwrUun09GoUaOsc6tXr859GADIs6SFzKOOOirHScq2a+3atTF16tQ8pAEAqpKmTZsmmvM9PABUHx999FFcffXVW5z54x//GPXr189TIgAg1x566KEoLS3NOnfBBRfkIQ1UPwqZANXQ0qVLEz2R4phjjokmTZrkIREAsK346quv4ic/+ckWZ2666aZo2bJlnhIBADVFYWFhhcwAQHWTpNTYsGHD6NKlSx7S/NMRRxyRaO7ll1/OcRIAoKpJ+r257+EBoHrIZDIxaNCgWLt27WZnvve978VJJ52Ux1QAQK4lORyqcePGceyxx+YhDVQ/CpkA1dBTTz0VGzZsyDp32mmn5SENALAtueiii2Lx4sWbfb179+5x/vnn5zERAFBTLF26NOtMvXr18pAEAPJn+fLlMW/evKxzXbp0iVQqlYdE/9S1a9dEc9OnT89xEgCgqkny/XuE7+EBoLoYMWJEvPjii5t9vVGjRnHbbbflMREAkGuffvppvPHGG1nnevfuHUVFRXlIBNWPQiZANfTCCy8kmjvmmGNynAQA2Jb87W9/i4cffnizrxcXF8eoUaPy+gFQAKBm+PLLL7f49O3/0axZszykAYD8mT59emQymaxz++23Xx7S/K927dpF48aNs8699dZbeUgDAFQl8+fPTzTne3gAqPo++eSTGDJkyBZnbr75Zn+uA8A2ZtKkSYnmnI4Jm6eQCVANJbkJ6tSpkx+EAACJLVu2LOvJl0OGDIlOnTrlKREAUJMkPV1rt912y3ESAMivt99+O9HcXnvtldsg32LPPffMOjN//vxYtmxZ7sMAAFXC6tWr44MPPsg617hx42jatGkeEgEAW2Pw4MGxcuXKzb5+2GGHxcCBA/OYCADIhyRdhFQqFUceeWQe0kD1VFjZAQAomwULFsS8efOyzh166KGJ3/Ozzz6LmTNnxnvvvRdffvllrFixItatWxe1a9eOOnXqxI477hht2rSJdu3axV577eXocQDYBl166aXx+eefb/b1PfbYI375y1/mMREAUJM888wzieb23nvvHCcBgPz66KOPEs21b98+x0n+02677RZTp07NOjdnzpzo2rVrHhIBAJVt4sSJUVpamnXO9+8AUPXdf//9MWHChM2+XqtWrRg1alSkUqk8pgIA8mHy5MlZZ/bYY4/YYYcdEr3f8uXLY+bMmTFz5sz49NNPY8WKFbF69eooLi6OOnXqRJMmTWKXXXaJNm3axD777BP16tXbyq8AKp9CJkA189ZbbyWa69KlyxZfnzFjRjzwwAPx5JNPxvvvv594f+3ataNr165x3HHHRd++fWOPPfZIfC0AUDVNnDgx7rnnns2+nkqlYtSoUVGrVq08pgIAaorS0tJ45JFHEs0efvjhOU4DAPmV5AGMEZVzSnTSnfPmzVPIBIAaYty4cYnmfP8OAFXbokWL4qc//ekWZ6666iqfDQSAbdDy5csT/W4iWxfhiy++iD//+c/xxBNPxLRp06KkpCTR/oKCgujUqVN85zvfib59+8bBBx8c6XQ60bVQlfi3FqCamTlzZqK5zd0EPffcc3HkkUfGPvvsEzfffHOZypgREWvXro0pU6bEL3/5y+jQoUMcfPDBMW7cuMQ3UQBA1bJ69eo455xztjgzaNCgOOyww/KUCACoaZ544olYsGBB1rn69evHwQcfnIdEAJA/ST70UFRUFDvttFMe0vyrVq1aJZpLWioFAKq3L7/8Mv76178mmj322GNznAYA2BoXXXRRLFmyZLOvd+rUKYYMGZLHRABAvmxtF2H27Nnxwx/+MHbZZZcYMmRITJkypUw9gpKSkpgxY0YMHz48evToEe3atYvhw4fHypUrE78HVAUKmQDVTNKboH9/OtWCBQuiT58+ccwxx8SkSZMqLM8rr7wS3/ve92Lfffet0PcFAPLjyiuvjPnz52/29WbNmsVvf/vb/AUCAGqcW265JdFc3759Y7vttstxGgDIr48//jjrzE477RSpVCoPaf5Vs2bNEs0l+RoAgOrvtttui/Xr12eda9u2bXTv3j0PiQCA8njkkUe2eOp1Op2O0aNHR1FRUR5TAQD5Ut4uwpo1a+KKK66Izp07x/333x8bNmyokDwff/xxXHLJJdGuXbsYNWpUlJaWVsj7Qq4pZAJUMx988EHWmaZNm0aDBg2++fsJEybEvvvuG48++mjOcs2cOTOOPPLIGDRoUKxduzZnewCAijN16tT44x//uMWZ22+/PRo1apSfQABAjfPII4/ElClTEs0OHDgwx2kAIL9Wr16d6OfpSYuRFS3p3q+++irHSQCAyvbpp5/G8OHDE80OGDAgx2kAgPJaunRpXHjhhVucOf/88+Pggw/OUyIAIN+SdBEiItq1a/fN//7www/joIMOit/85jcVVsT8d19//XUMHjw4evToEQsWLMjJDqhICpkA1czChQuzzvzfG6Dhw4fHCSecEEuXLs1lrG/86U9/igMPPNCNEABUcevXr4+BAwdu8YlSJ510Upx66ql5TAUA1CRr1qyJyy67LNFsjx49okePHjlOBAD5tXjx4kRz22+/fY6TfLsddtgh0VzSrwMAqL4uu+yyWLNmTda5+vXrZy15AACV52c/+1l88cUXm329ZcuWceONN+YxEQCQb0m6CBERbdu2jYiIv//979GtW7d49913cxnrG9OmTYsuXbrExIkT87IPykshE6Aa2bRpU3z99ddZ5/7nqdW/+93v4pJLLolMJpPraP/i3XffjR49eiR+ggYAkH/XXHPNFv+srl+/ftx55515TAQA1DRDhgyJuXPnJpodOnRojtMAQP4tWbIk0Vz9+vVznGTr9ib9OgCA6um///u/Y+zYsYlmf/zjH0fjxo1znAgAKI9nnnkm7rvvvi3O/PGPf4wGDRrkKREAUBk+//zzrDP169ePunXrxksvvRTHH398rFixIg/J/teSJUvixBNPjEcffTSve6EsFDIBqpFFixZt8RSr/7HDDjvEww8/HJdeemkeUn27Tz75JI444oj49NNPKy0DAPDt3nrrrbjlllu2OHPjjTdGq1at8pQIAKhpJk6cGH/84x8Tzfbu3TuOOuqoHCcCgPxLWmSsrA9C1qtXL9Lp7L9OVsgEgG3XF198Eeedd16i2VatWsWVV16Z40QAQHmsWrUqzj333C3O9O3bN7773e/mKREAUFmSFDJ32GGH+PDDD+Okk06K1atX5yHVf1q/fn2cdtpp8eyzz1bKfsimsLIDAJDcV199lWhu0aJFMWDAgESzbdq0iVNOOSUOPfTQ6NChQ7Rs2TLq1q0b69evj2XLlsWcOXPitddei2effTaef/75KCkpSZz3888/jxNOOCGmTp0a9erVS3wdAJA7mzZtigEDBsSmTZs2O3PggQfGBRdckMdUAEBNsnDhwujXr19kMpmss7Vr147hw4fnIRUA5N+aNWsSzVXmz9fr1auX9cnXSb8OAKB6KSkpiTPOOCO+/vrrRPO33npr1K1bN8epAIDyuOKKK2LBggWbfb1hw4Zx++235zERAFBZkvQRateuHX369Inly5dnnW3YsGH07t07jjjiiOjcuXPssssu0aBBgygtLY2VK1fG/Pnz45133okXXnghHn/88Vi1alXirJs2bYrvfe978fLLL0enTp0SXwf5oJAJUI2sXbs20dz48eOzznTt2jWuv/766NWrV6RSqf94vU6dOlGnTp1o0aJFHHrooXHppZfGwoULY9iwYTFixIgtljj+rxkzZsTPfvazGD16dKJ5ACC3fvOb38Tbb7+92deLiopi9OjRiU7AAAAoq40bN8Zpp50WX375ZaL53/72t9GmTZvchgKASrJx48ZEc0VFRTlOsnW7N2zYkIckAEC+XXHFFfHiiy8mmu3Tp0+cdtppOU4EAJTHlClT4s4779zizG9+85to3rx5nhIBAJUpSR/hH//4R9aZ5s2bx1VXXRUDBgyI7bbb7ltnatWqFdtvv31069YtBg4cGKtXr46RI0fGjTfeGIsXL06Ud8WKFXHGGWfEG2+8EbVq1Up0DeSDT9gCVCPr1q3b6vcoKCiIYcOGxWuvvRbHHXfct5YxN6dly5Zx++23x2uvvRZ77LFH4uvuvvvumDBhQnniAgAV6P3334/rr79+izOXX355dO7cOU+JAICa5sILL4yXX3450ezRRx8dF154YY4TAUDlSVpkrMxCZmFh9uf7Ji2WAgDVx4MPPhi33HJLotlmzZrFyJEjc5wIACiPdevWxcCBAyOTyWx2pkePHnHuuefmMRUAUFkymUyFPGTx+9//frz33ntxwQUXbLaM+W3q1q0bl1xySbz33ntx4oknJr5u5syZMXTo0PJEhZxRyASoRra2kLnddtvFE088EUOGDNmqU6+6dOkSr7zyShxyyCGJr7nkkkuipKSk3DsBgK1TWloaAwcOjPXr1292Zrfddourrroqj6kAgJrk5ptvjtGjRyea3XHHHePee+8t04OkAKC6SVpkTFKKzBUnZAJAzTN16tQYOHBgotl0Oh333XdfbL/99jlOBQCUx9ChQ2P27Nmbfb24uDhGjRrlZ/EAUENUxOFQQ4cOjb/85S/RqFGjcr/HjjvuGH/729/i4osvTnzN8OHDY968eeXeCRVNIROgGtmap0ynUql4+OGH47jjjquQLI0aNYqnnnoq8Qlas2bNivvuu69CdgMAZXfbbbfFtGnTtjgzatSoMj2xCgAgqUcffTSuuOKKRLMFBQUxduzYaNGiRY5TAUDlKi0tTTRXmR+KTPJwx6RfBwBQ9X300UfRu3fvLT7c8f+65ppr4phjjslxKgCgPN5888249dZbtzjzi1/8Ijp27JinRABAZduaLkJExKWXXhrXXHNNhWRJp9Nx2223Rf/+/RPNb9iwwSmZVCmV9zhVoMb69NNP4+23367sGJWiR48eW/U0iIKCgnJfe+GFF8ZJJ51U7uu/TYMGDeLBBx+Mbt26JXoC9vDhw2PAgAEVmgGAbZd7hkYV9n7z5s3LevLlwIEDo2fPnhW2EwDywf1Co8qOkciUKVPizDPPTFzWuPHGG+OII47IcSoAqHxJTp+MiNi0aVOOk2xekg9nJP06AICqbdGiRdGrV6/4+uuvE80ff/zxWX/3AABUjo0bN8aAAQOipKRkszMdO3aMK6+8Mo+pAIDKtjVdhC5dusSwYcMqMM0/3XHHHfHSSy/FnDlzss6OHTs2fvvb30azZs0qPAeUlUImkHcTJ06Ms88+u7JjVIpp06bFQQcdVO7ri4uLy3Vd+/bt4ze/+U25925J586dY+jQofHLX/4y6+zMmTNjypQp0aNHj5xkAWDb4p6h/PcM/27QoEGxevXqzb6+0047xc0331xh+wAgX9wvVNz9Qq688847cdJJJ8W6desSzQ8cODAuv/zyHKcCgKqhOhQyk+wu7+8uAICqY/ny5dGrV69EH36MiNh3331jzJgxlXqSNwCweTfddFPMmDFjs6+nUqkYPXq07+kBoIYp75/9xcXFcd9990VhYcVX0OrWrRv33ntvHH744Vkf8rxx48a4++67PSCKKiFd2QEASK68N0E33XRT1KlTp4LT/K/LL788WrVqlWh2zJgxOcsBAPyn0aNHxwsvvLDFmT/84Q/RuHHjPCUCAGqK2bNnxzHHHBPLli1LNN+nT58YOXJkbkMBQBWS9Gf+CpkAQC6tWbMmTjjhhHj77bcTze+2227xzDPPRIMGDXIbDAAol3/84x9xww03bHFm8ODBccghh+QpEQBQVRQVFZXr4UrnnHNOdO7cOQeJ/qlHjx5x2mmnJZrVRaCqUMgEqEZq1apV5mtatGgRvXv3rvgw/0dhYWGce+65iWbHjx+f0ywAwP/67LPP4rLLLtvizAknnBCnn356nhIBADXFxx9/HEcddVR8+eWXieaPOeaYGDNmTBQUFOQ4GQBUHUl/5r9mzZocJ9m81atXZ51RyASA6mv9+vXx3e9+N6ZOnZpovnXr1jFx4sTYcccdc5wMACiP0tLSGDhwYGzYsGGzMy1atIhhw4blMRUAUJWU52f6F1xwQQ6SlG/He++9F/PmzctxGshOIROgGqlXr16ZrznnnHNycjz4t+0pKirKOvfxxx/Hhx9+mPM8AEDEeeedF8uXL9/s6/Xq1Ys777wzj4kAgJrgs88+i+985zvxySefJJrv0aNHPProo8ocANQ4DRs2TDS3cuXKHCf5dhs2bNjiBzj/R6NGjXIfBgCocBs3bozTTjstJk6cmGh+p512iueffz523nnnHCcDAMrr97//fbz66qtbnLn99tsT/0wCANj2lLWPcPjhh8eee+6ZozT/69BDD42999470WzSn2VALilkAlQj22+/fZmv6dOnTw6S/KdmzZrFIYcckmj29ddfz3EaAGDMmDHxxBNPbHHm17/+tQ9OAAAV6ssvv4zvfOc7MWfOnETz3bp1i/Hjx0edOnVynAwAqp6mTZsmmluxYkWOk2zd3qRfBwBQdZSUlES/fv3i8ccfTzTfpEmTeO6552K33XbLcTIAoLzmzJkTv/rVr7Y407t377x9nhAAqJrK2kfI571D0l26CFQFCpkA1UhZP9RQr1696NSpU47S/KcDDzww0dz06dNznAQAaravvvoqfvzjH29x5oADDoiLL744T4kAgJpg8eLFcdRRR8WsWbMSze+1117x9NNPR4MGDXKcDACqpiZNmiSaW7ZsWW6DbOXepF8HAFA1lJaWRv/+/eOvf/1rovkGDRrEM888E507d85xMgCgvDKZTJxzzjmxZs2azc40aNAg7rjjjjymAgCqorL2EQ466KAcJflPughUJwqZANVIUVFRmT6k2K1btygoKMhhon+V9CYo6SkZAED5/PjHP46vv/56s68XFhbG6NGjI532LSEAUDGWLVsWxxxzTLz77ruJ5vfYY4+YOHGiE7UAqNEaN26c6HvzL774Ig9pyr/Xn+cAUH1kMpk499xz44EHHkg0X7du3XjqqaeiW7duOU4GAGyNUaNGxaRJk7Y4c9NNN0XLli3zlAgAqKrKckJmrVq1Yt99981dmH9zwAEHRCqVyjqni0BV4NO3ANVMixYtEs/m8wYoIqJLly6J5j755JMcJwGAmuvxxx+PsWPHbnHm5z//eey99955SgQAbOtWrFgRxx57bOKnULZt2zYmTpwYO+20U46TAUDVlk6no3nz5lnnFi1alIc0/ylpIbNVq1Y5TgIAVJQLL7ww/vSnPyWa3W677eLxxx+PQw45JMepAICt8emnn8bll1++xZnu3bvH+eefn6dEAEBVVpYuQseOHaO4uDiHaf5VkyZNYuedd846t2zZsli1alUeEsHmKWQCede/f//IZDI18q+KOLK7bdu2iWfL8gSLipD0Kdiff/55jpMAsC1wz1B2y5cvz/pLlPbt28fVV19drvcHgKrG/ULlW7VqVRx33HHx2muvJZpv3bp1vPDCC4obAPD/JfmZ/4oVK2L16tV5SPOvkv4svyy/twAAKs9PfvKTuOuuuxLNFhcXx3//93/HkUcemeNUAMDWOu+882LFihWbfb24uDhGjRqV6LQpAGDbV5W7CBH6CFQfCpkA1Uy7du0SzzZq1Ch3Qb5F/fr1o7CwMOtcZXxwBABqgsmTJ8dnn322xZmRI0dG7dq185QIANiWrVmzJk444YR4+eWXE803b948nn/++WjTpk1ugwFANZL0z8U5c+bkNsi3+OijjxLN+bMdAKq+n//853Hbbbclmi0sLIyHHnoojj/++BynAgC21vLly2P8+PFbnBkyZEh06tQpT4kAgKquKncRIiIaN26caE4fgcqWvTUDQJWy6667Jp5NekNSkRo1ahRff/31FmfWrl2bpzQAULNkMpktvt64ceP485//HH/+859zliHphzUfe+yxmD9/fta5nXfeOa677rqtTAUAVLS1a9fGiSeeGH//+98Tze+www4xceLE2G233XKcDACql6QffPjwww9j7733znGaf5X0e3wnZAJA1XbllVfGrbfemmi2oKAgHnjggejdu3duQwEAFSLbZwQi/vkzhf79++csw6pVqxLNzZo1K3GOO++8M+rUqbMVqQCAzanqXYSkO/URqGwKmQDVzJ577pl4tqioKIdJyr+zpKQkD0kAgH+3dOnSuO+++yo7RkREvPPOO/HOO+9kndtnn30UMgGgilm3bl1897vfjUmTJiWab9KkSUycOLFMP9MAgJpir732SjT3wQcf5DhJ+XbWr18/dtlllzykAQDK4+qrr45hw4Ylmk2lUnHPPffE6aefnuNUAEA+jR07trIjRETEokWLEn9e4fe//71CJgDkyB577BEFBQWJPs9fVbsIEfoIVL50ZQcAoGy6deuWeHbZsmW5C7IVO/2wBAAAAKqn9evXxymnnBLPPfdcovmGDRvGs88+m/cTvQCguthvv/0SzU2fPj3HSf7V8uXLY+7cuVnn9t1330ilUnlIBACU1bXXXhvXX399otlUKhUjR46MH/7whzlOBQAAAFSmOnXqRMeOHRPNVtUuQoQ+ApVPIROgmmnatGm0adMm0ezSpUtzG+bfrF+/PtHx37Vr185DGgAAAKAibdiwIfr27RtPP/10ovn69evH008/HV27ds1xMgCovnbddddo1KhR1rl8FzLffPPNyGQyWeeSFkoBgPy66aab4pprrkk8f/vtt8c555yTu0AAAABAlZH0gKh8dxHKslMfgcqmkAlQDR1wwAGJ5vL9VIqkN0A77bRTjpMAAAAAFWnjxo1x+umnx/jx4xPN161bN8aPHx8HHXRQjpMBQPWX5OEF8+bNiy+++CIPaf5p2rRpieb233//HCcBAMrq5ptvjl/84heJ52+99da48MILc5gIAAAAqEqqahchQh+B6kMhE6AaOuqooxLNzZ49O8dJyrdvl112yXESAAAAoKKUlJTEmWeeGY899lii+dq1a8fjjz8ehx56aG6DAcA24jvf+U6iuYkTJ+Y4yf967rnnEs0deeSROU4CAJTFH/7wh7j88ssTz994441xySWX5DARAAAAUNVU1S7Cxo0bY/78+Vnn6tWrF02aNMl9INgChUyAaqhXr16J5l555ZUcJynfvrZt2+Y4CQAAAFARSkpK4qyzzopx48Ylmq9Vq1Y8+uijyhkAUAZJP/jw7LPP5jjJP61atSrRCZl77bVXNG/ePA+JAIAk7rzzzvjpT3+aeP6aa66JK6+8MneBAAAAgCppt912i3bt2mWdW7x4cXz00Ud5SPRPb731Vqxfvz7rnC4CVYFCJkA11Lp169hzzz2zzi1cuDAWLlyYh0T/9Oqrryaa22+//XKcBAAAANhapaWlcfbZZ8eYMWMSzRcVFcW4cePi2GOPzXEyANi2dO3aNdGTnB9//PFEH0TYWo899lhs2LAh69zRRx+d8ywAQDKjR4+Oiy66KPH8lVdeGUOHDs1hIgAAAKAqS3pAVNJ+QEXQRaA6UcgEqKb69u2baG7ixIk5TvJPGzZsiJdeeinR7AEHHJDjNABQM/Xu3TsymUyl/vVf//VfibIOHTo00fu9/fbbuf2HBgB8q0wmE+ecc07cf//9ieYLCwvjoYceihNPPDHHyQBg25NOp+OUU07JOrd8+fJ46qmncp4n6cMYTj311BwnAQCSuPfee2Pw4MGRyWQSzV9yySVx44035jgVAJAPjRo1qvTPCMybNy9R1sMPPzzxezZq1Ci3/+AAgCrXRSjLLl0EqgKFTIBqqn///pFKpbLOjRgxIg9pIsaNGxdfffVV1rkWLVpEx44d85AIAAAAKK8LLrgg7rnnnkSzBQUF8eCDDyYqkgAA3+4HP/hBork777wzpznmzp0bTz/9dNa5du3aRffu3XOaBQDI7sEHH4yBAwcmLmNefPHFceutt+Y4FQAAAFDVHXHEEbHLLrtknXvooYdi2bJlOc/zySefxPjx4xPNHnXUUTlOA9kpZAJUU+3atYsePXpknXvllVfycrJU0g+BnHzyyYmKpAAAAEDl+MlPfpL4AU/pdDruvffeOO2003KcCgC2bYcffnjsvPPOWecmTpwY77zzTs5y/P73v4/S0tKsc/369ctZBgAgmYcffjh+9KMfJfqzOyLi3HPPjT/84Q85TgUAAABUB6lUKn74wx9mnVu7dm3ce++9Oc8zcuTIKCkpyTrXoUOH2H333XOeB7JRyASoxi6++OJEc9dff31Oc0yaNCmmTp2aaPb000/PaRYAAACg/C677LK47bbbEs2mUqkYPXp04hO9AIDNS6VScf755yeavfLKK3OSYe7cuTFq1Kisc0VFRXHuuefmJAMAkMxjjz0W/fr1S/RBxYiIs88+O0aMGOHhyQAAAMA3Bg8eHMXFxVnnhg8fHqtWrcpZjq+++ipGjhyZaFYXgapCIROgGuvbt2906NAh69wjjzwSY8eOzUmGVatWxYABAxLN7rXXXtGzZ8+c5AAAAAC2zlVXXRW33HJLotlUKhV33XVX4p8JAADZnX/++VG/fv2scxMmTIgnnniiwvf/7Gc/i/Xr12edO/PMM6NVq1YVvh8ASGb8+PFx+umnx6ZNmxLN9+vXL+6++25lTAAAAOBftGzZMn70ox9lnVuwYEH8/Oc/z1mOCy64IL7++uusc0VFRTF48OCc5YCyUMgEqMbS6XT84he/SDR70UUXxWeffVbhGX72s5/F/PnzE88CAAAAVc/1118fN9xwQ+L52267zS86AKCCNWzYMM4777xEswMHDozPP/+8wnaPGDEiHn/88axz6XQ6LrvssgrbCwCUzXPPPRd9+/aNDRs2JJo//fTT47777ot02kfEAAAAgP90xRVXRGFhYda5kSNHxjPPPFPh+x988MEYN25cotkzzjgjmjdvXuEZoDz8tA2gmuvXr18ccMABWecWL14cxx13XCxZsqTCdg8bNizuvvvuRLOdOnVK9AQNAAAAIL9uvvnmuPrqqxPP33rrrXHRRRflMBEA1FxXXnll7LDDDlnnvvrqq+jdu3esXLlyq3c+//zziR+oOHDgwOjUqdNW7wQAyu7FF1+M7373u4lOtI6I6NOnTzzwwANRUFCQ42QAAABAddWuXbv4yU9+kmj2tNNOizfffLPCdk+ePDkGDRqUaLZWrVpx/fXXV9hu2FoKmQDVXDqdjhEjRiT6JcqMGTOie/fu8eGHH27Vzk2bNsWll14aV155ZeJrhg8f7hc9AAAAUMXcdtttcfnllyeeHzZsWFxyySU5TAQANVvjxo3jxhtvTDT72muvxbHHHhtffvllufeNHz8+Tj755Fi3bl2FZgMAKtbLL78cJ554YqxduzbR/Mknnxxjx45NdMIFAAAAULNde+21sfPOO2edW7FiRRxxxBExfvz4rd45Zsy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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_activation_function(torch.nn.Identity())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Sigmoid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_activation_function(torch.sigmoid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Rectified Linear Unit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_activation_function(torch.relu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Hyperbolic Tangent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TD/5bf39/XHbZZXHOOefEI488UrfnXHfddXHMMcfEN77xjbo9o9GsXr06Lr/88li0aFE85znPiSuuuCLuvffeuj+3v78//uM//iMWL14cl156aXR3d9f9mQAAAAAAjA7d1+bUHXNKRPtLHEkBjCQPbEljMGMea0wx4ph2YXwYKjPOL0RxQj618voeCAAAAAAwGjn9JiIiNm3aFC960Yvic5/73JA8b/fu3XHJJZfEX/7lX+bSFbJR/cd//EeccMIJsWzZsviHf/iHWL9+/bDMI03T+PKXvxxHH310fP7znx+WOQAAAAAAMHLsub8ae1bn8/f7jpcXozBGIAdgJFndk7073rEzk2gpWv9hqBTHJTHzwny6ZPb+Io19j+qSCQAAAADwVAQyie7u7njxi18cv/jFL4b0uWmaxgc/+MF417veNaTPHUqf/vSnh6QTZq16e3vjda97Xbzuda+LgYGB4Z4OAAAAAAANqvs/c+qOOTVi+pmOowBGmlXd2UP5Szus/zDU2s8rRHFiPrV0yQQAAAAAeGpOQJrc9u3b44wzzoiHH3542Obw8Y9/PN7//vcP2/Ob0ec///k4//zzY+/evcM9FQAAAAAAGszutdXYs1Z3TIBmtWt/Gut3Zt8Hls2y/sNQK45NYuZFOXXJvCuNfQ/rkgkAAAAA8H8JZDaxNE3j0ksvjfvuu6/mnykUCnHaaafFVVddFXfeeWf09PTEwMBA7N69Ox577LH4zne+E3/xF38R8+fPP6i5fOhDH4prr732YH8FMrj11lvjwgsvjMHBweGeCgAAAAAADSJN09y6Y7ZM0x0TYCRa05M9gDV5TMRhkwUyYTi0n1OI4qR8aumSCQAAAADw20rDPQGGz0c+8pG4+eabax7/8pe/PD7ykY/EkUce+Vv/rKWlJSZMmBDz58+P888/Pz70oQ/FddddF+9973tj/fr1NdV/4xvfGMuXL3/K+s2kra0tli9fHs9+9rPj+OOPjwULFsSCBQtiypQpMX78+KhUKrFt27bYvn17rFu3Ln74wx/GD3/4w7j33nsjTQ/uTbUrVqyIN7/5zfG5z32uTr8NAAAAAAAjyZ61aey9P5/umDMvLkahVRgHYKRZ1Z19H1g6qxCFxB4Aw+G/umR2fTF7mLJ3ZRp7H6rG+KO8ZAMAAAAA4L8IZDaptWvXxl/91V/VNHbcuHHxyU9+Ml796lfXXD9JknjlK18Z5513Xlx22WVx3XXXHfBndu/eHX/4h38YP/3pTyNpssO5ww47LF7+8pfH2WefHaecckq0tbU94/i5c+fG3LlzY+nSpfHSl740IiLuu++++OhHPxpf+cpXDqrr5b//+7/HWWedFa985Suz/AqZnXLKKfGDH/xgWOcAAAAAANDMcu2OOT1i+hku7gOMNGmaxqocOmQu62iu815oNO3nFGLLtytR7s1eq/vaShz+l77XAQAAAAD8F38xbVLveMc7olwuH3DcuHHj4qabbjqoMOb/NmHChLj22mvjzW9+c03jf/azn8UXv/jFQ3rWSDNhwoT4oz/6o/jJT34Sjz32WFx55ZVx1llnHTCM+XSOO+64+PznPx/33XdfLF++/KB+9m1ve1vs2LHjkJ4LAAAAAMDosGd1GnsfyKc7ZsclxSi0COMAjDRduyO27steZ+ksVxFgOBXbkpj50mIutXbfk8beB7MHtQEAAAAARgunIE3oq1/9as2dCK+55po45ZRTMj/z6quvjosuuqimsZdffnns2bMn8zMb1dFHHx1XXXVVbNq0Ka6++up44QtfmGtH0COPPDJ+9rOfxdvf/vaaf2bbtm3x0Y9+NLc5AAAAAAAwsuTaHbM9YtppjqAARqI8umPOmRTRPk4oH4Zb+zmFKE3Jp1b3tfl8TwQAAAAAGA2chjehv/u7v6tp3Lve9a648MILc3lmkiTx7//+7zFv3rwDju3u7o7PfOYzuTy3kZxwwglx3XXXxf333x9ve9vbYuLEiXV7Vmtra/zrv/5rXH755TX/zMc//vHo7e2t25wAAAAAAGhcv+58pDsmQLNb1Z09kLm0wzUEaASFMUnMfFlOXTLvTWPP/bpkAgAAAABECGQ2nZtuuinWrFlzwHFz586NK664ItdnT506Na688sqaxl555ZUxODiY6/OHyzHHHBNf//rXY+XKlfG7v/u7USgM3b92H/7wh2vuTLp379647rrr6jwjAAAAAAAaTXUwjSf/vZxLrZYZEdNOdfwEMBJVqmms3Zw9nL9sln0AGkX7S/LrkvnkZyuRVvJ5gQcAAAAAwEjmJKTJ/PM//3NN4z70oQ/FuHHjcn/+xRdfHCeffPIBxz3xxBOjIhz4wQ9+MNauXRsvf/nLh+X5SZLEpz/96Zg2bVpN46+99to6zwgAAAAAgEaz5YZq9D+ZT61ZumMCjFiPbE9jX8Z35haSiMUz7QPQKApjkuh4eT5dMvvWp7HtFl0yAQAAAAAEMpvIE088EStWrDjguHnz5sXv//7v120el19+eU3jvvCFL9RtDkPlxS9+cRSL+RxuHKqZM2fGe97znprG/vSnP43+/v46zwgAAAAAgEYxsDWNnq9WcqnV2qE7JsBItqo7e+e7I6cnMU4wHxrK9DMLUZqaT62ur1SivEuXTAAAAACguTkVbyJf+cpXIk0P/Ifxt7/97VEqleo2j3PPPTeOOuqoA45bsWJFdHd3120ezeRNb3pTtLS0HHBcX19f3HPPPUMwIwAAAAAAGsGmL1Siuj+fWh2XFCMpCeEAjFSre7J3vlvWYR+ARpNnl8zK3ohNX8rnZR4AAAAAACOVQGYTueaaaw44plAoxKte9aq6ziNJkrj00ksPOK5SqcS1115b17k0i/b29jj55JNrGvvQQw/VeTYAAAAAADSC3WuqsfOn2cM3ERGtsyKmneLYCWCk6htM46Ft2bveLZtlL4BGNP3MQrRMy6fW9tursfehfL5DAgAAAACMRE5DmsSmTZti1apVBxx30kknxZw5c+o+n9///d+vadzNN99c55k0jxe+8IU1jXv00UfrPBMAAAAAAIZbWk7jyX/Lr7vRrN/VHRNgJLtvSxrljPmqsaWII6fbC6ARFVqT6Lg4ny6ZEREbP1OJtJI9xA0AAAAAMBIJZDaJ2267raZx5513Xp1n8mtHHHFEHHnkkQcc96Mf/Sj6+/uHYEaj31FHHVXTuF27dtV5JgAAAAAADLctN1Vj/xP5XKIf0xkx9UWOnABGstXd2bvdHTcziVJBIBMa1bQzCtHSnk+tvkfT2Ha7LpkAAAAAQHNyOt4kag1knnHGGXWeycE9q6+vL376058OwWxGv+nTp9c0bu/evXWeCQAAAAAAw2lwexrd1+bXHbPjFcVIigI4ACPZqp7sIf1ls1w/gEZWaEmi45L8umR2fakS5d26ZAIAAAAAzceJSJOoJdQ4efLkOOGEE4ZgNr926qmn1jTujjvuqPNMmkOpVMp1HAAAAAAAI9Om/6hEtS+fWuOOTmLqyY6bAEay7X1pPLErh0Bmh/0AGt300wsxdmE+L9Ko7Ino+nJ+L/kAAAAAABgpnIg0gV27dsX69esPOO6EE06IJBm6N1ifeOKJNY1buXJlnWfSHHbs2FHTuAkTJtR5JgAAAAAADJc991Vjx4+q+RQrRMx9YzGSgu6YACPZ6u7s+8K0sRFzJuUwGaCukmISc9+YX5fMbbdWY98jOX23BAAAAAAYIQQym8DKlSsjTQ/8RtPly5cPwWz+x6JFi2Lq1KkHHHfPPfcMwWxGv8cee6ymcbNmzarvRAAAAAAAGBZpJY2N/5ZfF6P2lxRi3CJHTQAj3aqefLpjDuXLf4FDN/6YQkw9NafvcGnExs9UIq1mX0cAAAAAAEYKp+RN4N57761p3OLFi+s7kadw7LHHHnDMY489Fjt37qz/ZEa5WjuNHnnkkXWeCQAAAAAAw2Hrd6uxf0M+l+WLkyJm/UF+3ZUAGB5pmubSIXPpLGFMGElmv7oYhXH51Nr3cBrbv69LJgAAAADQPAQym8AjjzxS07gjjjiizjP5bbWG/x599NE6z2R0q1Qqcfvtt9c0dunSpXWeDQAAAAAAQ21wZxpd1+TXHXP2pcUoTRC+ARjpnuhNY8f+7HWWdrh6ACNJy5QkOn8/v5drbPpiJcp7dMkEAAAAAJpDabgnQP2tX7++pnHD0Rmx1meuX78+TjzxxDrPZvT6wQ9+EFu3bj3guMMOOywWLFhQ/wk9g+7u7vjpT38ad911V9x3333x2GOPRVdXV+zduzf6+/ujra0txo4dGxMnTow5c+bE3Llz44gjjogTTjghli9fHgsXLhzW+QMAAAAANKJNX6xEdV8+tcYdmcS00wRvAEaD1d3ZA1TzJycxdayQPow07WcXYttt+XRQr/RGdF9TiblvdA0JAAAAABj9/CW0CdQSyGxpaYmOjo4hmM1vmjt3bk3jag2V8tSuuuqqmsadddZZdZ7J0/vVr34Vy5cvj3vvvTfS9OkPfPbt2xf79u2Lbdu2xWOPPfZb/3zBggVx7rnnxste9rI4/fTTI0kc/gIAAAAAzW3vr6qx4/vVfIolEXPfWIyk4G+vAKPBqp7s+8PSWfYEGImSYhJz31CMR/6ynEu9rd+rxrQzqjFuoRd3AAAAAACjm7+CNoENGzYccExHR8ewBNdmzZpV07hafgee2kMPPRTXX399TWNf9apX1Xk2T6+npyfuueeeZwxj1uKxxx6LT3ziE3HmmWfG4YcfHh/+8Iejt7c3p1kCAAAAAIwsaSWNjZ+p5FZv+hmFGHeE4yWA0WCwksZ9m7N3xlvWYV+AkWrCcYWY+qKc/h2uRjz56Uqk1ezrCgAAAABAI3MyMsrt3bs3+vr6Djiu1mBk3mp97pYtW+o8k9HrT//0T6NaPfCbbY844oh40YteNAQzGjrr16+P973vfbFo0aL46Ec/GoODg8M9JQAAAACAIbXtlmr0rc/nUnxxQkTnpcVcagEw/B7elsb+jI3xSoWIY2fqkAkj2ezXFKPQlk+tvQ+mseOHOXVmBwAAAABoUAKZo9y2bdtqGtfe3l7nmTy1GTNm1DSu1t+D3/S9730vvvOd79Q09i/+4i+GpUvqUNi2bVv8+Z//eZx44omxcuXK4Z4OAAAAAMCQKO9Ko+sr+XXH7HxVMUoTR+ffkQGa0aqe7KGpo6cn0VayN8BI1jItiVmvzO+lG5u+WInKXl0yAQAAAIDRSyBzlNu+fXtN4yZOnFjnmWR7bq2/B/9j165d8YY3vKGmsQsXLozXvOY1dZ7R8FuzZk0897nPjauvvnq4pwIAAAAAUHebvlSJyt58ao1dlMT0MxwrAYwmq7uzB6aWzbI3wGgw47xCtM3LJ1xd3hnR9Z/5vRQEAAAAAKDROB0Z5WoNMk6aNKnOM3lqEyZMiELhwB9DgcyD9/a3vz02btxY09grr7wyWlpa6jyjxlAul+Otb31rvOMd74g09VZOAAAAAGB02vtwNbbfnr3z2X+Z+8ZiJEUd0ABGi70DaTy8PftZ2dJZ9gYYDZJSEnPekF+XzK03V6NvQ37fRQEAAAAAGklpuCdAfe3bt6+mcRMmTKjzTJ752b29vc84ptbfg1/7zGc+E1/60pdqGnv22WfHRRddVOcZNZ6rrroqBgcH45Of/ORwT+U3VKvV6O/vH+5pMIIMDAzU9L8BAI3Nng4AI5/9nEaSViOe+FRERD4hmckvTqO0YDD86RIY7ZppP79nU0Q1zbZPjG9JY954+wOMFq1HRUx6fkTvz3L4DlmNePxTgzH/ryISuW2GQTPt6QAwWtnPAWB0sKeTl2q1sV4AJ5A5yg0ODtY0bji7I9bybAtu7VauXBnveMc7aho7ZcqU+MxnPlPnGR3Y5MmTY+nSpXHcccfFcccdF8cee2zMmDEjJk2a9N//Vy6Xo6+vL7q7u2Pjxo2xdu3auPvuu+P222+Prq6uQ3rupz71qZg2bVp86EMfyvk3OnQ7duyIe++9d7inwQi3YsWK4Z4CAJADezoAjHz2c4bLhIfmxfR1i3OpVWkdjLUdP4rV3/V3eqA5jdb9/OcDx0bE/Ew1pld64pbv3ZPPhICGUJzTFrNLJ0ehnP06Ud+vkvjx1ffGvkWHdp4PeRutezoANBP7OQCMDvZ0DsXxxx8fU6ZMGe5p/DeBzFGu1iDjcAYyS6UDfwxrDZY2u+7u7njZy15Wc4fFq666KubOnVvnWf22JEni+OOPj3POOSfOPvvseP7zn3/Az0GxWIwxY8bElClT4phjjokzzjjjv//ZnXfeGZ/97Gfji1/8Yuzfv/+g5vKRj3wknvvc5zZll1AAAAAAYPQp7G+JKSuPyq3ezhMeimqbMCbAaNNVnZ65RmdxWw4zARpJZfz+2LX00Zi68uhc6k2965jom7sl0tZyLvUAAAAAABpBYbgnQH3VGmSsJRRZLzpk5qOvry8uvPDCePzxx2saf+mll8arXvWqOs/qN3V2dsb73ve+WLduXaxcuTKuuOKKOPnkkzN//p773OfGpz/96Vi3bl286U1viiRJav7ZNE3jta99bXR3d2eaAwAAAABAI5hyz1FR7G/NpdbAtN7Yc1Rtf3MGYOTYU22L3nRC5jqzC1tzmA3QaHqPXR+Dk/bkUqvU1xaTVx2eSy0AAAAAgEYhkDnKVavVmsYdTIAtb4XCgT+Gtf4ezaparcall14av/zlL2sav2TJkvjUpz5V51n9j3nz5sU3v/nNePzxx+OKK66IBQsW1OU5nZ2d8alPfSq+//3vR2dnZ80/t3PnzvjTP/3TuswJAAAAAGCotG6bFBMempdbve3Pvc9JEsAo1FVtz1xjfLIvJib7cpgN0HCKaWx/7v25lZv0wIJo2Zk9BA4AAAAA0CiGry0iQ6KW7pMREeVyuc4zeXq1dPGs9fdoVu985zvjG9/4Rk1jJ02aFF//+tdj3LhxdZ7V/zj88MPj8MOH7q2Xp5xyStx1111x7rnnxqpVq2r6mS9/+cvxx3/8x/E7v/M7dZ7dM5s6dWqcffbZwzoHRpaBgYFYsWLFb/xvp512WrS25tMFAQAYGvZ0ABj57OcMt7Qa8dhfR+yPfF7AOPnkNJ71muflUgtgpGiW/fyhX0bExmw1fuewsXHOcmdaMJpt3JXG7l9k/26ZpIU44uGT4rAPRAzju8JpMs2ypwPAaGY/B4DRwZ5OXvr7+yNN0+Gexn8TyBzlRkIgs5ZnW2yf3t/+7d/GVVddVdPY1tbW+MY3vhFHHnlknWc1/GbPnh233357nHLKKXHffffV9DN///d/H1//+tfrPLNnVigUYsyYMcM6B0a+1tZWnyMAGAXs6QAw8tnPGUrbbq/E/kcqudQqjIuY+7rWaBnjxjzAaNvPq2ka92058AtzD2T5nFKMGVPMYUZAo5p3WRoP3DsY6UD2WvvuT6Lv7mJMfaF1g+Ez2vZ0AGhG9nMAGB3s6RyKwcHBqFTyOQ/PQ2G4J0B91RpkFMgcmf7lX/4l/uZv/qamscViMb7yla/E6aefXt9JNZDp06fHt7/97ZgyZUpN47/1rW/FY489Vtc5AQAAAADkrbwnjU1fzO/wqfP3itEyRRgTYDTasDON3v5sNZKIWNLhqgGMdq0zkui4JL8A5aZ/r0Slr3HeYA8AAAAAcKickoxytabG9+3bV+eZPL29e/cecIxA5m/77Gc/G+9+97trGpskSXz605+Oiy++uM6zajyHH354/OM//mNNY6vValx77bV1nhEAAAAAQL66r6lEpTefWm2HJdF+juMjgNFqVU/2MNTCqUlM0kUZmsLMiwrR2plPrcHtET1fa5w32AMAAAAAHCon6qPc5MmTaxq3e/fuOs/kqQ0MDMTAwMABx9Xa4bBZXHPNNfGmN70p0rS2A9OPfexj8frXv77Os2pcr3/96+PEE0+saezXvva1Os8GAAAAACA/+9ZXY+v3qrnVm/vGYiRFIRuA0Wp1d/Y9Y9ks+wQ0i0JLEnMvK+VWb8t3qrH/SV0yAQAAAICRTSBzlJs+fXpN43p7c3p19kGq9bm1/h7N4Jvf/Ga85jWviWq1tsPSK664Iv74j/+4zrNqbEmSxF/8xV/UNHblypWxa9euOs8IAAAAACC7NE3jyc9UInLKY049uRATjnN0BDBaDVTSuH9L9iDU0g57BTSTScsLMel38glip+WIJ/+tXPPLpwEAAAAAGpGTklFu2rRpNY3buXNnfSeS8bm1/h6j3Y033hi/93u/F+Vyuabx73vf++J973tfnWc1Mlx00UUxderUA46rVqvx85//fAhmBAAAAACQzY4fVGPvr/K5zF5oi5j9h8VcagHQmB7cmsZAJVuN1mLEs2bokAnNZs7rSpG05lNr96o0dt0pkAkAAAAAjFwCmaPc1KlTo1A48P+bu7u7h2A2h/5cHTIjbrnllrj44otjYGCgpvHvfOc744orrqjzrEaOlpaWOO+882oae88999R5NgAAAAAA2VT2prHpixlTNf/LrFcWo2WagA3AaLaqO3tL5WPak2gt2i+g2YzpSKLjZfm9vOPJz5Wj2i+UCQAAAACMTAKZo1yhUIjOzs4Djuvp6RmC2fy2WgOZc+fOrfNMGtv3v//9eOlLXxr9/f01jX/Tm94UH/vYx+o7qRHo5JNPrmnc+vXr6zwTAAAAAIBsuq+tRHlnPrXGzI2YcZ4jI4DRblVP9vDTsln2C2hWM19aiNaOfGoNbo3o+Xp+LxcBAAAAABhKTkuawMKFCw84pre3N/bu3TsEs/lNXV1dNY2r5XcYrX7yk5/EBRdcEH19fTWNf81rXhNXX311nWc1Mh133HE1jXvsscfqOxEAAAAAgAz6NlRjy03Zu5z9l7lvLEVS0u0MYDTb3Z/Guu15BDLtF9CsCmOSmPP6Um71Nn+rGv2bdMkEAAAAAEYegcwmsGDBgprGPfroo/WdyFN45JFHahpX6+8w2vzsZz+Lc889t+aw7Cte8Yr43Oc+F4WCf7WfSq3B3h07dtR5JgAAAAAAhyZN09j4mUpETnnMKS8oxMQl/qYMMNqt6Ukja+xp0piIBVMEMqGZTX5OISadmM86kJYjNn6uHGkqlAkAAAAAjCxO2JvAokWLahr38MMP13kmv63WQGYzdsj8xS9+EWeffXbs3r27pvEvfelL48tf/nIUi8U6z2zkmjx5ck3jhqNbLAAAAABALXb+uBp778/n0nqhLWL2a/1NGaAZrOrJnuRf0lGIQiKQCc1uzmWlSHJqlLl7ZRq9vxTIBAAAAABGFoHMJrB48eKaxj344IN1nsmhPXPixIkxf/78IZhN47j77rvjrLPOit7e3prGn3POOXHttddGqZTTqcco1dbWVtO4/fv313kmAAAAAAAHr9KXxpNfqORWr+OSYrS2C9YANIPV3dkDmUs77BlAxJhZScx8aX7XjZ78XDmq/UKZAAAAAMDIIZDZBJYvX17TuJUrV9Z5Jr9p165dsW7dugOOO/744yNpojet3nvvvXHmmWfGzp07axp/xhlnxDe+8Y1obW2t78RGgVqDlrUGNwEAAAAAhlL3dZUo78in1pjZETMucEwE0Ay696TRszd7nWWz7BvAr3VcXIyWGfnUGtgc0fPN/F46AgAAAABQb05MmsDhhx8eU6ZMOeC4oQ5k3n333ZGmB37LYa2B0tFgzZo1ccYZZ8SOHbXdqDnllFPi29/+tgBhjXbt2lXTuPHjx9d5JgAAAAAAB2f/E2lsuSF7d7P/MucNpSi0NM/LEAGa2aocumN2ToyYOd6+AfxaYUwSc15Xyq3e5m9Wo79bl0wAAAAAYGQQyGwSJ5544gHHrF+/Prq7u4dgNr/2s5/9rKZxz3nOc+o8k8Zw//33x+mnnx7btm2rafwLXvCCuOGGG2LcuHF1ntnosX79+prG1RJgBgAAAAAYKmmaxsZ/K0fk1Dho8vOSmHS8IyKAZpFHIHNph30D+E2Tn5vExOPzCWqngxFPfq6cSy0AAAAAgHpzatIkTj/99JrG3XbbbXWeyf+49dZbaxp32mmn1Xkmw+/BBx+M008/PbZs2VLT+Oc85zlx8803x4QJE+o8s9Hlvvvuq2ncggUL6jsRAAAAAICDsPOOauxZk0/HoKQ1cu1mBEBjq1TTWLs5+x6ybJarBcBvSpIk5ryhFElOXy1770pj1135dYQHAAAAAKgXpyZN4owzzqhp3C233FLnmfzanj17auqQuXjx4ujs7ByCGQ2fRx55JE477bSau5OecMIJ8b3vfS8mTZpU55mNPj/5yU9qGrdw4cI6zwQAAAAAoDaVvjQ2fT6n1pgR0XFJMVpn5NPJCIDGt25HGnsGstUoJBFLZto7gN/WNjuJGRfmd/Xoyc+VozqQz4tIAAAAAADqRSCzSZx44okxbdq0A467/vrro7+/v+7z+da3vhUDAwc++TvzzDPrPpfhtH79+jjttNNi06ZNNY1fsmRJ3HrrrTF16tQ6z2z0GRwcjBtvvLGmsUuXLq3zbAAAAAAAatPz9UoMbsunVmtnxMyLHA0BNJPVPdmDTYdPS2J8q0Am8NQ6LilGy/R8ag10R2z+ti6ZAAAAAEBjc+reJAqFQrzsZS874Lhdu3bFTTfdVPf5XHPNNTWNu+SSS+o8k+Hz+OOPx6mnnhpPPPFETeOf9axnxW233RbTp+d0ktFkvvOd78T27dsPOC5Jknj+858/BDMCAAAAAHhm+59MY8v1+V1In3tZKQotAjUAzWRVd/Z9ZFmHvQN4esW2JOa8rpRbvZ6vV2Jgsy6ZAAAAAEDjEshsIpdeemlN4z7xiU/UdR7r1q2L7373uwcct2jRonjBC15Q17kMlyeffDJOO+202LBhQ03jjzzyyLj99ttj5syZdZ7Z6PWRj3ykpnGLFy+uqZssAAAAAEA9pWkaT362HGk5n3qTnpPEpOWOhQCaSX85jV9tzR5qWjbL/gE8s8nPT2LC0nzC2+lAxJP/ntOXYAAAAACAOnBy0kROOeWUOOywww447rbbbotVq1bVbR4f+9jHolo98JtYX/WqV9VtDsOpu7s7TjvttHj00UdrGr9o0aJYsWJFdHZ21nlmo9fnP//5+OUvf1nT2NHclRUAAAAAGDl23ZnG7nvz6QyUtEbMeX1+XYsAGBnu35JGOWODzDHFiKOm65AJPLMkSWLuG0oRxXzq7bozjd578usUDwAAAACQJ4HMJpIkSbzlLW+paex73/veusxh3bp18elPf/qA41paWuJNb3pTXeYwnLZs2RKnnXZaPPTQQzWNnz9/fqxYsSLmzp1b55mNXuvXr48/+ZM/qXn87/3e79VxNgAAAAAAB1btT+PJz+XXFajjZcUY0yFMA9BsVnVnDzMdNzOJlqI9BDiwtrlJzDg/v2tIT362HNXBfF5QAgAAAACQJ4HMJvOWt7wlJk6ceMBxN998c3znO9/J/fnvfve7o7+//4Dj/uAP/mDUhRC3b98eZ5xxRjzwwAM1jZ87d26sWLEi5s+fX+eZjV47duyIiy66KHbs2FHT+LPOOiuOOuqoOs8KAAAAAOCZ9Xy9EoNb86nV2hEx86WOgwCa0eqe7EGmZbPsIUDtZr2iGC3T8qnVvyliy3d0yQQAAAAAGo/TkyYzefLk+KM/+qOaxl522WXR1dWV27M/+clPxvXXX3/AcYVCIf7sz/4st+f+l9e+9rWRJMkB/++1r31t7s/euXNnnHnmmbF69eqaxnd2dsaKFSti0aJFuc9lqNx1113xjW98I9J0eN5Y2dPTE6effnqsWbOm5p+pV2dYAAAAAIBa9Xelsflb+V08n/P6UhTG6GwG0Gx27k/jsZ3Zz+mW6rAMHITi2CRm/2Ext3o9X63EwFZdMgEAAACAxiKQ2YTe+973xowZMw44bsuWLfHSl740du/enfmZt99+e7z73e+uaexll10Wxx13XOZnNordu3fH2WefHStXrqxp/MyZM2PFihVx5JFH1nlm9bVx48a4+OKLY/ny5fGVr3wlBgcHh+zZP/3pT+PZz3523HPPPTX/zAUXXBCnnHJKHWcFAAAAAPDM0koaGz5ejrScT71Jy5OY9GxBGoBmtLo7e7h/SlvEYZPtI8DBmXJSIcYfl8/aUe2PePxfy5FWhTIBAAAAgMYhkNmEpk6dGh/60IdqGvuLX/wizjrrrNi8efMhP+/GG2+MCy+8MPbv35/r3EaCffv2xXnnnRd33nlnTePb29tjxYoVccwxx9R5ZkPn3nvvjVe96lVx2GGHxfve9764//776/asnp6eeNvb3hYvetGLYuPGjTX/3Pjx4+Oqq66q27wAAAAAAGrR/dVK7Hswn8vmSSlizmWlSBJBGoBmtLon+36yrKNgHwEOWpIkMfcNxdxuJO1Zk8bmb+fXQR4AAAAAICuBzCZ12WWX1dwN8Gc/+1mccMIJccMNNxzUM/bs2RN//ud/HhdccEHs27evpp/5p3/6p2hvbz+o5zSq/fv3x4UXXhg//vGPaxo/bdq0uO2220ZVd9D/rbu7Oz784Q/HcccdF0uXLo33vve98cMf/rCmoO6B3HXXXfHWt741Fi1aFJ/4xCeiWj24w5irr746DjvssMzzAAAAAAA4VHseqEbP1/K7aD7zpYUY0ylEA9CM0jSNVTl0yFw6yz4CHJqx8wsx49z8riR1faUS+x4RygQAAAAAGkNpuCfA8EiSJK655po4/vjja+p+uWnTprjgggvi5JNPjje/+c1x0UUXxYQJE55y7MMPPxxf+cpX4uqrr46enp6a5/TqV786Xve619U8vtH9/Oc/j9tvv73m8du3b4/jjz++fhM6CGmazxvYn86aNWtizZo18ZGPfCRaWlpi2bJlccIJJ8RRRx0VRx55ZHR2dkZHR0dMnTo1xowZE62trTE4OBh9fX2xefPmeOKJJ+K+++6Lu+++O2677bZ48sknD3ku7373u+PVr351jr8dAAAAAMDBKe9NY8OV5Yic7pi3zIjouLiYTzEARpxNuyO29WWvs7TD+52BQzfrlcXY8ZNqlHfmUKwSseHKchz1jy1RHCssDgAAAAAML4HMJtbZ2Rlf/vKX49xzz43BwcGafubHP/5x/PjHP45CoRDHHHNMLFy4MCZPnhwDAwOxffv2WLt2bU0Bz/9ryZIlcfXVVx/0zzHyDQ4Oxl133RV33XXXkD/79a9/ffzjP/7jkD8XAAAAAOC/pGkaGz9ZicGt+dWc87pSFMa4qA7QrPLojjlvUhLTx9lLgENXHJ/E7NcU4/GPV3Kp198V8eTnKnHY21x1AgAAAACGl79SNrkzzjgjvvSlL8Uf/MEfRKVS+x/Bq9Vq3H///XH//fdnnsNRRx0Vt956a4wfPz5zLajV2972tvjXf/3XSBIHyQAAAADA8Nnxg2rs/GlOrTEjYuLxSUx+rr97AjSzVT3Z95Wls+wlQHZTTynEtlursfeBNJd622+vxqQTqjHlBTr4AgAAAADDx18oiVe84hXxhS98IVpbW4f82cccc0zcfvvt0dHRMeTPpjm1tbXFZz/72bjqqquEMQEAAACAYdXflcbGz+TTMSgiIilFzHlDyd8+AZpYpZrG2p7swadlHa4SANklSRJz31DM9XbSE1eXY2BLPgFPAAAAAIBD4RSFiIh41ateFStWrIhZs2YN2TMvuOCCuPPOO2Pu3LlD9kya20knnRR33XVXvP71rx/uqQAAAAAATS4tp7HhynJU9+dXc8aFhWibLYwJ0Mwe3p5GXzlbjWIScdxM+wmQj7ELC9F+Vn7Xkyp7Izb8SznSilAmAAAAADA8BDL5by984Qtj5cqVcckll9T1OZMmTYqPfexj8e1vfzsmTZpU12cxfBrpDexHHnlkfOELX4gf/ehHcdxxxw33dAAAAAAAous/K7HvkfwukbdMj+i4pJhbPQBGplXd2feWo6YnMbalcc76gJFv1h8Uo5Tj9ZC996fR881qfgUBAAAAAA6CQCa/obOzM7761a/GLbfcEs9+9rNzrd3a2hqve93r4le/+lW8853vbKjAHvm74IIL4q677oqPfOQjccYZZ8TYsWOH9PlJksSLX/ziuOaaa+KBBx6I17zmNT5zAAAAAEBD2L2mGptzvkA+722lKLb5GyhAs1vdnX1/WTbLNQIgX6XxScz9o1KuNbv/sxJ7HxTKBAAAAACGXr5/7WTUOPPMM+PMM8+Mn/zkJ3H11VfHTTfdFDt37jykWsccc0y88pWvjLe85S3R0dGR70RpWIVCIU488cQ48cQT4/LLL4/+/v6444474s4774yVK1fGPffcE48++mikaX5vgB8/fnycfPLJ8ZKXvCQuueSSmDdvXm61AQAAAADyUN6dxuP/Uo7I70+jMeOCQkw6XngGoNn1Dabx0LbsG8zSWQL+QP6mPK8Q088sxLZbcwpRViM2fKwcR/9TSxTHWbcAAAAAgKEjkMkzOumkk+Kkk06KSqUSd9xxR9xxxx1x3333xQMPPBDd3d2xZ8+e2LNnT5RKpZgwYUJMmjQpFi5cGMcee2wsWbIkzjzzzFiwYMFw/xoREfH5z38+Pv/5zw/Z81784hfnGjYc6caMGROnnnpqnHrqqf/9v/X29sbq1atj3bp18fjjj8eGDRvi8ccfj66urti7d2/s3bs39u3bF319fZGmabS1tUVbW1tMnjw5Ojs7o7OzMxYuXBiLFy+OJUuWxOLFi6OlpWUYf0sAAAAAgKeXpmk8cXU5BrfnV3PswiQ6Ly3mVxCAEeu+zWlUMh5Pji1FHDlNsAmoj9mvK8ae+6vR/2Q+9QZ6IjZ+phLz3+n6EwAAAAAwdPxFkpoUi8U4+eST4+STTx7uqTCKTJo06b9DvwAAAAAAo93226qx6+f5vcgvaY2Y/+5SFFoEZwCIWNWTvevc4o4kigX7ClAfxbYk5r+7FA//RTnScj41d/ywGhOPr8S0U7ykBAAAAAAYGoXhngAAAAAAAMBot39jGhs/W8m15pzXF6NtrtAMAL+2qjt7IHNZhysEQH2NW1TIvcP7xk9Xor8nvxefAAA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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_activation_function(torch.tanh)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Neural Network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define a simple neural network by creating a new class that inherits form `nn.Module`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "class SimpleNet(nn.Module):\n",
    "    def __init__(self, n_features):\n",
    "        super(SimpleNet, self).__init__()\n",
    "        # Linear regression with one output\n",
    "        self.linear = nn.Linear(n_features, 1)  \n",
    "\n",
    "    def forward(self, x):\n",
    "        x = self.linear(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we load our dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "anscombe = np.loadtxt('data/Anscombe1.dat', delimiter=' ')\n",
    "anscombe = torch.from_numpy(anscombe).float()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And extract our instances and labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = anscombe[:, 0].reshape(-1, 1)\n",
    "y = anscombe[:, 1].reshape(-1, 1)\n",
    "n_features = X.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([11, 1])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can instantiate our model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = SimpleNet(n_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Defining the loss function and the optimizer are the next steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "criterion = nn.MSELoss()\n",
    "optimizer = optim.Adam(model.parameters(), lr=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Training loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "272f799eb9104fd18a6890a555112bd1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/2000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_epochs = 2_000\n",
    "\n",
    "for epoch in tqdm(range(num_epochs), total=num_epochs):\n",
    "    # Forward pass\n",
    "    outputs = model(X)\n",
    "    loss = criterion(outputs, y)\n",
    "    \n",
    "    # Backward pass and optimization\n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract model parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OrderedDict([('linear.weight', tensor([[0.5630]])), ('linear.bias', tensor([2.3707]))])\n"
     ]
    }
   ],
   "source": [
    "trained_params = model.state_dict()\n",
    "print(trained_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_ = outputs.detach().numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x35a513550>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.plot(X, y, \n",
    "        marker='o', \n",
    "        markersize=10, \n",
    "        linestyle='None', \n",
    "        label='Data')\n",
    "\n",
    "ax.plot(X, y_,\n",
    "        linestyle='-', \n",
    "        label='Linear Regression')\n",
    "\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.legend(loc='lower right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Network Classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the MNIST dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "transform = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.5,), (0.5,))])\n",
    "\n",
    "# This will download the data the first time you run it and store it in the `data` folder\n",
    "train_dataset = datasets.MNIST(root='./data', train=True, download=True, transform=transform)\n",
    "test_dataset = datasets.MNIST(root='./data', train=False, download=True, transform=transform)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each data set is an array of tuples. The first element of the tuple is the image itself:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 28, 28])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "instance = 3\n",
    "train_dataset[instance][0].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which we can plot easily"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 27.5, 27.5, -0.5)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.imshow(train_dataset[instance][0].squeeze(), cmap='gray')\n",
    "ax.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second element is the label"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is a picture of the number: 1\n"
     ]
    }
   ],
   "source": [
    "print(f\"This is a picture of the number: {train_dataset[instance][1]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have examples of all digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 4200x1680 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs_lst = plt.subplots(2, 5, figsize=(14, 5.6))\n",
    "axs_lst = np.array(axs_lst).flatten()\n",
    "\n",
    "instances = [1, 3, 5, 7, 2, 0, 13, 15, 17, 19]\n",
    "\n",
    "for i, instance in enumerate(instances):\n",
    "    axs_lst[i].imshow(train_dataset[instance][0].squeeze(), cmap='gray')\n",
    "    axs_lst[i].set_title(train_dataset[instance][1])\n",
    "    axs_lst[i].axis('off')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "hist_train = Counter([train_dataset[i][1] for i in range(len(train_dataset))])\n",
    "hist_train = pd.DataFrame.from_dict(hist_train.items())\n",
    "hist_train.columns = ['Number', 'Frequency']\n",
    "\n",
    "hist_test = Counter([test_dataset[i][1] for i in range(len(test_dataset))])\n",
    "hist_test = pd.DataFrame.from_dict(hist_test.items())\n",
    "hist_test.columns = ['Number', 'Frequency']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/lr/j1bs1q851k15cj5y777nxwph0000gn/T/ipykernel_97340/4174146417.py:8: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.\n",
      "  ax.set_yticklabels([f'{int(label):,}' for label in ax.get_yticks()])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x35a67ff50>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.bar(hist_train['Number']-0.15, hist_train['Frequency'], width=0.3)\n",
    "ax.bar(hist_test['Number']+0.15, hist_test['Frequency'], width=0.3)\n",
    "ax.set_xlabel('Digits')\n",
    "ax.set_xticks(range(10))\n",
    "ax.set_xticklabels(range(10))\n",
    "ax.set_ylabel('Count')\n",
    "ax.set_yticklabels([f'{int(label):,}' for label in ax.get_yticks()])\n",
    "ax.legend(['Train', 'Test'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the network architecture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MNISTClassifier1(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(MNISTClassifier1, self).__init__()\n",
    "        self.fc1 = nn.Linear(28*28, 128)\n",
    "        self.fc2 = nn.Linear(128, 64)\n",
    "        self.fc3 = nn.Linear(64, 10)\n",
    "    \n",
    "    def forward(self, x):\n",
    "        x0 = x.view(-1, 28*28)  # Flatten the input\n",
    "        x1 = torch.relu(self.fc1(x0))\n",
    "        x2 = torch.relu(self.fc2(x1))\n",
    "        x3 = self.fc3(x2)\n",
    "        \n",
    "        return torch.sigmoid(x3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the neural network architecture using `nn.Sequential`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MNISTClassifier(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(MNISTClassifier, self).__init__()\n",
    "        # Define the layers\n",
    "        self.fc1 = nn.Linear(28*28, 128)\n",
    "        self.fc2 = nn.Linear(128, 64)\n",
    "\n",
    "        # Build the model\n",
    "        self.network = nn.Sequential(\n",
    "            nn.Linear(28*28, 128),\n",
    "            nn.ReLU(),\n",
    "            nn.Linear(128, 64),\n",
    "            nn.ReLU(),\n",
    "            nn.Linear(64, 10),\n",
    "            nn.Sigmoid()\n",
    "        )\n",
    "        \n",
    "    def forward(self, x):\n",
    "        x = x.view(-1, 28*28)  # Flatten the input\n",
    "        x = self.network(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_loader = DataLoader(train_dataset, batch_size=128, shuffle=True)\n",
    "test_loader = DataLoader(test_dataset, batch_size=128, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = MNISTClassifier()\n",
    "criterion = nn.CrossEntropyLoss()\n",
    "optimizer = optim.Adam(model.parameters(), lr=0.002)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d9569f7f5f514423929e7a63d08648ec",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/20 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch [1/20], Loss: 1.5259  Training Accuracy: 91.46% Testing Accuracy: 91.52%\n",
      "Epoch [2/20], Loss: 1.5208  Training Accuracy: 93.31% Testing Accuracy: 93.11%\n",
      "Epoch [3/20], Loss: 1.5081  Training Accuracy: 95.50% Testing Accuracy: 95.09%\n",
      "Epoch [4/20], Loss: 1.4918  Training Accuracy: 95.90% Testing Accuracy: 95.39%\n",
      "Epoch [5/20], Loss: 1.4887  Training Accuracy: 96.65% Testing Accuracy: 96.17%\n",
      "Epoch [6/20], Loss: 1.4659  Training Accuracy: 96.82% Testing Accuracy: 96.41%\n",
      "Epoch [7/20], Loss: 1.4764  Training Accuracy: 97.05% Testing Accuracy: 96.44%\n",
      "Epoch [8/20], Loss: 1.4929  Training Accuracy: 96.58% Testing Accuracy: 95.93%\n",
      "Epoch [9/20], Loss: 1.4985  Training Accuracy: 97.14% Testing Accuracy: 96.00%\n",
      "Epoch [10/20], Loss: 1.4792  Training Accuracy: 97.53% Testing Accuracy: 96.82%\n",
      "Epoch [11/20], Loss: 1.4786  Training Accuracy: 97.83% Testing Accuracy: 97.09%\n",
      "Epoch [12/20], Loss: 1.5081  Training Accuracy: 97.55% Testing Accuracy: 96.93%\n",
      "Epoch [13/20], Loss: 1.4728  Training Accuracy: 97.84% Testing Accuracy: 97.04%\n",
      "Epoch [14/20], Loss: 1.4861  Training Accuracy: 97.66% Testing Accuracy: 97.15%\n",
      "Epoch [15/20], Loss: 1.4639  Training Accuracy: 97.92% Testing Accuracy: 97.06%\n",
      "Epoch [16/20], Loss: 1.4780  Training Accuracy: 97.25% Testing Accuracy: 96.43%\n",
      "Epoch [17/20], Loss: 1.5021  Training Accuracy: 97.64% Testing Accuracy: 97.11%\n",
      "Epoch [18/20], Loss: 1.4703  Training Accuracy: 97.97% Testing Accuracy: 96.82%\n",
      "Epoch [19/20], Loss: 1.4692  Training Accuracy: 97.96% Testing Accuracy: 97.05%\n",
      "Epoch [20/20], Loss: 1.4775  Training Accuracy: 98.41% Testing Accuracy: 97.47%\n"
     ]
    }
   ],
   "source": [
    "# Training loop\n",
    "num_epochs = 20\n",
    "history = {'train_loss': [], 'train_acc': [], 'test_acc': []}\n",
    "\n",
    "for epoch in tqdm(range(num_epochs), total=num_epochs):\n",
    "    model.train()\n",
    "    \n",
    "    for images, labels in train_loader:\n",
    "        # Forward pass\n",
    "        outputs = model(images)\n",
    "        loss = criterion(outputs, labels)\n",
    "        \n",
    "        # Backward pass and optimization\n",
    "        optimizer.zero_grad()\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "    \n",
    "    model.eval()\n",
    "\n",
    "    with torch.no_grad():\n",
    "        test_correct = 0\n",
    "        test_total = 0\n",
    "\n",
    "        for images, labels in test_loader:\n",
    "            outputs = model(images)\n",
    "            _, predicted = torch.max(outputs.data, 1)\n",
    "            test_total += labels.size(0)\n",
    "            test_correct += (predicted == labels).sum().item()\n",
    "\n",
    "        train_correct = 0\n",
    "        train_total = 0\n",
    "\n",
    "        for images, labels in train_loader:\n",
    "            outputs = model(images)\n",
    "            _, predicted = torch.max(outputs.data, 1)\n",
    "            train_total += labels.size(0)\n",
    "            train_correct += (predicted == labels).sum().item()\n",
    "\n",
    "    history['train_loss'].append(loss.item())\n",
    "    history['train_acc'].append(100 * train_correct / train_total)\n",
    "    history['test_acc'].append(100 * test_correct / test_total)\n",
    "\n",
    "    print(f'Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.4f}  Training Accuracy: {100 * train_correct / train_total:.2f}% Testing Accuracy: {100 * test_correct / test_total:.2f}%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.plot(history['train_acc'], label='Training')\n",
    "ax.plot(history['test_acc'], label='Testing')\n",
    "ax.set_xlabel('Epoch')\n",
    "ax.set_ylabel('Accuracy')\n",
    "ax.legend()\n",
    "ax.set_xticks(range(num_epochs));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "     <img src=\"data/D4Sci_logo_full.png\" alt=\"Data For Science, Inc\" border=\"0\" width=300px> \n",
    "</center>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
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   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
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   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
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  "varInspector": {
   "cols": {
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    "lenVar": 40
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   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
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     "delete_cmd_postfix": ") ",
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     "varRefreshCmd": "cat(var_dic_list()) "
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   "types_to_exclude": [
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   "window_display": false
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 "nbformat": 4,
 "nbformat_minor": 4
}