micrograd_notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "783b6253",
   "metadata": {},
   "source": [
    "# Micrograd Implementation Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e79b3eb9",
   "metadata": {},
   "source": [
    "## Necessary libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0ce07cc1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:11:31.235442Z",
     "start_time": "2023-08-22T08:11:30.320911Z"
    }
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "deaff290",
   "metadata": {},
   "source": [
    "## Derivative with one input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ea744692",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:11:31.260827Z",
     "start_time": "2023-08-22T08:11:31.235442Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def f(x):\n",
    "    return 3*x**2 - 4*x + 5\n",
    "\n",
    "f(3.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6df1a77e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:11:31.413105Z",
     "start_time": "2023-08-22T08:11:31.263044Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([100.    ,  91.6875,  83.75  ,  76.1875,  69.    ,  62.1875,\n",
       "        55.75  ,  49.6875,  44.    ,  38.6875,  33.75  ,  29.1875,\n",
       "        25.    ,  21.1875,  17.75  ,  14.6875,  12.    ,   9.6875,\n",
       "         7.75  ,   6.1875,   5.    ,   4.1875,   3.75  ,   3.6875,\n",
       "         4.    ,   4.6875,   5.75  ,   7.1875,   9.    ,  11.1875,\n",
       "        13.75  ,  16.6875,  20.    ,  23.6875,  27.75  ,  32.1875,\n",
       "        37.    ,  42.1875,  47.75  ,  53.6875])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs = np.arange(-5, 5, 0.25)\n",
    "ys = f(xs)\n",
    "ys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "505bed3e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:11:31.693285Z",
     "start_time": "2023-08-22T08:11:31.413105Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$f(x)=3x^2-4x+5$')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AOLpDRERU01h2LMT/JipncaIyERFRDWLZsRDdm/oiuJ4ztKXlWHc4W3QcIiIim8GyYyGUCglP3tcAALBsbxpkWRaciIiIyDaw7FiQxzuEwFGlwJEsLZIy8kXHISIisgksOxbEy9URD7WuD8A8ukNERET3jmXHwozp0hAAsD75PC4X6cSGISIisgEsOxambYgnWgdroDeasOpAhug4REREVo9lxwKNvjpR+bt96TCaOFGZiIjoXrDsWKCH2wTC08UBWfml2HYiV3QcIiIiq8ayY4GcHJQY3iEEAPDtPk5UJiIiuhcsOxZqVOcGkCRgx6mLSL1ULDoOERGR1WLZsVCh3i7o1cwXALCcoztERER3jWXHgl27DH31gQyU6rlfFhER0d1g2bFgPZv5ItTLBQVlBvySlCU6DhERkVVi2bFgCoWEJ+8z74b+LffLIiIiuissOxbu8Q4hUKsUOHa+AAfT80THISIisjosOxbO08URj7QJBGAe3SEiIqLqYdmxAtcmKm88ch4XC7lfFhERUXWw7FiByGAN2oR4otwoY1VCuug4REREVoVlx0qMubpf1oq/0mEwmgSnISIish4sO1ZiYOv68HJ1RLa2DH9wvywiIqIqY9mxEk4OSjx+db+sZZyoTEREVGUsO1ZkVOdQSBKw6/QlnLlYJDoOERGRVWDZsSIhXi7o08IPAEd3iIiIqoplx8qMvnoZ+prETBTrDGLDEBERWQGWHSvTvYkPGnq7oFBnwM/cL4uIiOiOWHasjHm/LPNl6Mu4XxYREdEdsexYoWFRIXByUOBETiESznG/LCIiotth2bFCGhcHPNomCADwzZ5zYsMQERFZOJYdK/VUdEMAwOaUHGTll4oNQ0REZMFYdqxUy0APdGnkDaNJxrd7z4mOQ0REZLFYdqzY093CAAAr/0pHiZ6XoRMREd0My44Vu7+FHxp4u6CgzIA1B3kZOhER0c2w7FgxpULCuKtzd77elQqTiZehExER/RPLjpUb2iEE7moVzl4qRvypi6LjEBERWRyWHSvnplZheEfzbuhf7U4VnIaIiMjysOzYgKeiG0IhATv/voRTFwpFxyEiIrIoFl12DAYDXn/9dYSFhcHZ2RmNGjXC22+/DZPJVPEYWZYxa9YsBAYGwtnZGb169UJKSorA1HUvxMsFMS0DAABfc3SHiIioEosuO3PmzMHnn3+O+fPn4/jx45g7dy7ef/99fPrppxWPmTt3LubNm4f58+cjISEBAQEB6NevHwoL7WuE45nu5svQfzqYhSvFesFpiIiILIdFl529e/fi0UcfxcCBA9GwYUMMHToUMTExOHDgAADzqM7HH3+MmTNnYsiQIYiIiMA333yDkpISrFixQnD6utWhQT1EBmmgM5iwcn+66DhEREQWw6LLTrdu3fDHH3/g1KlTAIDDhw9j165dePDBBwEAqampyMnJQUxMTMVz1Go1evbsiT179gjJLIokSXi6W0MA5v2y9AbT7Z9ARERkJ1SiA9zO9OnTodVq0aJFCyiVShiNRrz77rsYMWIEACAnJwcA4O/vX+l5/v7+SEtLu+Xr6nQ66HS6ip8LCgpqIX3dGxgZiLiNJ5BbqMPGI+cxqF2Q6EhERETCWfTIzqpVq7B8+XKsWLECBw8exDfffIMPPvgA33zzTaXHSZJU6WdZlm84dr24uDhoNJqKW0hISK3kr2uOKgXGdGkAwHwZuixzkUEiIiKLLjuvvPIKXn31VTzxxBOIjIzE6NGj8dJLLyEuLg4AEBBgvgLp2gjPNbm5uTeM9lxvxowZ0Gq1FbeMjIzaexN1bESnUKhVCiRnapGYlic6DhERkXAWXXZKSkqgUFSOqFQqKy49DwsLQ0BAALZu3Vpxv16vR3x8PKKjo2/5umq1Gh4eHpVutsLbTY3BV09fcZFBIiIiCy87Dz/8MN59911s2LAB586dw9q1azFv3jwMHjwYgPn0VWxsLGbPno21a9fi6NGjGDt2LFxcXDBy5EjB6cUZ19V8GfrmoznIzCsRnIaIiEgsi56g/Omnn+L//u//MGnSJOTm5iIwMBATJkzAG2+8UfGYadOmobS0FJMmTUJeXh46d+6MLVu2wN3dXWBysZoHuKNbEx/sOn0J3+w5h5kDW4qOREREJIwkcxYrCgoKoNFooNVqbeaU1rYTuRi3NAHuTirsndEHbmqL7rVERETVVtXvb4s+jUV3r2czXzTycUVhmQFrEjNFxyEiIhKGZcdGKRQSxnVtCMC8X5bJZPcDeEREZKdYdmzYkPbB8HBS4dzlEmw7mSs6DhERkRAsOzbMVa3CiE6hAHgZOhER2S+WHRs3JrohlAoJu09fxokc29gWg4iIqDpYdmxckKczHogwrzT91S6O7hARkf1h2bEDT19dZPDnpGxcKtLd4dFERES2hWXHDrQP9UTbEE/oDSZ8u+ec6DhERER1imXHDkiShIk9GwEAvtmbhmKdQXAiIiKiusOyYyf6tQxAmI8rtKXl+OGA7ezyTkREdCcsO3ZCqZAwvrt5dOeLnakoN5oEJyIiIqobLDt2ZEj7IPi4OSIrvxQbks+LjkNERFQnWHbsiJODEuOuXpn1efwZcA9YIiKyByw7dubJzg3g4qjEiZxC7Pj7kug4REREtY5lx85oXBwqtpBYFH9GcBoiIqLax7Jjh57uFgaVQsKeM5eRnJkvOg4REVGtYtmxQ0GeznikTSAAYNGOs4LTEBER1S6WHTv13NVFBjcdOY+0y8WC0xAREdUelh071SLAA72a+8Ikm9fdISIislUsO3ZsQo/GAIAfDmTgMjcIJSIiG8WyY8fua+SFNsEa6AwmfLM3TXQcIiKiWsGyY8ckScKEnubRnW/3nkOJnhuEEhGR7WHZsXP9WwWggbcL8kvK8UMCNwglIiLbw7Jj567fIHTJzlQYuEEoERHZGJYdwtCoYHi7Xt0g9Ag3CCUiItvCskNwclBibHRDAMCi+LPcIJSIiGwKyw4BAEZ3aQBnByWOnS/ArtPcIJSIiGwHyw4BADxdHPFEpxAAwOfcIJSIiGwIyw5VeKZbGJQKCbtPX8aRTK3oOERERDWCZYcqBNdzuW6DUI7uEBGRbWDZoUqe62G+DH3jkfNIv1wiOA0REdG9Y9mhSsLre6BnM/MGoUt2nhUdh4iI6J6x7NANJvQ0j+6sOpCB3IIywWmIiIjuDcsO3aBLI29ENagHvcHE0R0iIrJ6LDt0A0mS8ML9TQAAy/el43KRTnAiIiKiu8eyQzfVq5kvIoM0KC034qvdqaLjEBER3TWWHbqp60d3vtmTBm1JueBEREREd4dlh26pX7g/WgS4o0hnwNI950THISIiuissO3RLCoWEyb3Noztf7U5FYRlHd4iIyPqw7NBtPRhZH418XaEtLcfyfemi4xAREVUbyw7dllIhYXIv8+jOFzvPokRvEJyIiIioelh26I4ebRuIEC9nXC7WY+X+DNFxiIiIqoVlh+5IpVRg0tXRnUXxZ1BWbhSciIiIqOpYdqhKHmsfjPoaJ+QW6rD6AEd3iIjIerDsUJU4qhSY2LMxAODz+LPQG0yCExEREVUNyw5V2fCOIfB1VyMrvxRrD2WKjkNERFQlLDtUZU4OSjzX3bwj+oLtZ2AwcnSHiIgsH8sOVcuo+0JRz8UBaZdL8Gtytug4REREd8SyQ9Xi4qjCs1dHd+b/eRomkyw4ERER0e2x7FC1jenSAB5OKpy5WIxNR3NExyEiIrotlh2qNncnB4ztGgYA+PTPvyHLHN0hIiLLxbJDd+Xprg3h6qjEiZxC/H48V3QcIiKiW2LZobvi6eKIMdENAQDzObpDREQWjGWH7toz3cLg5KDA4Uwtdvx9SXQcIiKim2LZobvm46bGqM4NAACf/sHRHSIiskwsO3RPnuvRCI4qBQ6k5WHvmcui4xAREd2AZYfuib+HE57oGAIAmLf1FEd3iIjI4rDs0D2b3LsJ1FdHd+JPXRQdh4iIqBKWHbpn/h5OGNPFPHfnwy0c3SEiIsti8WUnKysLTz75JLy9veHi4oK2bdsiMTGx4n5ZljFr1iwEBgbC2dkZvXr1QkpKisDE9mliz8ZwcVTiSJYWW45dEB2HiIiogkWXnby8PHTt2hUODg7YtGkTjh07hg8//BCenp4Vj5k7dy7mzZuH+fPnIyEhAQEBAejXrx8KCwvFBbdD3m5qjOvaEAAwb8sp7plFREQWQ5It+JzDq6++it27d2Pnzp03vV+WZQQGBiI2NhbTp08HAOh0Ovj7+2POnDmYMGFClX5PQUEBNBoNtFotPDw8aiy/vdGWlKPb3D9RWGbApyPa4eE2gaIjERGRDavq97dFj+ysW7cOHTp0wLBhw+Dn54d27dphyZIlFfenpqYiJycHMTExFcfUajV69uyJPXv23PJ1dTodCgoKKt3o3mlcHDD+6o7oH/1+CgajSXAiIiIiCy87Z8+excKFC9G0aVP89ttvmDhxIv71r3/h22+/BQDk5Jh33Pb396/0PH9//4r7biYuLg4ajabiFhISUntvws6M69oQ9VwccPZiMX5OyhYdh4iIyLLLjslkQvv27TF79my0a9cOEyZMwPjx47Fw4cJKj5MkqdLPsizfcOx6M2bMgFarrbhlZGTUSn575O7kgIk9GwMA/vvHKegNHN0hIiKxLLrs1K9fHy1btqx0LDw8HOnp6QCAgIAAALhhFCc3N/eG0Z7rqdVqeHh4VLpRzRnTpSF83NTIuFKK1YkskkREJJZFl52uXbvi5MmTlY6dOnUKDRqY13QJCwtDQEAAtm7dWnG/Xq9HfHw8oqOj6zQr/Y+zoxKTe5tHdz794zTKyo2CExERkT2z6LLz0ksvYd++fZg9ezZOnz6NFStWYPHixZg8eTIA8+mr2NhYzJ49G2vXrsXRo0cxduxYuLi4YOTIkYLT27cRnUJRX+OEnIIyrNyfLjoOERHZMYsuOx07dsTatWuxcuVKRERE4J133sHHH3+MUaNGVTxm2rRpiI2NxaRJk9ChQwdkZWVhy5YtcHd3F5icnByUmHJ/UwDAZ9vOoERvEJyIiIjslUWvs1NXuM5O7Sg3mtDnw3ikXynBqwNaVExcJiIiqgk2sc4OWTcHpQIv9jGP7nwefwaFZeWCExERkT1i2aFaNahdEBr7uiK/pBxf7TonOg4REdkhlh2qVUqFhNi+zQAAX+w8i/wSveBERERkb1h2qNYNjKyPFgHuKNQZsGTnWdFxiIjIzrDsUK1TKCRM7Wce3fl69zlcKtIJTkRERPaEZYfqRL+W/mgdrEGJ3ojPt58RHYeIiOwIyw7VCUmS8HJMcwDAsn1puFBQJjgRERHZC5YdqjM9mvqgY8N60BlMmP/nadFxiIjITrDsUJ25fnRn5f50nLtULDgRERHZA5YdqlP3NfJGr+a+MJhkvP/byTs/gYiI6B6x7FCde3VAC0gSsOHIeRxKzxMdh4iIbBzLDtW5FgEeGNo+GAAQt/EEuD0bERHVJpYdEmJqTDOoVQrsP3cFvx/PFR2HiIhsGMsOCVFf44xnuoUBAN7bdBwGo0lwIiIislUsOyTMxF6NUc/FAWcuFuOHA5mi4xARUS3YfjIXL/9wGDlaceurseyQMB5ODvhXn6YAgI9+P4USvUFwIiIiqkkGownvbjiONQcz8fWeVGE5WHZIqFGdGyDUywUXC3X4Yqe4/xCIiKjmrTqQgb9zi+Dp4oBJvZoIy1HlspOZydMMVPMcVQq80t+80OCi+DO4WMhNQomIbEGRzoCPtp4CALzYpyk0zg7CslS57ERERGDZsmW1mYXs1MDI+mgTrEGx3ohP/vhbdBwiIqoBn28/g0tFeoT5uGJU5wZCs1S57MyePRuTJ0/GY489hsuXL9dmJrIzCoWEVweEAwBW7E/HmYtFghMREdG9yM4vxZKdZwGYF5J1VImdNVPl3z5p0iQcPnwYeXl5aNWqFdatW1ebucjOdGnsjT4t/GA0yXh/M7eRICKyZh/8dhI6gwmdwrwQ09JfdByoqvPgsLAw/Pnnn5g/fz4ee+wxhIeHQ6Wq/BIHDx6s0YBkP6YPaIFtJ3OxOSUHiWlXENXAS3QkIiKqpiOZWvx0KAsA8PrAcEiSJDhRNcsOAKSlpWHNmjXw8vLCo48+ekPZIbpbzfzd8XiHEHyfkIHZG0/gx4ldLOI/EiIiqhpZlvGfDccAAIPbBaF1sKfYQFdVq6ksWbIEL7/8Mvr27YujR4/C19e3tnKRnXqpXzP8nJSFxLQ8/JZyAQ9EBIiOREREVbT12AX8lXoF6uuutLUEVZ6z88ADD2D69OmYP38+fvrpJxYdqhX+Hk4Y370RAGDu5hMo5zYSRERWodxownubTgAAnu0ehkBPZ8GJ/qfKZcdoNCI5ORljxoypzTxEeK5HI3i7OuLspWJ8n5AhOg4REVXBd/vScPZSMXzcHPG8wAUEb6bKZWfr1q0IDg6uzSxEAAB3Jwe82Ne8jcR/fz+FIh23kSAismTa0nL89+o6abF9m8FNbVnzebldBFmkEZ1CEebjiktFeizecVZ0HCIiuo3Ptp1GXkk5mvq54YmOIaLj3IBlhyySg1KBaVcnty3ZcRa5BeJ2yyUiolvLuFKCpbvPAQBeezAcKqXlVQvLS0R01QMRAWgX6onSciPe/40LDRIRWaI5m09AbzShWxMf9GpumRcvseyQxZIkCf/3UEsAwOrETCRl5IsNRERElRxMz8P65POQJPOojqWujcayQxatfWg9DGkXBACYtS4FJpMsOBEREQFXFxBcb15AcFhUMFoGeghOdGssO2Txpg9oARdHJZIy8rH26hLkREQk1sYjOTiYng9nByVejrGcBQRvhmWHLJ6/hxOm3G++FP29zSd4KToRkWA6gxHvbT4OAJjQsxH8PZwEJ7o9lh2yCk93a4iG3i64WKjD/D9Pi45DRGTXvt2ThowrpfBzV+O5Ho1Ex7kjlh2yCmqVEq8PNE9W/mpXKlIvFQtORERkn/KK9fj0T/MCgv+OaQ4XR8taQPBmWHbIavQJ90OPZr7QG00Vk+KIiKhuvb/lJArKDAiv74HHoqxjZwWWHbIakiThjYdaQqWQ8MeJXGw/mSs6EhGRXUnOzMfK/ekAgLceaQWlwjIvNf8nlh2yKk383DA2uiEA4O31x6A3cFd0IqK6YDLJeOOXFMgyMKhtIDqFeYmOVGUsO2R1/tW3KXzcHHH2YjG+3XtOdBwiIrvw49XFXV0dlXjtwXDRcaqFZYesjoeTA165um/Wf3//GxcLdYITERHZNm1JOeZsPgHAvKu5n4Vfav5PLDtklYZFhSAySINCnQEfcN8sIqJaNW/rSVwu1punEnRtKDpOtbHskFVSKCTMesR8KfoPiRlIzswXG4iIyEalZGuxbF8aAODtR1rBwQJ3Nb8T60tMdFVUAy8MbhcEWTbvmyXL3DeLiKgmybKMN39JgUkGBrauj+gmPqIj3RWWHbJqr17dN+tgej5+TuK+WURENWntoSwcSMuDs4MSM61sUvL1WHbIqvl7OGFy7yYAgPc2nUAx980iIqoRhWXlmL3RPCl5Sp8mCPR0Fpzo7rHskNV7plsYQr1ccKFAh8+2cd8sIqKa8PHvf+NSkQ5hPq54pluY6Dj3hGWHrJ6TgxKvDzQPr36xMxVpl7lvFhHRvTh1oRBL95wDAMx6pBXUKqXYQPeIZYdsQr+W/uje1Ad6ownvrD8uOg4RkdWSZRlv/HIURpOM/q380bOZr+hI94xlh2yCJEl482Hzvlm/H7+ArccuiI5ERGSV1iefx76zV6BWKfD6wJai49QIlh2yGU383PFs90YAgDd/OcrJykRE1VSsM+DdDebR8cm9myDEy0VwoprBskM25cU+TRFczxnZ2jJ8tPWU6DhERFbl0z9PI6egDKFeLniuRyPRcWoMyw7ZFGdHJd4ZFAEA+Gp3Ko5maQUnIiKyDmcuFuHLXWcBAG8+3BJODtY9Kfl6LDtkc3o398PA1vVhkoGZa4/AaOLKykREtyPLMmatS0G5Ucb9LfzQJ9xfdKQaxbJDNunNh1rCXa3C4Uwtll/d04WIiG7ut5Qc7Pz7EhyVCrz5sG1MSr4eyw7ZJD8PJ0wb0AIA8P5vJ5GjLROciIjIMhXpDHjr12MAgAk9G6GBt6vgRDWPZYds1qhOoWgb4okinQFvr08RHYeIyCK9v/kEzmvNk5In9WoiOk6tYNkhm6VQSJg9OBJKhYSNR3Lwx3GuvUNEdL3EtDx8e/VU/+zBkXB2tJ1Jyddj2SGb1jLQA89e3dPljV9SUKLn2jtERACgN5jw6ppkyDIwNCoY3Zr6iI5Ua6yq7MTFxUGSJMTGxlYck2UZs2bNQmBgIJydndGrVy+kpPCUBf3Pi32bIsjTGVn5pfjv73+LjkNEZBEWbj+Dv3OL4O3qiJkPhouOU6uspuwkJCRg8eLFaN26daXjc+fOxbx58zB//nwkJCQgICAA/fr1Q2FhoaCkZGlcHFV4+9FWAIAvdqXiWHaB4ERERGKdzi3EZ9tOAwDefKQV6rk6Ck5Uu6yi7BQVFWHUqFFYsmQJ6tWrV3FclmV8/PHHmDlzJoYMGYKIiAh88803KCkpwYoVKwQmJkvTJ9wfD0YGwGiS8RrX3iEiO2YyyXh1zRHojSb0bu6Lh1vXFx2p1llF2Zk8eTIGDhyIvn37VjqempqKnJwcxMTEVBxTq9Xo2bMn9uzZc8vX0+l0KCgoqHQj2/fmw63gplYhKSMfK/ani45DRCTEiv3pOJCWBxdHJf4zOBKSJImOVOssvux8//33SExMRFxc3A335eTkAAD8/Suv9Ojv719x383ExcVBo9FU3EJCQmo2NFkkfw8nvNK/OQBg7qYTyC3g2jtEZF9ytGV4b9MJAMC0/s0R5OksOFHdsOiyk5GRgRdffBHfffcdnJycbvm4f7ZSWZZv21RnzJgBrVZbccvIyKixzGTZnryvAdoEa1CoM+Ct9cdExyEiqjOyLOP/fjmKIp0BbUM8MbpLQ9GR6oxFl53ExETk5uYiKioKKpUKKpUK8fHx+OSTT6BSqSpGdP45ipObm3vDaM/11Go1PDw8Kt3IPigVEt4dHAmFBGxIPo9tJ3NFRyIiqhObj+Zg67ELUCkkzHmsNZQK2z99dY1Fl50+ffrgyJEjSEpKqrh16NABo0aNQlJSEho1aoSAgABs3bq14jl6vR7x8fGIjo4WmJwsWUSQBk93Na+9838/H0Wp3ig4ERFR7dKWluONdeZlWZ7v1RjNA9wFJ6pbKtEBbsfd3R0RERGVjrm6usLb27vieGxsLGbPno2mTZuiadOmmD17NlxcXDBy5EgRkclKvNSvGTYeOY/MvFLM23oSMwfa3sZ3RETXvLfpOC4W6tDI1xWTe9vmlhC3Y9EjO1Uxbdo0xMbGYtKkSejQoQOysrKwZcsWuLvbV2ul6nFVq/DOIHNh/mJXKhLTrghORERUO/advYyV+81zU98b0hpODra5JcTtSLIs2/2CIwUFBdBoNNBqtZy/Y2de/uEw1hzMRJiPKzb+q7vN7gtDRPaprNyIAf/didRLxRjZORSzB0eKjlSjqvr9bfUjO0T34o2HW8LfQ43US8X4YMtJ0XGIiGrUp3/+jdRLxfBzV+PVAS1ExxGGZYfsmsbZAe89Zt6C5KvdqdifytNZRGQbjp8vwKL4swCAtx+NgIeTg+BE4rDskN3r3dwPj3cIhiwDr/x4mDujE5HVM5pkvLomGQaTjAdaBeCBiADRkYRi2SEC8PpDLVFf44S0yyWYu5mns4jIun256ywOZ2rh7qTCW1c3QrZnLDtEADycHDDn6umspXvOYe+Zy4ITERHdnZM5hfjgt1MAgNcHhsPf49Y7ENgLlh2iq3o088WITqEAzKezinU8nUVE1kVvMCF2VRL0RhP6tPDD4x249yPAskNUycyB4QjydEZmXiniNh0XHYeIqFr++8cpHD9fgHouDoh7zD52NK8Klh2i67ipVZg71Hw6a/m+dOw+fUlwIiKiqklMy8PC7WcAALMHR8LPnaevrmHZIfqHrk188OR95tNZ035MRmFZueBERES3V6I34OUfkmCSgSHtgjAgsr7oSBaFZYfoJmYMCEdwPWdk5Zdi9sYTouMQEd3W7I3Hce5yCeprnPDmI7z66p9YdohuwlWtwvtD2wAAVu5Px45TFwUnIiK6ufhTF7F8XzoA4INhbaBxtt/FA2+FZYfoFro09sbY6IYAgOlrklHA01lEZGHyS/R4ZfVhAMDY6Ibo2sRHcCLLxLJDdBvTHmiOBt4uOK8tw3/WHxMdh4iokv/7JQW5hTo08nXF9Afsd++rO2HZIboNF0fz6SxJAn44kIltJ3NFRyIiAgCsO5yNXw9nQ6mQ8NHjbeHsqBQdyWKx7BDdQacwL4yLDgMAvLomGXnFesGJiMje5WjL8H8/HwUAvNC7CdqEeIoNZOFYdoiq4JX+zdHIxxUXCnSYviYZsiyLjkREdkqWZUxbkwxtaTkigzR44f4moiNZPJYdoipwdlTikxHt4KCUsOXYBSz/K110JCKyU9/9Zb5C1FGlwEfD28BBya/yO+EnRFRFEUGaigmA76w/hhM5BYITEZG9Sb1UjHc3mLeymf5ACzTxcxecyDqw7BBVw9Ndw9CruS/0BhP+tfIQSvVG0ZGIyE4YjCa8/EMSSsuN6NLIG+OuLo1Bd8ayQ1QNCoWED4a1gY+bGqcuFOE/G3g5OhHVjUU7zuJgej7c1Sp88HgbKBTc5LOqWHaIqsnHTY2PhptXV/7ur3RsPnpecCIisnUH0/Pw0dZTAIA3H2mFIE9nwYmsC8sO0V3o3tQXE3o2AgBMX3ME2fmlghMRka3KL9FjyopDMJhkDGxdH4+1DxIdyeqw7BDdpZf7NUebYA20peWI/T4JRhMvRyeimiXLMv69OhlZ+aVo4O2C94ZEQpJ4+qq6WHaI7pKjSoFPRrSDm1qF/eeuYP6fp0VHIiIb8+WuVPx+/AIclQp8NrI93J24yefdYNkhugcNvF3xn0ERAID//nEKCeeuCE5ERLYiKSMfczafAAC8/lA4IoI0ghNZL5Ydons0qF0QhrQPgkkGXlx5CNoS7o5ORPdGW1qOF1YcRLlRxoORARh9XwPRkawayw5RDXj70Qg09HZBtrYMr/7E7SSI6O7JsoxpPx5GZl4pQryc8d5jrTlP5x6x7BDVADe1Cp+OaA8HpYRNR3Owcn+G6EhEZKW+2XMOv6VcgINSwmcj28OD83TuGcsOUQ2JDNZgWn/zdhJv/ZqCUxcKBSciImtzJFOL2RvN83RmDAhH62BPsYFsBMsOUQ16plsYejTzhe7qdhJl5dxOgoiqpqCsHJNXHITeaEJMS3+M69pQdCSbwbJDVIMUCgkfDmsDHzdHnMgpxNvruZ0EEd2ZLMt4dU0y0q+UILieM94f2obzdGoQyw5RDfN1V2Pe420hScCKv9LxQwLn7xDR7S3fl4aNR3KgUkj4dEQ7aFw4T6cmsewQ1YIezXwxtW8zAMDrvxxFcma+2EBEZLGOZmnxzvrjAIBXB7RAu9B6ghPZHpYdoloyuXcT9A33h95gwsRlibhUpBMdiYgsTGGZeT0dvdGEvuF+eKZbmOhINollh6iWKBQS5g1vg0Y+rsjWlpk38jOaRMciIgshyzJeW3sU5y6XIFDjhA+GcZ5ObWHZIapFHk4OWDQ6Cq6OSuw9e7li6XciouX70vDr4WzzPJ2R7eHp4ig6ks1i2SGqZU393fHBsDYAgCU7U7HucLbgREQk2r6zl/HWr+arNac90BxRDThPpzax7BDVgQGR9fF8r8YAgOk/JuNEToHgREQkSsaVEkz67iAMJhmPtAnE+O6NREeyeSw7RHXk3zHN0b2pD0rLjZiwLJEbhhLZoWKdAeO/PYArxXpEBHlgDve9qhMsO0R1RKmQ8MkT7RDk6Yy0yyWIXXUIJhM3DCWyF7Is49+rD+NETiF83NRYPLoDnB2VomPZBZYdojpUz9URi0ZHQa1SYNvJi/j4j79FRyKiOvLpn6ex6WgOHJQSPn+yPQI9nUVHshssO0R1LCJIg7ghkQCAT/74G1uPXRCciIhq228pOZi39RQA4D+DItChoZfgRPaFZYdIgCHtgzE2uiEAYOqqJJy9WCQ2EBHVmpM5hZi6KgkAMDa6IYZ3DBUbyA6x7BAJMnNgODo2rIdCnQETliWiSGcQHYmIalhesR7PfpuAYr0R0Y29MXNguOhIdollh0gQB6UCn41qDz93Nf7OLcK0Hw9DljlhmchWlBtNmLziIDKulCLEyxmfjWwPByW/dkXgp04kkJ+7ExY+GQUHpYSNR3Lw0dVz+kRk/d7dcBx7zlyGi6MSS8Z0QD1XrpAsCssOkWBRDerh3UFXJyz/eRo/HMgQnIiI7tUPCRlYuuccAGDe423RIsBDbCA7x7JDZAEe7xiCF3o3AQC89tMR7Pr7kuBERHS3EtOuYObPRwAAL/VthgciAgQnIpYdIgvxckwzPNo2EAaTjOeXJ3JLCSIrlJ1fignLDqLcKGNARACm3N9EdCQCyw6RxZAkCXOHtkbnMC8U6gx4+usEXCgoEx2LiKqo+OqVlZeKdGgRYN4AWKHgVhCWgGWHyIKoVUosHt0BjX1dka0tw7ivE3hJOpEVKDeaMOm7gziSpYWXqyOWjOkAV7VKdCy6imWHyMJoXBywdFwn+Lg54tj5AkxZcRAGo0l0LCK6BVmWMX1NMuJPXYSzgxJfPtUBIV4uomPRdVh2iCxQiJcLvniqI5wczHtovbEuhWvwEFmoub+dxE8Hs6BUSPhsVDu0C60nOhL9A8sOkYVqG+KJT55oB0kCVvyVjkU7zoqORET/8PXuVCzcfgYAEDckEve38BeciG6GZYfIgsW0CsAbD7UEALy36QR+PZwtOBERXbM+ORtvrz8GAHilf3M83iFEcCK6FZYdIgs3rmsYxnVtCAB4efVhJJy7IjYQEWHPmUuYuuowZBl4qksDTOrVWHQkug2WHSIr8PrAlujfyh96gwnjvz3AXdKJBErJ1uK5bxOhN5rwYGQA3ni4FSSJl5hbMpYdIiugVEj4eHg7tAnxRH5JOcYtTcDlIp3oWER2J+NKCcZeXRKic5gX5j3eFkqupWPxWHaIrISz47VLWp2RdrkETy9NQGFZuehYRHbjSrEeT321HxcLzYsGLh7TAU4OStGxqAosuuzExcWhY8eOcHd3h5+fHwYNGoSTJ09Weowsy5g1axYCAwPh7OyMXr16ISUlRVBiotrl46bG12M7oZ6LAw5navH00gSU6LnoIFFtK9Eb8PTSBJy9VIwgT2csHdcJGmcH0bGoiiy67MTHx2Py5MnYt28ftm7dCoPBgJiYGBQXF1c8Zu7cuZg3bx7mz5+PhIQEBAQEoF+/figsLBSYnKj2NPFzw7JnOsPdSYWEc3l49psDKCs3io5FZLPKjSZM/u4gkjLy4enigG+e7ogAjZPoWFQNkmxFK5VdvHgRfn5+iI+PR48ePSDLMgIDAxEbG4vp06cDAHQ6Hfz9/TFnzhxMmDChSq9bUFAAjUYDrVYLDw+P2nwLRDXmYHoeRn/xF4r1RvRq7otFo6OgVnFInagmybKMaT8mY3ViJpwcFPju2fsQ1YCLBlqKqn5/W/TIzj9ptVoAgJeXFwAgNTUVOTk5iImJqXiMWq1Gz549sWfPnlu+jk6nQ0FBQaUbkbVpH1oPX401r7K8/eRF/GvlIZRzWwmiGiPLMuI2ncDqxEwoJGD+iPYsOlbKasqOLMuYOnUqunXrhoiICABATk4OAMDfv/KKlf7+/hX33UxcXBw0Gk3FLSSEC0GRdercyBtfjOkIR5UCv6VcwNQfDsNosprBWiKLJcsy3tt0Aouvrlw+e3Ak+rbk6sjWymrKzgsvvIDk5GSsXLnyhvv+ub6BLMu3XfNgxowZ0Gq1FbeMjIwaz0tUV7o19cHnT7aHg1LCr4ezMX1NMkwsPER37VrRubZFyzuPtsITnUIFp6J7YRVlZ8qUKVi3bh22bduG4ODgiuMBAQEAcMMoTm5u7g2jPddTq9Xw8PCodCOyZve38McnT7SDUiHhx8RMvLHuKDcOJboLNys6o7s0FBuK7plFlx1ZlvHCCy/gp59+wp9//omwsLBK94eFhSEgIABbt26tOKbX6xEfH4/o6Oi6jksk1IDI+pj3eBtIErB8Xzr+s+E4Cw9RNbDo2C6V6AC3M3nyZKxYsQK//PIL3N3dK0ZwNBoNnJ2dIUkSYmNjMXv2bDRt2hRNmzbF7Nmz4eLigpEjRwpOT1T3Hm0bBF25CdPWJOPLXalwclDglf4tRMcisngsOrbNosvOwoULAQC9evWqdPzrr7/G2LFjAQDTpk1DaWkpJk2ahLy8PHTu3BlbtmyBu7t7HaclsgyPdwxBmcGIN35JwWfbzsBJpcSUPk1FxyKyWCw6ts+q1tmpLVxnh2zRkh1n8e7G4wCAmQ+GY3yPRoITEVkeFh3rZpPr7BBR1Y3v0QhT+zUDALy78Tg+jz8jOBGRZWHRsR8sO0Q2bMr9TTDl/iYAgPc2nUDcRk5aJgJYdOwNyw6RDZMkCS/HNMeMAeZJyot2nMWra47AwJWWyY6x6Ngflh0iOzChZ2PMfaw1FBKw6kAGXlhxiJuHkl26tgUEi459YdkhshOPdwzBglFRcFQqsDklB08vTUCRziA6FlGdKTeaMO3H5IotIFh07AfLDpEdeSAiAEvHdYSroxJ7zlzGyCX7cKVYLzoWUa0r1hnw7DcHKjb1fG9IJIuOHWHZIbIz0U18sGL8fajn4oDkTC2Gfb4H2fmlomMR1ZqLhTo8sXgf4k9dhJODAkvGdOBeV3aGZYfIDrUJ8cTqidGor3HCmYvFGLpwD85cLBIdi6jGnblYhCELd+NIlhZero74/rku6BPO3cvtDcsOkZ1q4ueGH5+PRiNfV2RryzDs8704kqkVHYuoxiSm5WHowj3IuFKKBt4u+On5aLQN8RQdiwRg2SGyY0Gezlg9oQsigzS4UqzHiCX7sOfMJdGxiO7Zbyk5GLlkH/JKytEmWIM1z0ejoY+r6FgkCMsOkZ3zdlNjxfjOuK+RF4p0Boz9KgGbj+aIjkV015btPYfnlydCZzChTws/rHzuPvi4qUXHIoFYdogI7k4OWDquE/q19IfeaMLz3yVi/p9/c7VlsiqyLGPO5hP4v19SYJKBEZ1CsWh0FFwcLXrPa6oDLDtEBABwclBi4aj2ePK+UMgy8MGWU3hhxSGU6LkWD1k+vcGEqT8cxsLt5j3gXu7XDLMHR0Cl5NccsewQ0XVUSgX+MygSswdHwkEpYcOR8xiyYA8yrpSIjkZ0S4Vl5Xh6aQLWHsqCUiFh7tDWmNKnKSRJEh2NLATLDhHdYGTnUKwYfx983BxxIqcQj8zfxYnLZJFO5xZi8II92HX6ElwclfhqbEc83iFEdCyyMCw7RHRTHRt6Yd0L3RAZpEFeSTlGf7kfS3ench4PWYxfD2fjkfm7cTq3CP4eaqx6rgt6NvMVHYssEMsOEd1SoKczVk/sgkFtA2E0yZj16zFMX5MMnYGbiJI4eoMJb/2agikrD6FEb0SXRt7Y8K/uiAzWiI5GFoplh4huy8lBiY+Gt8VrD7aAQgJ+OJCJEYv3IbegTHQ0skM52jKMWLIPX+8+BwCY1Ksxlj3TiZeW022x7BDRHUmShOd6NMbX4zrBw0mFg+n5eHj+LiRl5IuORnZkz+lLGPjJTiSm5cHdSYUlYzpg2gMteMUV3RH/DSGiKuvZzBfrXuiGpn5uuFCgw+OL9mJNYqboWGTjTCYZC7afxpNf/oXLxXqE1/fA+ind0K8l97iiqmHZIaJqaejjirWTu5oXIDSY8PLqw5j+YzKKdVyPh2qetrQczy1LxNzNJ2GSgaFRwVg7KRoNvLn1A1Udyw4RVZubWoVFT0bhX32aQpKAVQcyMOC/5tMLRDUlJVuLhz/dhd+PX4CjSoH3hkTi/aGt4eSgFB2NrAzLDhHdFYVCwtR+zbBy/H0I8nRG+pUSDPt8Dz7cchLlRpPoeGTFZFnGDwcyMGTBHqRfKUFwPWesmRiNJzqFcqFAuiuSzEUzUFBQAI1GA61WCw8PD9FxiKxOQVk5Zv2Sgp8OZQEAIoM0+Gh4WzTxcxOcjKzNxUId/u/no9icYt6MtndzX3w0vC08XRwFJyNLVNXvb5YdsOwQ1ZQNyecx8+cjyC8ph1qlwGsPhmNMlwb80zjdkSzL+CUpG7N+TUF+STlUCgmxfZtiUq8mUCj47w/dHMtONbDsENWcCwVl+Pfqw9j5t3l7iR7NfPH+0Nbw93ASnIws1YWCMsxcewS/H88FALQK9MDcoa3RKpCLBNLtsexUA8sOUc2SZRnf7k3D7I3HoTOY4OnigLjBkRgQWV90NLIgsixjdWIm3ll/DIVlBjgoJbzYpykm9GwMB66dQ1XAslMNLDtEteN0biFiVyXhaFYBAGBI+yDMeqQVPJwcBCcj0bLzSzHjpyOIP3URANA6WIP3h7ZB8wB3wcnImrDsVAPLDlHt0RtM+OSPv7Fg+2mYZKC+xgmvPRiOh1rX51weOyTLMr5PyMC7G46jSGeAo0qBl/o2w/juYVwJmaqNZacaWHaIat+Bc1cw9YfDSL9SAgDoFOaFWQ+3QstA/jdnLzKulGDGT0ew67R5Ple7UE+8P7QNr9qju8ayUw0sO0R1o6zciMU7zmLB9tMoKzdBIQEjO4fi5X7NUc+VlxbbKr3BhGX70vDhlpMo0Rvh5KDAv2OaY1zXMCh5pRXdA5adamDZIapbWfmlmL3xODYknwcAaJwd8O+YZhjRKZSnMmyILMvYcOQ85m4++b8RvYZemDO0NcJ8uN0D3TuWnWpg2SESY9/Zy5i1LgUncgoBAC0C3PHmw63QpbG34GR0r/advYy4jcdxOFMLAPB1V2Nqv2YY3iGE6+ZQjWHZqQaWHSJxDEYTViZk4MMtJ5FfUg4AGBhZH68NDEeQp7PgdFRdpy4UYs6mE/jjhHnNHFdHJSb0bIxnu4fBxVElOB3ZGpadamDZIRIvr1iPeVtP4bu/0mCSAScHBSb2bIznejTil6QVuFBQho+2nsIPBzJgkgGlQsLITqH4V5+m8HVXi45HNoplpxpYdogsx/HzBZi1LgV/pV4BANRzccC4rmEY06UB90eyQIVl5Vi84yyW7DyLsnLzBrAPtArAKw80R2NfXmVFtYtlpxpYdogsy80mtro6KjGycyie7d6IW09YgLJyI344kIH//v43LhfrAQDtQz3x2oPh6NDQS3A6shcsO9XAskNkmQxGEzYezcHC7Wdw/Lx5FWZHpQKPRQXhuR6NeUWPABcKyrB8XxpW/JVeUXLCfFwx/YHm6N8qgAtFUp1i2akGlh0iyybLMrafvIgF208j4VweAEAhAQMi6+P5no0REcQNI2tbUkY+vt6dig3J52Ewmb82AjVOmNirMUZ0CuVeViQEy041sOwQWY+Ec1ewcPsZ/Hn1ah8A6NnMF8/3aozOYV4cWahB5UYTNh3Nwde7U3EoPb/ieIcG9TCuaxj6t/LnukgkFMtONbDsEFmf4+cLsHD7GaxPzsbVgQa0CfHE0PZBGNg6EF5ckfmuXSnWY+X+dCzbm4acgjIAgINSwsOtAzGuaxgigzmSRpaBZacaWHaIrFf65RIs2nEGqxMzoTeYrwZSKST0au6LR9sGoV9Lfzg5KAWntHyyLONoVgG++ysNaw9lQXf1s/Rxc8Sozg0w6r5Q+LlzYjhZFpadamDZIbJ+Fwt1+CUpCz8nZeFoVkHFcTe1Cg9EBGBQ2yB0aezNvZiuYzLJOJieh81Hc7A5JQeZeaUV90UEeWBcdBgealMfahXLIlkmlp1qYNkhsi2ncwvx86Fs/JyUVekL3M9djUfbBuLRtkFoFehhl/N7yo0m7Dt7GZuP5mDLsQu4WKiruM/JQYE+4f4YG90QHRrUs8vPh6wLy041sOwQ2SZZlpGYloe1h7KwPvk8tKXlFfc19XPD/eF+uC/MGx0a1oO7k4PApLWrrNyInX9fwuajOfj9+IVKn4O7kwp9w/3Rv1UAejbzhbMjR3HIerDsVAPLDpHt0xtM2H4yFz8nZeH347kV83sA82XsrQI16BzmhU5Xb9a8WnNZuRHHzhcgOSMf+89dwfaTF1GiN1bc7+PmiH4tA/BARAC6NPKGo4pXVJF1YtmpBpYdIvtSUFaO349dwN4zl/FX6pWKVZqvkSSgub877mvkjc5hXugY5gUfN8vc38lgNOHUhSIkZ+bjcKYWyZn5OJlTWLEWzjVBns7o38pccKIa1OPcJbIJLDvVwLJDZN/Oa0uxP/UK9p29gr9SL+PsxeIbHhPm44oG3i4I9TLfQq77q5u69jcqNZlk5JXokVuow6kLhTicocXhzHykZGsr9qS6no+bI1oHe6JNsCd6t/BFZJCGc3DI5rDsVAPLDhFdL7ewDAmpefgr9TL+OnsFJy8U3vbxXq6OFeUn1MsZIfVc4OHsAJVCgoNSAaVCgkpp/vtrx1RKCSqFBJVCAZMs43KxHhcLdZVvRea/5haW4VKRHkbTzf937a5WITJYc7XcaNA6xBOBGieWG7J5LDvVwLJDRLdzpViPY9kFyMgrQcaVEqRf+d9f80rK7/wCNcjb1RGh3i5oE+yJ1sEatAnxRJi3KxQ8LUV2qKrf37U/9kpEZOW8XB3RranPTe8rKCtHxpUSZFwp/V8RyitBic6IcpMJBqOMcqMJBpMMQ8VfZRhMJpQbzccAwNtNDT93NXyv3dzU8PO49vdO8HVXw9vNkXtQEd0Flh0ionvg4eSAVoEatArkFgpElop/RCAiIiKbxrJDRERENo1lh4iIiGwayw4RERHZNJYdIiIismksO0RERGTTbKbsLFiwAGFhYXByckJUVBR27twpOhIRERFZAJsoO6tWrUJsbCxmzpyJQ4cOoXv37hgwYADS09NFRyMiIiLBbGK7iM6dO6N9+/ZYuHBhxbHw8HAMGjQIcXFxd3w+t4sgIiKyPlX9/rb6kR29Xo/ExETExMRUOh4TE4M9e/YISkVERESWwuq3i7h06RKMRiP8/f0rHff390dOTs5Nn6PT6aDT6Sp+LigoqNWMREREJI7Vj+xcI0mVd/yVZfmGY9fExcVBo9FU3EJCQuoiIhEREQlg9WXHx8cHSqXyhlGc3NzcG0Z7rpkxYwa0Wm3FLSMjoy6iEhERkQBWX3YcHR0RFRWFrVu3Vjq+detWREdH3/Q5arUaHh4elW5ERERkm6x+zg4ATJ06FaNHj0aHDh3QpUsXLF68GOnp6Zg4cWKVnn/tgjTO3SEiIrIe176373RhuU2UneHDh+Py5ct4++23cf78eURERGDjxo1o0KBBlZ5fWFgIAJy7Q0REZIUKCwuh0Whueb9NrLNzr0wmE7Kzs+Hu7n7LSc32pqCgACEhIcjIyOBpvjrAz7vu8TOvW/y86549fOayLKOwsBCBgYFQKG49M8cmRnbulUKhQHBwsOgYFolzmuoWP++6x8+8bvHzrnu2/pnfbkTnGqufoExERER0Oyw7REREZNNYduim1Go13nzzTajVatFR7AI/77rHz7xu8fOue/zM/4cTlImIiMimcWSHiIiIbBrLDhEREdk0lh0iIiKyaSw7VGU6nQ5t27aFJElISkoSHccmnTt3Ds888wzCwsLg7OyMxo0b480334RerxcdzaYsWLAAYWFhcHJyQlRUFHbu3Ck6ks2Ki4tDx44d4e7uDj8/PwwaNAgnT54UHctuxMXFQZIkxMbGio4iFMsOVdm0adMQGBgoOoZNO3HiBEwmExYtWoSUlBR89NFH+Pzzz/Haa6+JjmYzVq1ahdjYWMycOROHDh1C9+7dMWDAAKSnp4uOZpPi4+MxefJk7Nu3D1u3boXBYEBMTAyKi4tFR7N5CQkJWLx4MVq3bi06inC8GouqZNOmTZg6dSrWrFmDVq1a4dChQ2jbtq3oWHbh/fffx8KFC3H27FnRUWxC586d0b59eyxcuLDiWHh4OAYNGoS4uDiByezDxYsX4efnh/j4ePTo0UN0HJtVVFSE9u3bY8GCBfjPf/6Dtm3b4uOPPxYdSxiO7NAdXbhwAePHj8eyZcvg4uIiOo7d0Wq18PLyEh3DJuj1eiQmJiImJqbS8ZiYGOzZs0dQKvui1WoBgP9O17LJkydj4MCB6Nu3r+goFoF7Y9FtybKMsWPHYuLEiejQoQPOnTsnOpJdOXPmDD799FN8+OGHoqPYhEuXLsFoNMLf37/ScX9/f+Tk5AhKZT9kWcbUqVPRrVs3REREiI5js77//nskJibiwIEDoqNYDI7s2KlZs2ZBkqTb3g4cOIBPP/0UBQUFmDFjhujIVq2qn/f1srOz8cADD2DYsGF49tlnBSW3TZIkVfpZluUbjlHNe+GFF5CcnIyVK1eKjmKzMjIy8OKLL+K7776Dk5OT6DgWg3N27NSlS5dw6dKl2z6mYcOGeOKJJ/Drr79W+iIwGo1QKpUYNWoUvvnmm9qOahOq+nlf+59TdnY2evfujc6dO2Pp0qVQKPjnkpqg1+vh4uKC1atXY/DgwRXHX3zxRSQlJSE+Pl5gOts2ZcoU/Pzzz9ixYwfCwsJEx7FZP//8MwYPHgylUllxzGg0QpIkKBQK6HS6SvfZC5Yduq309HQUFBRU/JydnY3+/fvjxx9/ROfOnREcHCwwnW3KyspC7969ERUVheXLl9vl/5hqU+fOnREVFYUFCxZUHGvZsiUeffRRTlCuBbIsY8qUKVi7di22b9+Opk2bio5k0woLC5GWllbp2Lhx49CiRQtMnz7dbk8fcs4O3VZoaGiln93c3AAAjRs3ZtGpBdnZ2ejVqxdCQ0PxwQcf4OLFixX3BQQECExmO6ZOnYrRo0ejQ4cO6NKlCxYvXoz09HRMnDhRdDSbNHnyZKxYsQK//PIL3N3dK+ZGaTQaODs7C05ne9zd3W8oNK6urvD29rbbogOw7BBZlC1btuD06dM4ffr0DWWSg7A1Y/jw4bh8+TLefvttnD9/HhEREdi4cSMaNGggOppNunaJf69evSod//rrrzF27Ni6D0R2iaexiIiIyKZx1iMRERHZNJYdIiIismksO0RERGTTWHaIiIjIprHsEBERkU1j2SEiIiKbxrJDRERENo1lh4iIiGwayw4RERHZNJYdIrI5RqMR0dHReOyxxyod12q1CAkJweuvvy4oGRGJwO0iiMgm/f3332jbti0WL16MUaNGAQDGjBmDw4cPIyEhAY6OjoITElFdYdkhIpv1ySefYNasWTh69CgSEhIwbNgw7N+/H23bthUdjYjqEMsOEdksWZZx//33Q6lU4siRI5gyZQpPYRHZIZYdIrJpJ06cQHh4OCIjI3Hw4EGoVCrRkYiojnGCMhHZtK+++gouLi5ITU1FZmam6DhEJABHdojIZu3duxc9evTApk2bMHfuXBiNRvz++++QJEl0NCKqQxzZISKbVFpaiqeeegoTJkxA37598cUXXyAhIQGLFi0SHY2I6hjLDhHZpFdffRUmkwlz5swBAISGhuLDDz/EK6+8gnPnzokNR0R1iqexiMjmxMfHo0+fPti+fTu6detW6b7+/fvDYDDwdBaRHWHZISIiIpvG01hERERk01h2iIiIyKax7BAREZFNY9khIiIim8ayQ0RERDaNZYeIiIhsGssOERER2TSWHSIiIrJpLDtERERk01h2iIiIyKax7BAREZFNY9khIiIim/b/WiVzFVS61xMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xs, ys)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('$f(x)=3x^2-4x+5$')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6421075e",
   "metadata": {},
   "source": [
    "No one in real life tries to find the derivatives by hand. To calculate it we need to understand what the derivative does.\n",
    "\n",
    "For example we can take our `x=3` and a very small `h=0.001`. If we plug it to our function $f(x+h)$ we will see that the value has slightly increased. Therefore slightly going in a positive direction will increase the value for our function. \n",
    "\n",
    "We can take $\\large\\frac{f(x+h)-f(x)}{h}$ to obrain the slope of the function, which is roughly 14.\n",
    "If we differentiate by hand, we can see that the approximation is correct:\n",
    "\n",
    "$f(x)'=6x-4$\n",
    "\n",
    "$f(3.0)=18-4=14$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6e55dc82",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:11:31.709298Z",
     "start_time": "2023-08-22T08:11:31.693285Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20.00000014"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h = 0.00000001\n",
    "x = 3.0\n",
    "f(x + h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "16a32253",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:11:31.725278Z",
     "start_time": "2023-08-22T08:11:31.709298Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.00000009255109"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(f(x + h) - f(x)) / h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3da9211d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:11:31.741285Z",
     "start_time": "2023-08-22T08:11:31.725278Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "43.999999779999996"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h = 0.00000001\n",
    "x = -3.0\n",
    "f(x + h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a07a9560",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:11:31.757280Z",
     "start_time": "2023-08-22T08:11:31.741285Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-22.00000039920269"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(f(x + h) - f(x)) / h"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2026daf5",
   "metadata": {},
   "source": [
    "We can find where the slop is zero by solving the $f(x)'=0$\n",
    "\n",
    "The answer is $\\large\\frac{2}{3}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5e52acc0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:11:31.773279Z",
     "start_time": "2023-08-22T08:11:31.757280Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.666666666666667"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h = 0.00000001\n",
    "x = 2 / 3\n",
    "f(x + h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b51916e4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:11:31.789314Z",
     "start_time": "2023-08-22T08:11:31.773279Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(f(x + h) - f(x)) / h"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d087cb95",
   "metadata": {},
   "source": [
    "## Derivative with Multiple Inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9bdfa648",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:11:31.805334Z",
     "start_time": "2023-08-22T08:11:31.789314Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d1: 4.0\n",
      "d2: 3.999699999999999\n",
      "slope:  -3.000000000010772\n"
     ]
    }
   ],
   "source": [
    "h=0.0001\n",
    "a = 2.0\n",
    "b = -3.0\n",
    "c = 10.0\n",
    "d1 = a * b + c\n",
    "print('d1:',d1)\n",
    "a += h # Derivative of d with respect to a\n",
    "d2 = a * b + c\n",
    "print('d2:',d2)\n",
    "print('slope: ', (d2 - d1) / h)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26b986a1",
   "metadata": {},
   "source": [
    "## Value object for micrograd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "id": "56df0c33",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:41:01.731315Z",
     "start_time": "2023-08-22T08:41:01.692082Z"
    }
   },
   "outputs": [],
   "source": [
    "import math\n",
    "class Value:\n",
    "    \"\"\" stores a single scalar value and its gradient \"\"\"\n",
    "\n",
    "    def __init__(self, data, _children=(), _op='', label=''):\n",
    "        self.data = data\n",
    "        self.grad = 0\n",
    "        # internal variables used for autograd graph construction\n",
    "        self._backward = lambda: None\n",
    "        self._prev = set(_children)\n",
    "        self.label = label\n",
    "        self._op = _op # the op that produced this node, for graphviz / debugging / etc\n",
    "\n",
    "    def __add__(self, other):\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "        out = Value(self.data + other.data, (self, other), '+')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += out.grad\n",
    "            other.grad += out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "\n",
    "    def __mul__(self, other):\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "        out = Value(self.data * other.data, (self, other), '*')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += other.data * out.grad\n",
    "            other.grad += self.data * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    \n",
    "    def exp(self):\n",
    "        out = Value(math.exp(self.data), (self, ), 'exp')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += self.data * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "\n",
    "    def __pow__(self, other):\n",
    "        assert isinstance(other, (int, float)), \"only supporting int/float powers for now\"\n",
    "        out = Value(self.data**other, (self,), f'**{other}')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += (other * self.data**(other-1)) * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "\n",
    "    def relu(self):\n",
    "        out = Value(0 if self.data < 0 else self.data, (self,), 'ReLU')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += (out.data > 0) * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "\n",
    "    def tanh(self):\n",
    "        n = self.data\n",
    "        t = (math.exp(2*n)-1) / (math.exp(2*n)+1)\n",
    "        out=Value(t, (self, ), 'tanh')\n",
    "        def _backward():\n",
    "            self.grad += (1-out.data**2) * out.grad\n",
    "        out._backward = _backward\n",
    "        \n",
    "        return out\n",
    "    \n",
    "\n",
    "    def backward(self):\n",
    "\n",
    "        # topological order all of the children in the graph\n",
    "        topo = []\n",
    "        visited = set()\n",
    "        def build_topo(v):\n",
    "            if v not in visited:\n",
    "                visited.add(v)\n",
    "                for child in v._prev:\n",
    "                    build_topo(child)\n",
    "                topo.append(v)\n",
    "        build_topo(self)\n",
    "\n",
    "        # go one variable at a time and apply the chain rule to get its gradient\n",
    "        self.grad = 1.0\n",
    "        for node in reversed(topo):\n",
    "            node._backward()\n",
    "\n",
    "    def __neg__(self): # -self\n",
    "        return self * -1\n",
    "\n",
    "    def __radd__(self, other): # other + self\n",
    "        return self + other\n",
    "\n",
    "    def __sub__(self, other): # self - other\n",
    "        return self + (-other)\n",
    "\n",
    "    def __rsub__(self, other): # other - self\n",
    "        return other + (-self)\n",
    "\n",
    "    def __rmul__(self, other): # other * self\n",
    "        return self * other\n",
    "\n",
    "    def __truediv__(self, other): # self / other\n",
    "        return self * other**-1\n",
    "\n",
    "    def __rtruediv__(self, other): # other / self\n",
    "        return other * self**-1\n",
    "\n",
    "    def __repr__(self):\n",
    "        return f\"Value(data={self.data}, grad={self.grad})\"\n",
    "    \n",
    "\n",
    "def trace(root):\n",
    "    # Build the set of all nodes and edges in a graph\n",
    "    nodes, edges = set(), set()\n",
    "\n",
    "    def build(node):\n",
    "        if node not in nodes:\n",
    "            nodes.add(node)\n",
    "            for child in node._prev:\n",
    "                edges.add((child, node))\n",
    "                build(child)\n",
    "\n",
    "    build(root)\n",
    "    return nodes, edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "id": "53a05933",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:41:02.827379Z",
     "start_time": "2023-08-22T08:41:02.805855Z"
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   "outputs": [],
   "source": [
    "a = Value(2.0, label='a')\n",
    "b = Value(-3.0, label='b')\n",
    "c = Value(10.0, label='c')\n",
    "e = a * b\n",
    "e.label = 'e'\n",
    "d = e + c  # a.__mul__(b).__add__(c)\n",
    "d.label='d'\n",
    "f = Value(-2.0, label='f')\n",
    "L = d * f\n",
    "L.label='L'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cd7416d",
   "metadata": {
    "heading_collapsed": true
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   "source": [
    "## Vizualization of Propogation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "af8d0e61",
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    "ExecuteTime": {
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     "start_time": "2023-08-22T08:14:39.376796Z"
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   "source": [
    "from graphviz import Digraph\n",
    "\n",
    "\n",
    "def trace(root):\n",
    "    # Build the set of all nodes and edges in a graph\n",
    "    nodes, edges = set(), set()\n",
    "\n",
    "    def build(node):\n",
    "        if node not in nodes:\n",
    "            nodes.add(node)\n",
    "            for child in node._prev:\n",
    "                edges.add((child, node))\n",
    "                build(child)\n",
    "\n",
    "    build(root)\n",
    "    return nodes, edges\n",
    "\n",
    "\n",
    "def draw_dot(root):\n",
    "    dot = Digraph(format='png', graph_attr={'rankdir':\n",
    "                                            'LR'})  # LR means Left-to-Right\n",
    "    nodes, edges = trace(root)\n",
    "    for n in nodes:\n",
    "        uid = str(id(n))\n",
    "        # If value, create a rectangular node\n",
    "        dot.node(name=uid, label=f'{{ {n.label} | data {n.data:.4f} | grad {n.grad:.4f} }}', shape='record')\n",
    "        if n._op:\n",
    "            # If operation, create circular node\n",
    "            dot.node(name=uid + n._op, label=n._op)\n",
    "            dot.edge(uid + n._op, uid)\n",
    "\n",
    "    for n1, n2 in edges:\n",
    "        dot.edge(str(id(n1)),\n",
    "                 str(id(n2)) + n2._op)  # Connect Nodes throught the operation\n",
    "        \n",
    "#     if you uncomment the below code you'll be able to download the graph\n",
    "#     graph_name = \"computation_graph\"\n",
    "#     dot.render(filename=graph_name, directory=\"images\", cleanup=True)\n",
    "    \n",
    "    return dot"
   ]
  },
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     "start_time": "2023-08-22T08:14:39.419497Z"
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   "source": [
    "## Manual Backpropogation"
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   "cell_type": "markdown",
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   "source": [
    "$\\large\\frac{dL}{dL}=1$"
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   "id": "71a50523",
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    "$L = df$\n",
    "\n",
    "$\\large\\frac{dL}{dd}=f=-2;  \\large\\frac{dL}{df}=d=4$"
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    "a.grad=6.0\n",
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    "draw_dot(L)"
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      "-7.286496\n"
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    "a.data += 0.01 * a.grad\n",
    "b.data += 0.01 * b.grad\n",
    "c.data += 0.01 * c.grad\n",
    "f.data += 0.01 * f.grad\n",
    "e = a * b\n",
    "d = e + c\n",
    "L = d * f\n",
    "print(L.data)"
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    "def gradient_check():\n",
    "    h = 0.000001\n",
    "    a = Value(2.0, label='a')\n",
    "    b = Value(-3.0, label='b')\n",
    "    c = Value(10.0, label='c')\n",
    "    e = a * b\n",
    "    e.label = 'e'\n",
    "    d = e + c  # a.__mul__(b).__add__(c)\n",
    "    d.label = 'd'\n",
    "    f = Value(-2.0, label='f')\n",
    "    L = d * f\n",
    "    L.label = 'L'\n",
    "    L1 = L.data\n",
    "\n",
    "    a = Value(2.0, label='a')\n",
    "    b = Value(-3.0, label='b')\n",
    "    c = Value(10.0, label='c')\n",
    "    e = a * b\n",
    "    e.label = 'e'\n",
    "    d = e + c  # a.__mul__(b).__add__(c)\n",
    "    d.label = 'd'\n",
    "    f = Value(-2.0, label='f')\n",
    "    L = d * f\n",
    "    L.label = 'L'\n",
    "    L2 = L.data\n",
    "\n",
    "    print((L2 - L1) / h)\n",
    "\n",
    "\n",
    "gradient_check()"
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   "source": [
    "## Backpropogating through a neuron"
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    {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.arange(-5.0, 5, 0.2), np.tanh(np.arange(-5, 5, 0.2)))\n",
    "plt.grid();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "95b98711",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:41:06.043200Z",
     "start_time": "2023-08-22T08:41:05.970589Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 2.46.0 (20210118.1747)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"1559pt\" height=\"210pt\"\n",
       " viewBox=\"0.00 0.00 1559.00 210.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 206)\">\n",
       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-206 1555,-206 1555,4 -4,4\"/>\n",
       "<!-- 2859373728816 -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>2859373728816</title>\n",
       "<polygon fill=\"none\" stroke=\"black\" points=\"1050,-54.5 1050,-90.5 1237,-90.5 1237,-54.5 1050,-54.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"1061.5\" y=\"-68.8\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">n</text>\n",
       "<polyline fill=\"none\" stroke=\"black\" points=\"1073,-54.5 1073,-90.5 \"/>\n",
       "<text text-anchor=\"middle\" x=\"1113.5\" y=\"-68.8\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">data 2.0000</text>\n",
       "<polyline fill=\"none\" stroke=\"black\" points=\"1154,-54.5 1154,-90.5 \"/>\n",
       "<text text-anchor=\"middle\" x=\"1195.5\" y=\"-68.8\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">grad 0.0000</text>\n",
       "</g>\n",
       "<!-- 2859371710928tanh -->\n",
       "<g id=\"node14\" class=\"node\">\n",
       "<title>2859371710928tanh</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"1300\" cy=\"-72.5\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"1300\" y=\"-68.8\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">tanh</text>\n",
       "</g>\n",
       "<!-- 2859373728816&#45;&gt;2859371710928tanh -->\n",
       "<g id=\"edge14\" class=\"edge\">\n",
       "<title>2859373728816&#45;&gt;2859371710928tanh</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M1237.05,-72.5C1246.06,-72.5 1254.79,-72.5 1262.7,-72.5\"/>\n",
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   "source": [
    "# Inputs\n",
    "x1 = Value(2.0, label='x1')\n",
    "x2 = Value(0.0, label='x2')\n",
    "\n",
    "# Weights\n",
    "w1 = Value(-3.0, label='w1')\n",
    "w2 = Value(1.0, label='w2')\n",
    "\n",
    "# Bias\n",
    "b = Value(8.0, label='b')\n",
    "\n",
    "# x1w1 + x2w2 + b\n",
    "x1w1 = x1 * w1\n",
    "x1w1.label = 'x1w1'\n",
    "x2w2 = x2 * w2\n",
    "x2w2.label = 'x2w2'\n",
    "x1w1x2w2 = x1w1 + x2w2\n",
    "x1w1x2w2.label = 'x1w1+x2w2'\n",
    "n = x1w1x2w2 + b\n",
    "n.label = 'n'\n",
    "o = n.tanh()\n",
    "o.label='o'\n",
    "o.grad = 1.0\n",
    "\n",
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   "id": "261488a6",
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     "start_time": "2023-08-22T08:41:06.388036Z"
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    "x1.grad = x1w1.grad*w1.data\n",
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    "x2.grad = x2w2.grad*w2.data\n",
    "w2.grad = x2w2.grad*x2.data\n",
    "draw_dot(o)"
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   "source": [
    "## Implementing Backward Propogation for the entire expression\n",
    "\n",
    "The below code will be implemented inside the Value class above"
   ]
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   "cell_type": "code",
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    "ExecuteTime": {
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     "start_time": "2023-08-22T08:41:08.569561Z"
    },
    "scrolled": true
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    {
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       "[Value(data=8.0, grad=0.0707),\n",
       " Value(data=0.0, grad=0.0707),\n",
       " Value(data=1.0, grad=0.0),\n",
       " Value(data=0.0, grad=0.0707),\n",
       " Value(data=-3.0, grad=0.1414),\n",
       " Value(data=2.0, grad=-0.2121),\n",
       " Value(data=-6.0, grad=0.0707),\n",
       " Value(data=-6.0, grad=0.0707),\n",
       " Value(data=2.0, grad=0.07065082485316443),\n",
       " Value(data=0.9640275800758169, grad=1.0)]"
      ]
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     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
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    "o.grad=1.0\n",
    "topo = list()\n",
    "visited = set()\n",
    "def build_topological_sort(vertex):\n",
    "    if vertex not in visited:\n",
    "        visited.add(vertex)\n",
    "        for child in vertex._prev:\n",
    "            build_topological_sort(child)\n",
    "        topo.append(vertex)\n",
    "        \n",
    "build_topological_sort(o)\n",
    "topo"
   ]
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   "id": "e5be45e4",
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     "start_time": "2023-08-22T08:41:08.705485Z"
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   "id": "24289f98",
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    "x = Value(3)\n",
    "q = Value(4)\n"
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     "execution_count": 199,
     "metadata": {},
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   "source": [
    "# Inputs\n",
    "x1 = Value(2.0, label='x1')\n",
    "x2 = Value(0.0, label='x2')\n",
    "\n",
    "# Weights\n",
    "w1 = Value(-3.0, label='w1')\n",
    "w2 = Value(1.0, label='w2')\n",
    "\n",
    "# Bias\n",
    "b = Value(6.8813735870195432, label='b')\n",
    "\n",
    "# x1w1 + x2w2 + b\n",
    "x1w1 = x1 * w1\n",
    "x1w1.label = 'x1w1'\n",
    "x2w2 = x2 * w2\n",
    "x2w2.label = 'x2w2'\n",
    "x1w1x2w2 = x1w1 + x2w2\n",
    "x1w1x2w2.label = 'x1w1+x2w2'\n",
    "n = x1w1x2w2 + b\n",
    "n.label = 'n'\n",
    "e = (2*n).exp()\n",
    "e.label='e'\n",
    "o = (e - 1) / (e + 1)\n",
    "o.label='o'\n",
    "o.backward()\n",
    "draw_dot(o)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "858416bc",
   "metadata": {},
   "source": [
    "## Pytorch implementation of micrograd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "id": "525eebf0",
   "metadata": {
    "ExecuteTime": {
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     "start_time": "2023-08-22T08:41:10.072648Z"
    },
    "scrolled": true
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7071066904050358\n",
      "----------\n",
      "x2 0.5000001283844369\n",
      "w2 0.0\n",
      "x1 -1.5000003851533106\n",
      "w1 1.0000002567688737\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "x1 = torch.Tensor([2.0]).double() # Python uses float64 instead of 32; therefore, we cast it to double()\n",
    "x1.requires_grad = True\n",
    "x2 = torch.Tensor([0.0]).double()\n",
    "x2.requires_grad = True\n",
    "w1 = torch.Tensor([-3.0]).double()\n",
    "w1.requires_grad = True\n",
    "w2 = torch.Tensor([1.0]).double()\n",
    "w2.requires_grad = True\n",
    "b1 = torch.Tensor([6.8813735870195432]).double()\n",
    "b1.requires_grad = True\n",
    "n = x1 * w1 + x2 * w2 + b1\n",
    "o = torch.tanh(n)\n",
    "print(o.data.item())\n",
    "o.backward()\n",
    "print('-' * 10)\n",
    "print('x2', x2.grad.item())\n",
    "print('w2', w2.grad.item())\n",
    "print('x1', x1.grad.item())\n",
    "print('w1', w1.grad.item())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "494f9de6",
   "metadata": {},
   "source": [
    "## Neuron Implementation for Micrograd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "id": "1f647175",
   "metadata": {
    "ExecuteTime": {
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     "start_time": "2023-08-22T08:41:10.545802Z"
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    "scrolled": true
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   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "\n",
    "class Neuron:\n",
    "\n",
    "    def __init__(self, nin):\n",
    "        self.w = [Value(random.uniform(-1,1)) for _ in range(nin)]\n",
    "        self.b = Value(random.uniform(-1, 1))\n",
    "\n",
    "    def __call__(self, x):\n",
    "        act = sum((wi*xi for wi,xi in zip(self.w, x)), self.b)\n",
    "        out = act.tanh()\n",
    "        return out\n",
    "    \n",
    "    def parameters(self):\n",
    "        return self.w + [self.b]\n",
    "    \n",
    "class Layer:\n",
    "\n",
    "    def __init__(self, nin, nout):\n",
    "        self.neurons = [Neuron(nin) for _ in range(nout)]\n",
    "\n",
    "    def __call__(self, x):\n",
    "        out = [n(x) for n in self.neurons]\n",
    "        return out[0] if len(out) == 1 else out\n",
    "    \n",
    "    def parameters(self):\n",
    "        return [p for neuron in self.neurons for p in neuron.parameters()]\n",
    "    \n",
    "class MLP:\n",
    "\n",
    "    def __init__(self, nin, nouts):\n",
    "        sz = [nin] + nouts\n",
    "        self.layers = [Layer(sz[i], sz[i+1]) for i in range(len(nouts))]\n",
    "\n",
    "    def __call__(self, x):\n",
    "        for layer in self.layers:\n",
    "            x = layer(x)\n",
    "        return x\n",
    "    \n",
    "    def parameters(self):\n",
    "        return [p for layer in self.layers for p in layer.parameters()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "id": "f0af02e9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:44:41.338765Z",
     "start_time": "2023-08-22T08:44:41.322244Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Value(data=-0.500125717895315, grad=0)"
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [2.0, 3.0, -1.0]\n",
    "n = MLP(3, [4, 4, 1])\n",
    "n(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "id": "a286d410",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:44:41.723110Z",
     "start_time": "2023-08-22T08:44:41.707114Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "41"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(n.parameters())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "id": "f865a0f8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:44:42.288399Z",
     "start_time": "2023-08-22T08:44:42.261826Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Value(data=-0.500125717895315, grad=0),\n",
       " Value(data=0.010934130006537571, grad=0),\n",
       " Value(data=0.05296482666250498, grad=0),\n",
       " Value(data=-0.723735336342726, grad=0)]"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs = [\n",
    "    [2., 3., -1.],\n",
    "    [3., -1., 0.5],\n",
    "    [0.5, 1., 1.],\n",
    "    [1., 1., -1.]\n",
    "]\n",
    "ys = [1., -1., -1., 1.]\n",
    "\n",
    "y_pred = [n(x) for x in xs]\n",
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "id": "31750b2d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:44:44.679776Z",
     "start_time": "2023-08-22T08:44:44.665462Z"
    }
   },
   "outputs": [],
   "source": [
    "loss = sum((yout - ygt)**2 for ygt, yout in zip(ys, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "id": "2cc900a4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:44:45.594934Z",
     "start_time": "2023-08-22T08:44:45.569909Z"
    }
   },
   "outputs": [],
   "source": [
    "loss.backward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "id": "9478b746",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:45:47.024590Z",
     "start_time": "2023-08-22T08:45:47.011092Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Value(data=7.352363420647979, grad=1.0)"
      ]
     },
     "execution_count": 221,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "id": "9401a0f8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:45:47.443056Z",
     "start_time": "2023-08-22T08:45:47.418526Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6298891537960987"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.layers[0].neurons[0].w[0].data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "id": "2911e377",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:45:48.180877Z",
     "start_time": "2023-08-22T08:45:48.164941Z"
    }
   },
   "outputs": [],
   "source": [
    "for p in n.parameters():\n",
    "    p.data += -0.01 * p.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "id": "6d7964de",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:45:50.473391Z",
     "start_time": "2023-08-22T08:45:50.460861Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Value(data=0.6276861980733973, grad=0.22029557227013996),\n",
       " Value(data=0.14247985178168907, grad=0.22108682357643697),\n",
       " Value(data=-0.7159417827227784, grad=0.28772651405576183),\n",
       " Value(data=0.9570681872171765, grad=0.28904207825260053),\n",
       " Value(data=0.1361935907796439, grad=0.20698078043665746),\n",
       " Value(data=-0.8169861066169137, grad=-1.0049459433201684),\n",
       " Value(data=-0.7781613166541099, grad=0.8265654086858196),\n",
       " Value(data=-0.4135085812230849, grad=-0.18232395265054707),\n",
       " Value(data=-0.576211375818651, grad=-0.5923890741626072),\n",
       " Value(data=0.577695383444034, grad=-1.241071498322192),\n",
       " Value(data=0.35599880824422325, grad=0.9677251100689415),\n",
       " Value(data=0.040121494232944345, grad=-0.0509199658972484),\n",
       " Value(data=-0.376185270374361, grad=0.6659154613417253),\n",
       " Value(data=-0.3524551570759722, grad=6.518839457661915),\n",
       " Value(data=-0.8504102432347376, grad=-4.365291442937846),\n",
       " Value(data=0.6197431037470096, grad=0.22205103593726294),\n",
       " Value(data=0.5693402658687644, grad=-0.27308939359417517),\n",
       " Value(data=-0.454713796135094, grad=-0.3017090789609661),\n",
       " Value(data=-0.7461576335828916, grad=0.35254430529184494),\n",
       " Value(data=0.981817786376759, grad=0.7462090320969056),\n",
       " Value(data=-0.210714283373858, grad=-0.5025684667142162),\n",
       " Value(data=0.46421492219571986, grad=0.6798684880150927),\n",
       " Value(data=-0.9138070864778636, grad=0.472245562388005),\n",
       " Value(data=0.5608884750118722, grad=-0.8233083062421428),\n",
       " Value(data=0.07979955648184525, grad=-0.7358491214358744),\n",
       " Value(data=0.5944654542466472, grad=0.7190583339064854),\n",
       " Value(data=0.2030457862414017, grad=1.2377455763963303),\n",
       " Value(data=-0.21632843265883533, grad=-1.0252449853514523),\n",
       " Value(data=0.38177998197319457, grad=-0.16328504001176858),\n",
       " Value(data=0.3941057173550797, grad=2.863923276942757),\n",
       " Value(data=-0.26999266275150824, grad=0.4408966017704785),\n",
       " Value(data=-0.8006698188056314, grad=-0.23360547875757587),\n",
       " Value(data=-0.4895331512138711, grad=-0.6456735818911254),\n",
       " Value(data=-0.6558683032822594, grad=0.5063984925133462),\n",
       " Value(data=0.42790440580688316, grad=1.9729374388756435),\n",
       " Value(data=0.9970321140439826, grad=-0.8064637839529889),\n",
       " Value(data=-0.31123906920142663, grad=-2.9490916875687856),\n",
       " Value(data=0.48954398296210194, grad=-1.3056668157619997),\n",
       " Value(data=-0.9595287849835126, grad=-1.9706672275139807),\n",
       " Value(data=-0.7414075974119004, grad=-0.8389411317019391),\n",
       " Value(data=-0.3019122451920319, grad=0.23012690871905983)]"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.parameters()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e23f989",
   "metadata": {},
   "source": [
    "## Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "id": "c6ef9e8b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:54:35.767517Z",
     "start_time": "2023-08-22T08:54:35.751440Z"
    }
   },
   "outputs": [],
   "source": [
    "x = [2.0, 3.0, -1.0]\n",
    "n = MLP(3, [4, 4, 1])\n",
    "n(x)\n",
    "xs = [\n",
    "    [2., 3., -1.],\n",
    "    [3., -1., 0.5],\n",
    "    [0.5, 1., 1.],\n",
    "    [1., 1., -1.]\n",
    "]\n",
    "ys = [1., -1., -1., 1.]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "id": "7092ece8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:54:36.107405Z",
     "start_time": "2023-08-22T08:54:36.081772Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 5.962957435742434\n",
      "1 2.8367889107151063\n",
      "2 0.6220173236185722\n",
      "3 0.33354559394825\n",
      "4 0.2376172319988082\n",
      "5 0.18535803052247046\n",
      "6 0.1522275473770352\n",
      "7 0.12925554329434613\n",
      "8 0.112350547542584\n",
      "9 0.09936981336920848\n"
     ]
    }
   ],
   "source": [
    "for k in range(10):\n",
    "    y_pred = [n(x) for x in xs]\n",
    "    loss = sum((yout - ygt)**2 for ygt, yout in zip(ys, y_pred))\n",
    "    \n",
    "    for p in n.parameters():\n",
    "        p.grad=0\n",
    "    \n",
    "    loss.backward()\n",
    "    \n",
    "    for p in n.parameters():\n",
    "        p.data += -0.05 * p.grad\n",
    "        \n",
    "    print(k, loss.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "id": "43f232f0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-22T08:54:46.119404Z",
     "start_time": "2023-08-22T08:54:46.102760Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Value(data=0.8538423510443532, grad=-0.2923152979112935),\n",
       " Value(data=-0.84240949644129, grad=0.3151810071174199),\n",
       " Value(data=-0.8539326106673404, grad=0.29213477866531923),\n",
       " Value(data=0.8215698848775245, grad=-0.35686023024495106)]"
      ]
     },
     "execution_count": 247,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "91d6ea19",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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