3_how_does_a_nn_work.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ipywidgets import interact\n",
    "from fastai.basics import *\n",
    "\n",
    "def plot_function(f, title=None, min=-2.1, max=2.1, color=\"r\", ylim=None):\n",
    "    x = torch.linspace(min, max, 100)[:, None]\n",
    "    if ylim:  plt.ylim(ylim)\n",
    "    plt.plot(x, f(x), color)\n",
    "    if title: plt.title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x): return 3*x**2 + 2*x + 1\n",
    "\n",
    "plot_function(f, \"$3x^2 + 2x + 1$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def quad(a, b, c, x): return a*x**2 + b*x +c\n",
    "def mk_quad(a, b, c): return partial(quad, a, b, c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f2 = mk_quad(3, 2, 1)\n",
    "plot_function(f2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def noise(x, scale): return np.random.normal(scale=scale, size=x.shape)\n",
    "def add_noise(x, mult, add): return x * (1+noise(x, mult)) + noise(x, add)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "x = torch.linspace(-2, 2, steps=20)[:, None]\n",
    "y = add_noise(f(x), 0.15, 1.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[-2.0000],\n",
       "         [-1.7895],\n",
       "         [-1.5789],\n",
       "         [-1.3684],\n",
       "         [-1.1579]]),\n",
       " tensor([[11.8690],\n",
       "         [ 6.5433],\n",
       "         [ 5.9396],\n",
       "         [ 2.6304],\n",
       "         [ 1.7947]], dtype=torch.float64))"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[:5], y[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f890aaa8290>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nSwMAAGmSzPe34yMf77//vvLy4n9tfn4+j9oCAABJabjno7a2Vo8++qhmz56tT3ziE+rs7NQTTzyhP/uzP3P6VAAAwIUcn3YZGBjQN77xDW3fvl39/f0qLS3VXXfdpW9+85uaMWPGhJ9n2gUAAPdJ5vvb8fBxoQgfAAC4T0bv+QAAABgP4QMAAFhF+AAAAFYRPgAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGAV4QMAAFhF+AAAAFYRPgAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABYRfgAAABWTct0AbliKGrU3nNa/QODKin0qrq8WPl5nkyXBQBA1iF8OKC1K6iGlm4FQ4OxYwGfV/W1FaqpDGSwMgAAsg/TLheotSuouuaOuOAhSX2hQdU1d6i1K5ihygAAyE6EjwswFDVqaOmWSfCzkWMNLd0aiiZqAQDA1ET4uADtPadHjXicy0gKhgbV3nPaXlEAAGQ5wscF6B8YO3ik0g4AgKmA8HEBSgq9jrYDAGAqIHxcgOryYgV8Xo31QK1Hw0+9VJcX2ywLAICsRvi4APl5HtXXVkjSqAAy8r6+toL1PgAAOAfh4wLVVAbUtLJKfl/81Irf51XTyirW+QAA4DwsMuaAmsqAllT4WeEUAIBJIHw4JD/Po4VzZ2a6DAAAsh7TLgAAwCrCBwAAsCot4ePEiRNauXKlZs6cqYsvvlif/vSndejQoXScCgAAuIzj93y8++67+sxnPqPFixfrJz/5iUpKSnT06FFdeumlTp9qyhiKGm5mBQDkDMfDx6ZNm1RWVqatW7fGjs2ZM8fp00wZrV1BNbR0x+0hE/B5VV9bwWO8AABXcnza5cUXX9S1116rO++8UyUlJZo3b56eeeaZMdtHIhGFw+G4F4a1dgVV19wxavO6vtCg6po71NoVzFBlAACkzvHw8etf/1pNTU268sor9dOf/lT333+/HnroIf3rv/5rwvaNjY3y+XyxV1lZmdMludJQ1KihpVsmwc9GjjW0dGsomqgFAADZy2OMcfTba8aMGbr22mu1b9++2LGHHnpIBw4cUFtb26j2kUhEkUgk9j4cDqusrEyhUEhFRUVOluYqbUdP6a5n9k/Y7rl7F7C+CAAg48LhsHw+36S+vx0f+QgEAqqoqIg79vGPf1zHjx9P2L6goEBFRUVxL0j9A4MTN0qiHQAA2cLx8PGZz3xGb775ZtyxI0eO6IorrnD6VDmtpNA7caMk2gEAkC0cDx8PP/yw9u/fr8cee0xvvfWWnn32WT399NNas2aN06fKadXlxQr4vKN2yx3h0fBTL9XlxTbLAgDggjkePq677jpt375dzz33nCorK/U3f/M3evLJJ3XPPfc4faqclp/nUX3t8PTV+QFk5H19bQXrfQAAXMfxG04vVDI3rEwFrPMBAHCDZL6/2dU2y9VUBrSkws8KpwCAnEH4cIH8PA+P0wIAcga72gIAAKsY+QAAxGEzS6Qb4QMAEMNN7rCBaRcAgCQ2s4Q9hA8AAJtZwirCBwBA7T2nR414nMtICoYG1d5z2l5RyFmEDwAAm1nCKsIHAIDNLGEV4QMAwGaWsIrwAQBgM0tYRfgAAEga3kuqaWWV/L74qRW/z6umlVWs8wHHsMgYACCGzSxhA+EDABCHzSyRboQPAIBV7B0DwgcAwBr2joHEDacAAEvYOwYjCB8AgLRj7xici/ABAEg79o7BuQgfAIC0Y+8YnIvwAQBIO/aOwbl42gXAlMTjnnaN7B3TFxpMeN+HR8MrqbJ3zNRA+AAw5fC4p30je8fUNXfII8UFEPaOmXqYdgEwpfC4Z+awdwxGMPIBYMqY6HFPj4Yf91xS4edf4GnC3jGQCB8AppBkHvdkb5P0Ye8YMO0CYMrgcU8gOxA+AEwZPO4JZAfCB4ApY+Rxz7HuLvBo+KkXHvcE0ovwAWDKGHncU9KoAMLjnoA9hA8AUwqPewKZx9MuAKYcHvcEMovwAWBK4nFPIHOYdgEAAFYRPgAAgFWEDwAAYFXaw0djY6M8Ho/Wrl2b7lMBAAAXSGv4OHDggJ5++ml96lOfSudpAACAi6QtfLz33nu655579Mwzz+gjH/lIuk4DAABcJm3hY82aNVq+fLk++9nPjtsuEokoHA7HvQAAQO5KyzofP/rRj9TR0aEDBw5M2LaxsVENDQ3pKAMAAGQhx0c+ent79Zd/+Zdqbm6W1zvxzpAbN25UKBSKvXp7e50uCQAAZBGPMcY4+Qt37NihO+64Q/n5+bFjQ0ND8ng8ysvLUyQSifvZ+cLhsHw+n0KhkIqKipwsDQAApEky39+OT7vcdttteu211+KOfelLX9LVV1+t9evXjxs8AABA7nM8fBQWFqqysjLu2CWXXKKZM2eOOg4AAKYeVjgFAABWWdnVdvfu3TZOAwAAXICRDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGAV4QMAAFhF+AAAAFYRPgAAgFWEDwAAYJWVXW0BYKoZihq195xW/8CgSgq9qi4vVn6eJ9NlAVmB8AEADmvtCqqhpVvB0GDsWMDnVX1thWoqAxmsDMgOTLsAgINau4Kqa+6ICx6S1BcaVF1zh1q7ghmqDMgehA8AcMhQ1KihpVsmwc9GjjW0dGsomqgFMHUQPgDAIe09p0eNeJzLSAqGBtXec9peUUAWInwAgEP6B8YOHqm0A3IV4QMAHFJS6HW0HZCrCB8A4JDq8mIFfF6N9UCtR8NPvVSXF9ssC8g6hA9oKGrUdvSU/uPwCbUdPcXNcECK8vM8qq+tkKRRAWTkfX1tBet9YMpjnY8pjvUIAGfVVAbUtLJq1N8rP3+vgBiPMSar/pkbDofl8/kUCoVUVFSU6XJy2sh6BOf/H2Dk32RNK6v4DyWQIlY4xVSTzPc3Ix9T1ETrEXg0vB7Bkgo//8EEUpCf59HCuTMzXQaQlbjnY4piPQIAQKYQPqYo1iMAAGQK4WOKYj0CAECmED6mKNYjAABkCuFjimI9AgBAphA+prCR9Qj8vvipFb/Py2O2AIC04VHbKa6mMqAlFX7WIwAAWEP4AOsRAACsYtoFAABYRfgAAABWET4AAIBVhA8AAGCV4+GjsbFR1113nQoLC1VSUqIVK1bozTffdPo0AADApRwPH3v27NGaNWu0f/9+7dy5Ux9++KGWLl2qM2fOOH0qAADgQh5jTKJd1R3zm9/8RiUlJdqzZ49uvvnmCduHw2H5fD6FQiEVFRWlszTkiKGoYZ0SAMiwZL6/077ORygUkiQVFyfeIyQSiSgSicTeh8PhdJeEHNLaFVRDS7eCof/bfTfg86q+toIVWgEgS6X1hlNjjNatW6cbb7xRlZWVCds0NjbK5/PFXmVlZeksCRkwFDVqO3pK/3H4hNqOntJQ1JnBttauoOqaO+KChyT1hQZV19yh1q6gI+cBADgrrdMua9as0UsvvaRXX31Vl19+ecI2iUY+ysrKmHbJEekamRiKGt246eVRwWOER8N71Ly6/lamYADAgmSmXdI28vHggw/qxRdf1K5du8YMHpJUUFCgoqKiuBdyQzpHJtp7To8ZPCTJSAqGBtXeczrlcwAA0sPx8GGM0QMPPKBt27bp5ZdfVnl5udOngAsMRY0aWrqVaFht5FhDS3fKUzD9A2MHj1TaAQDscTx8rFmzRs3NzXr22WdVWFiovr4+9fX16be//a3Tp0IWS/fIREmh19F2AAB7HA8fTU1NCoVCWrRokQKBQOz1/PPPO30qZLF0j0xUlxcr4PNqrLs5PBq+t6S6PPFTVgCAzHH8Uds0LxsCl0j3yER+nkf1tRWqa+6QR4qb3hkJJPW1FdxsCgBZiL1dkBY2RiZqKgNqWlklvy8+wPh9XjWtrGKdDwDIUmlfZAxTk62RiZrKgJZU+FnhFABcJO3LqyeL5dVzCyuQjo+l4QHkiqxaXh1TGyMTYyOYAZiqGPkAMmBkAbbz//KNRDLuWcFEGDVDtmHkA8hiEy3A5tHwAmxLKvx8mSAhRs3gdjztAljG0vC4EGyoiFxA+AAsY2l4pCrd2xYAthA+AMtYGh6pYtQMuYLwAVjG0vBIFaNmyBWED8CykQXYJI0KICwNj/EwaoZcQfgAMoCl4ZEKRs2QK3jUFsgQFmBDsthQEbmCRcYAwGVY5wPZiEXGACCHMWoGtyN8AIAL5ed5tHDuzEyXAaSEG04BAIBVhA8AAGAV4QMAAFhF+AAAAFYRPgAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVaxwCiBlQ1HDEt8Akkb4AJASNjcDkCqmXQAkrbUrqLrmjrjgIUl9oUHVNXeotSuYocoAuAHhA0BShqJGDS3dMgl+NnKsoaVbQ9FELQCA8AEgSe09p0eNeJzLSAqGBtXec9peUQBchXs+ACSlf2Ds4JFKu7FwMyuQuwgfAJJSUuh1tF0i3MwK5DamXQAkpbq8WAGfV2ONQXg0HBSqy4tT+v3czArkPsIHgKTk53lUX1shSaMCyMj7+tqKlKZIuJkVmBoIHwCSVlMZUNPKKvl98VMrfp9XTSurUp4a4WZWYGrgng8AKampDGhJhd/Rm0Jt3cwKILMIHwBSlp/n0cK5Mx37fTZuZgWQeWmbdnnqqadUXl4ur9er+fPn65VXXknXqQDkiHTfzAogO6QlfDz//PNau3atvv71r6uzs1M33XSTli1bpuPHj6fjdAByRDpvZgWQPTzGGMdvG7/++utVVVWlpqam2LGPf/zjWrFihRobG8f9bDgcls/nUygUUlFRkdOlAXAB1vkA3CeZ72/H7/k4e/asDh06pA0bNsQdX7p0qfbt2zeqfSQSUSQSib0Ph8NOlwTAZdJxMyuA7OF4+HjnnXc0NDSkWbNmxR2fNWuW+vr6RrVvbGxUQ0OD02UAcDmnb2YFkD3SdsOpxxP/LxRjzKhjkrRx40aFQqHYq7e3N10lAQCALOD4yMdll12m/Pz8UaMc/f39o0ZDJKmgoEAFBQVOlwE4wu2bm7m9fgC5yfHwMWPGDM2fP187d+7UHXfcETu+c+dO3X777U6fDkgbt9/06Pb6AeSutEy7rFu3Tv/8z/+sf/mXf9Evf/lLPfzwwzp+/Ljuv//+dJwOcJzbNzdze/0AcltaVjj9whe+oFOnTulb3/qWgsGgKisr9eMf/1hXXHFFOk4HOGqizc08Gt7cbEmFPyunMNxeP4Dcl7YbTr/85S/r7bffViQS0aFDh3TzzTen61SAo9y+uZnb6weQ+9jVFjiP2zc3c3v9AHIf4QM4j9s3N3N7/QByH+EDOI/bNzdze/0Ach/hAziP2zc3c3v9AHIf4QNIoKYyoKaVVfL74qcm/D6vmlZWZf06GW6vH0BuS8uutheCXW2RTdy+Qqjb6wfgHhnd1RbIJW7f3Mzt9QPITUy7AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKuyboXTkdXew+FwhisBAACTNfK9PZldW7IufAwMDEiSysrKMlwJAABI1sDAgHw+37htsm5juWg0qpMnT6qwsFAej7MbYIXDYZWVlam3tzcnN63L9f5Jud9H+ud+ud7HXO+flPt9TFf/jDEaGBhQaWmp8vLGv6sj60Y+8vLydPnll6f1HEVFRTn5f6gRud4/Kff7SP/cL9f7mOv9k3K/j+no30QjHiO44RQAAFhF+AAAAFZNqfBRUFCg+vp6FRQUZLqUtMj1/km530f653653sdc75+U+33Mhv5l3Q2nAAAgt02pkQ8AAJB5hA8AAGAV4QMAAFhF+AAAAFbldPh4++239ed//ucqLy/XRRddpLlz56q+vl5nz54d93PGGD3yyCMqLS3VRRddpEWLFun111+3VHVyHn30Ud1www26+OKLdemll07qM3/6p38qj8cT91qwYEF6C01RKv1z0/WTpHfffVerVq2Sz+eTz+fTqlWr9L//+7/jfiabr+FTTz2l8vJyeb1ezZ8/X6+88sq47ffs2aP58+fL6/Xqox/9qLZs2WKp0tQl08fdu3ePulYej0dvvPGGxYonb+/evaqtrVVpaak8Ho927Ngx4WfcdA2T7Z/brl9jY6Ouu+46FRYWqqSkRCtWrNCbb7454edsX8OcDh9vvPGGotGo/umf/kmvv/66vvvd72rLli362te+Nu7nHn/8cT3xxBPavHmzDhw4IL/fryVLlsT2nckmZ8+e1Z133qm6urqkPldTU6NgMBh7/fjHP05ThRcmlf656fpJ0t13363Dhw+rtbVVra2tOnz4sFatWjXh57LxGj7//PNau3atvv71r6uzs1M33XSTli1bpuPHjyds39PToz/4gz/QTTfdpM7OTn3ta1/TQw89pBdeeMFy5ZOXbB9HvPnmm3HX68orr7RUcXLOnDmja665Rps3b55Ue7ddw2T7N8It12/Pnj1as2aN9u/fr507d+rDDz/U0qVLdebMmTE/k5FraKaYxx9/3JSXl4/582g0avx+v/n2t78dOzY4OGh8Pp/ZsmWLjRJTsnXrVuPz+SbVdvXq1eb2229Paz1Om2z/3Hb9uru7jSSzf//+2LG2tjYjybzxxhtjfi5br2F1dbW5//77445dffXVZsOGDQnbf/WrXzVXX3113LH77rvPLFiwIG01Xqhk+7hr1y4jybz77rsWqnOWJLN9+/Zx27jxGo6YTP/cfP2MMaa/v99IMnv27BmzTSauYU6PfCQSCoVUXFw85s97enrU19enpUuXxo4VFBTolltu0b59+2yUaMXu3btVUlKij33sY7r33nvV39+f6ZIc4bbr19bWJp/Pp+uvvz52bMGCBfL5fBPWm23X8OzZszp06FDcn70kLV26dMy+tLW1jWr/uc99TgcPHtQHH3yQtlpTlUofR8ybN0+BQEC33Xabdu3alc4yrXLbNUyVW69fKBSSpHG/9zJxDadU+Dh69Ki+973v6f777x+zTV9fnyRp1qxZccdnzZoV+5nbLVu2TP/2b/+ml19+WX//93+vAwcO6NZbb1UkEsl0aRfMbdevr69PJSUlo46XlJSMW282XsN33nlHQ0NDSf3Z9/X1JWz/4Ycf6p133klbralKpY+BQEBPP/20XnjhBW3btk1XXXWVbrvtNu3du9dGyWnntmuYLDdfP2OM1q1bpxtvvFGVlZVjtsvENXRl+HjkkUcS3gB07uvgwYNxnzl58qRqamp055136i/+4i8mPIfH44l7b4wZdSxdUulfMr7whS9o+fLlqqysVG1trX7yk5/oyJEjeumllxzsxdjS3T8ps9dPSq6PieqaqN5MX8PxJPtnn6h9ouPZJJk+XnXVVbr33ntVVVWlhQsX6qmnntLy5cv1ne98x0apVrjxGk6Wm6/fAw88oF/84hd67rnnJmxr+xpOS8tvTbMHHnhAX/ziF8dtM2fOnNj/PnnypBYvXqyFCxfq6aefHvdzfr9f0nASDAQCseP9/f2jkmG6JNu/CxUIBHTFFVfoV7/6lWO/czzp7F82XD9p8n38xS9+of/5n/8Z9bPf/OY3SdVr+xomctlllyk/P3/UCMB4f/Z+vz9h+2nTpmnmzJlpqzVVqfQxkQULFqi5udnp8jLCbdfQCW64fg8++KBefPFF7d27V5dffvm4bTNxDV0ZPi677DJddtllk2p74sQJLV68WPPnz9fWrVuVlzf+YE95ebn8fr927typefPmSRqe592zZ482bdp0wbVPRjL9c8KpU6fU29sb92WdTunsXzZcP2nyfVy4cKFCoZDa29tVXV0tSfr5z3+uUCikG264YdLns30NE5kxY4bmz5+vnTt36o477ogd37lzp26//faEn1m4cKFaWlrijv3sZz/Ttddeq+nTp6e13lSk0sdEOjs7M3qtnOS2a+iEbL5+xhg9+OCD2r59u3bv3q3y8vIJP5ORa5i2W1mzwIkTJ8zv//7vm1tvvdX893//twkGg7HXua666iqzbdu22Ptvf/vbxufzmW3btpnXXnvN3HXXXSYQCJhwOGy7CxM6duyY6ezsNA0NDeZ3fud3TGdnp+ns7DQDAwOxNuf2b2BgwHzlK18x+/btMz09PWbXrl1m4cKF5vd+7/dyon/GuOv6GWNMTU2N+dSnPmXa2tpMW1ub+eQnP2n+8A//MK6NW67hj370IzN9+nTz/e9/33R3d5u1a9eaSy65xLz99tvGGGM2bNhgVq1aFWv/61//2lx88cXm4YcfNt3d3eb73/++mT59uvn3f//3THVhQsn28bvf/a7Zvn27OXLkiOnq6jIbNmwwkswLL7yQqS6Ma2BgIPb3TJJ54oknTGdnpzl27Jgxxv3XMNn+ue361dXVGZ/PZ3bv3h33nff+++/H2mTDNczp8LF161YjKeHrXJLM1q1bY++j0aipr683fr/fFBQUmJtvvtm89tprlqufnNWrVyfs365du2Jtzu3f+++/b5YuXWp+93d/10yfPt3Mnj3brF692hw/fjwzHZhAsv0zxl3XzxhjTp06Ze655x5TWFhoCgsLzT333DPqsT43XcN//Md/NFdccYWZMWOGqaqqinvEb/Xq1eaWW26Ja797924zb948M2PGDDNnzhzT1NRkueLkJdPHTZs2mblz5xqv12s+8pGPmBtvvNG89NJLGah6ckYeLT3/tXr1amOM+69hsv1z2/Ub6zvv3P9GZsM19Pz/YgEAAKxw5dMuAADAvQgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArPp/aiJyWTMqzvcAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b4a9a44378e04a37a267d7fb14cce98e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.1, description='a', max=3.3000000000000003, min=-1.1), FloatSlider(v…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact(a=1.1, b=1.1, c=1.1)\n",
    "def plot_quad(a, b, c):\n",
    "    plt.scatter(x, y)\n",
    "    plot_function(mk_quad(a,b,c), ylim=(-3, 13))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_abs_err(preds, acts): return torch.abs(preds - acts).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "743b920c26fc408091ae6fde710cc05a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.1, description='a', max=3.3000000000000003, min=-1.1), FloatSlider(v…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact(a=1.1, b=1.1, c=1.1)\n",
    "def plot_quad(a, b, c):\n",
    "    f = mk_quad(a, b, c)\n",
    "    plt.scatter(x, y)\n",
    "    loss = mae(f(x), y)\n",
    "    plot_function(f, ylim=(-3, 12), title=f\"MAE: {loss.item():.2f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def quad_mae(params):\n",
    "    f = mk_quad(*params)\n",
    "    return mae(f(x), y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TensorBase(2.4219)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quad_mae([1.1, 1.1, 1.1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TensorBase(2.4219, grad_fn=<AliasBackward0>)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abc = torch.tensor([1.1, 1.1, 1.1], requires_grad=True)\n",
    "loss = quad_mae(abc)\n",
    "loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "loss.backward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-1.3529, -0.0316, -0.5000])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abc.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TensorBase(2.4010)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    abc -= 0.01*abc.grad\n",
    "    loss = quad_mae(abc)\n",
    "loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 TensorBase(2.4010, grad_fn=<AliasBackward0>)\n",
      "1 TensorBase(2.3594, grad_fn=<AliasBackward0>)\n",
      "2 TensorBase(2.2970, grad_fn=<AliasBackward0>)\n",
      "3 TensorBase(2.2137, grad_fn=<AliasBackward0>)\n",
      "4 TensorBase(2.1097, grad_fn=<AliasBackward0>)\n",
      "5 TensorBase(1.9848, grad_fn=<AliasBackward0>)\n",
      "6 TensorBase(1.8535, grad_fn=<AliasBackward0>)\n",
      "7 TensorBase(1.7166, grad_fn=<AliasBackward0>)\n",
      "8 TensorBase(1.5825, grad_fn=<AliasBackward0>)\n",
      "9 TensorBase(1.4628, grad_fn=<AliasBackward0>)\n"
     ]
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    loss = quad_mae(abc)\n",
    "    loss.backward()\n",
    "    with torch.no_grad(): abc -= 0.01*abc.grad\n",
    "    print(i, loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1.9634, 1.1381, 1.4100], requires_grad=True)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def rectified_linear_unit(m, b, x):\n",
    "    y = m*x + b\n",
    "    return torch.clip(y, 0)\n",
    "\n",
    "plot_function(partial(rectified_linear_unit, 1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XXiNE/ADvMADAM3zwgXTLLSZERo6UXn+dEPETvMsAAPuWLpVuvlkqKpJuv90scNawoe2pUE+IEQCAXcuXSzfdZELkD38wC5wRIn6FGAEA2PPRR9Lvfy+dOGEO0bzxBiHih4gRAIAdK1dKw4aZELnpJunNN6WAANtTwQJiBABQ/1atkoYOlQoLzZ6Rt94iRPwYMQIAqF+rV0tDhpgQufFGs9IqIeLXiBEAQP1JSZEGD5YKCkyQvPOO1KiR7algGTECAKgfa9dKN9wg/fKL+XPxYkIEkogRAEB9SE2VBg0yITJokFnyvXFj21PBQxAjAIC6lZYmXX+9dPy4+ZMQwa8QIwCAurN+/akQiY+X3n9fCgy0PRU8DDECAKgbn34qDRwo/fyz1L+/ufZMUJDtqeCBiBEAQO37xz/MnpD8fKlfP2nJEkIEFSJGAAC1a9MmacAA6dgxKTZWWrZMatLE9lTwYMQIAKD2bN5sDskcOyb16WMugkeI4AyIEQBA7fjXv0yIHD0q9e4tffihdNZZtqeCFyBGAAA1t2WLFBcnOZ1Sz54mRJo2tT0VvAQxAgComa1bzUmqeXnSNdeYq/E2a2Z7KngRYgQAUH0ZGSZEjhyRevQgRFAtxAgAoHq2bZOuu0766ScpJkb6+GMpONj2VPBCxAgAwH1ffGFC5PBh6corTYiEhNieCl7KrRhJSkpS9+7dFRwcrLCwMA0ZMkS7du064+vS09MVHR2toKAgtW/fXrNmzar2wAAAy776yqwfcuiQ1L27tGqVFBpqeyp4MbdiJD09XWPGjNHmzZuVkpKioqIixcXFKT8/v8LX7NmzRwMHDlTPnj2VkZGhSZMm6YEHHlBycnKNhwcA1LOvv5b69pVyc6Vu3aTVq6XmzW1PBS/ncLlcruq++ODBgwoLC1N6erp69epV7nMeffRRLV++XDt27CjdlpCQoO3bt2vTpk1V+j5Op1OhoaHKy8tTCLsBAcCOb74xC5kdOCB17SqtWSOdfbbtqeDBqvr7u0bnjOTl5UmSWrRoUeFzNm3apLi4uDLb+vfvry1btujEiRPlvqagoEBOp7PMDQBg0c6dZo/IgQPSZZdJKSmECGpNtWPE5XIpMTFR11xzjTp37lzh83JychQeHl5mW3h4uIqKipSbm1vua5KSkhQaGlp6i4yMrO6YAICa2rXL7BH58UepSxezR6SS/xMKuKvaMTJ27Fh98cUXWrRo0Rmf63A4yjw+eWTo19tPmjhxovLy8kpv+/btq+6YAICa+Pe/TYjk5EiXXmpCpGVL21PBxwRU50Xjxo3T8uXLtX79erVt27bS57Zu3Vo5OTllth04cEABAQFqWcH/oAMDAxUYGFid0QAAtWX3bhMi2dlS584mRFq1sj0VfJBbe0ZcLpfGjh2rDz74QOvWrVNUVNQZXxMTE6OUlJQy21avXq1u3bqpUaNG7k0LAKgf331nQmT/fqlTJ2ntWumcc2xPBR/lVoyMGTNGCxcu1Ntvv63g4GDl5OQoJydHx48fL33OxIkTNXLkyNLHCQkJ2rt3rxITE7Vjxw7NnTtXc+bM0YQJE2rvpwAA1J7vvzchkpUldexoQiQszPZU8GFuxcjMmTOVl5en3r17KyIiovS2ePHi0udkZ2crMzOz9HFUVJRWrlyptLQ0XXbZZXrmmWf00ksvadiwYbX3UwAAascPP5gQ2bdPuugiad066VcfQgBqW43WGakvrDMCAPVg717p2mvNnx06SKmpUkSE7angxeplnREAgI/IzJR69zYhcuGFZo8IIYJ6QowAgL/bt88cmvnhB+mCC8wekTZtbE8FP0KMAIA/+89/TIh8/710/vkmRH7zG9tTwc8QIwDgr7KyTIh8953Uvr0JkTOsHQXUBWIEAPzR/v0mRL79VoqKMiHCpTdgCTECAP4mO9tc9G73buncc02ItGtneyr4MWIEAPzJjz+aENm1ywRIaqoJEsAiYgQA/MXJENm505wbkppqDtEAlhEjAOAPDhyQYmOlb74xn5ZJSzMnrQIegBgBAF938KAJka+/NuuHpKWZj/ECHoIYAQBflpsrXXed9NVXZkXVtDSzsBngQYgRAPBVhw6ZEPniC6l1a3OOyIUX2p4KOA0xAgC+6PBhqV8/aft2c9Xd1FRz8TvAAxEjAOBrfvrJhEhGhhQWZi56d9FFtqcCKkSMAIAvOXLEhMjnn0vnnGNC5OKLbU8FVIoYAQBfkZcnxcVJW7dKrVpJa9dKnTrZngo4I2IEAHyB0yn17y999pnUsqW0Zo10ySW2pwKqhBgBAG/ndEoDBkj//KfUooUJkS5dbE8FVBkxAgDe7OhRKT5e2rRJOvtsEyKXXWZ7KsAtxAgAeKtjx6SBA6WNG6XmzaWUFOnyy21PBbiNGAEAb3QyRD79VAoNNSESHW17KqBaiBEA8Db5+dLvfidt2CCFhEirV0vdutmeCqg2YgQAvMnPP0uDBknp6VJwsAmRK66wPRVQI8QIAHiL48elG24wS7s3ayZ98ol05ZW2pwJqjBgBAG9w/Lg0eLBZyKxZM2nVKikmxvZUQK0gRgDA0/3yizR0qDlJtWlT6eOPpauvtj0VUGuIEQDwZAUF0o03mkMyZ50lrVwpXXON7amAWkWMAICnKiiQhg0ze0JOhkivXranAmodMQIAnqigQPr976UVK6QmTaSPPpKuvdb2VECdIEYAwNMUFko332wCJChI+vBDqU8f21MBdYYYAQBPcuKECZFly6TAQGn5cik21vZUQJ0iRgDAU5w4Id1yi7R0qQmRZcukfv1sTwXUOWIEADzBiRPSH/4gffCB1LixCZL+/W1PBdQLYgQAbCsqkm6/XXr/fRMiS5ZIAwbYngqoN8QIANhUVCSNGCG9+67UqJGUnGyuxgv4EWIEAGwpLpZGjZLeeceEyPvvm6vxAn6GGAEAG4qLpTvukN5+WwoIMHtGbrjB9lSAFcQIANS34mLprrukhQtPhciQIbanAqwhRgCgPpWUSPfcIy1YIDVsaA7RDB1qeyrAKmIEAOpLSYn0xz9K8+ebEHn7bXPtGcDPESMAUB9KSqT77pPmzpUaNJDeeku66SbbUwEegRgBgLpWUiKNHi29/roJkTffNEu+A5BEjABA3XK5pLFjpdmzJYdDeuMNs9IqgFJux8j69es1aNAgtWnTRg6HQ0uXLq30+WlpaXI4HKfddu7cWd2ZAcA7uFzSuHHSzJkmRObPNyutAigjwN0X5Ofnq0uXLrrzzjs1zI0Tr3bt2qWQkJDSx+ecc4673xoAvIfLJT34oDRjhgmROXOkkSNtTwV4JLdjJD4+XvHx8W5/o7CwMDVv3tzt1wGA13G5pPHjpZdfNo9ff1268067MwEerN7OGbn88ssVERGh2NhYpaamVvrcgoICOZ3OMjcA8Aoul/Tww9K0aebxa6+ZBc4AVKjOYyQiIkKzZ89WcnKyPvjgA3Xo0EGxsbFav359ha9JSkpSaGho6S0yMrKuxwSAmnO5pEcekV580Tx+9VWzwBmASjlcLper2i92OLRkyRINcXMZ40GDBsnhcGj58uXlfr2goEAFBQWlj51OpyIjI5WXl1fmvBMA8Bgul/TYY9Jzz5nHr7xiPs4L+DGn06nQ0NAz/v628tHeq666Srt3767w64GBgQoJCSlzAwCP5XJJkyefCpHp0wkRwA1WYiQjI0MRERE2vjUA1C6XS/rzn6WkJPP4pZekMWPszgR4Gbc/TXPs2DF9++23pY/37Nmjbdu2qUWLFmrXrp0mTpyorKwsLViwQJI0depUnXfeeerUqZMKCwu1cOFCJScnKzk5ufZ+CgCw5cknpWefNfenTjXrigBwi9sxsmXLFvXp06f0cWJioiRp1KhRmj9/vrKzs5WZmVn69cLCQk2YMEFZWVlq0qSJOnXqpBUrVmjgwIG1MD4AWPTUU9LTT5v7L7xg1hUB4LYancBaX6p6AgwA1Jv/9//M4RlJev55acIEu/MAHsijT2AFAK/2l7+cCpG//Y0QAWqIGAEAd/ztb+aTM5I5afWRR+zOA/gAYgQAqmrKFLOWiGQO05y8D6BGiBEAqIoXXpD+9Cdz/+mnT+0dAVBjxAgAnMnUqeZ6M5L0xBOnzhcBUCuIEQCozEsvmSvwSiZCnnjC7jyADyJGAKAi06efWjtk8mSzrojDYXcmwAcRIwBQnpkzT62m+thj0jPPECJAHSFGAODXXn1Vuv9+c/9PfzLrihAiQJ0hRgDgf732mpSQYO4//LBZV4QQAeoUMQIAJ82ZI917r7k/frxZ5p0QAeocMQIAkjRvnvTHP5r7Dz4o/f3vhAhQT4gRAHjjDenuuyWXy5y0+uKLhAhQj4gRAP7tzTelO+80IXL//dK0aYQIUM+IEQD+6623pDvuMCEyerRZV4QQAeodMQLAPy1aJI0cKZWUmJNWCRHAGmIEgP9ZvFi6/XYTIvfcYxY4a8B/DgFb+NcHwL+89550220mRO66yyxwRogAVvEvEID/SE6Wbr1VKi4254q89hohAngA/hUC8A9Llki33GJCZMQI6fXXCRHAQ/AvEYDvW7ZMuukmqajIHKKZN09q2ND2VAD+ixgB4Ns+/FAaPtyEyK23mgXOCBHAoxAjAHzXRx9Jw4ZJJ06YPSMLFhAigAciRgD4ppUrT4XI8OFmgbOAANtTASgHMQLA96xaJd14o1RYaIKEEAE8GjECwLesXi0NGSIVFEhDh5qVVhs1sj0VgEoQIwB8x5o10uDBJkQGD5beeYcQAbwAMQLAN6xbJw0aJP3yi/nz3Xelxo1tTwWgCogRAN4vLU363e9MiFx/vVnynRABvAYxAsC7paebADl+XBo40Cz5HhhoeyoAbiBGAHivDRtMiPz8szRgACECeCliBIB3+sc/pPh4KT9f6tfPXHsmKMj2VACqgRgB4H02bjR7QvLzpeuuM9eeIUQAr0WMAPAumzebEDl2TOrb14RIkya2pwJQA8QIAO/xr39J/ftLR49KffqYi+CddZbtqQDUEDECwDt89pkUFyc5ndK11xIigA8hRgB4vq1bTYjk5Uk9e5qr8TZtansqALWEGAHg2T7/3Hxa5sgR6eqrpRUrpGbNbE8FoBYRIwA817Zt5tMyP/0k9eghffyxFBxseyoAtYwYAeCZtm+XYmNNiFx1FSEC+DBiBIDn+fJLEyKHD0tXXCGtWiWFhNieCkAdIUYAeJavvjLrhxw6JHXvLn3yiRQaansqAHWIGAHgOb75xoRIbq4UHS2tXi01b257KgB1zO0YWb9+vQYNGqQ2bdrI4XBo6dKlZ3xNenq6oqOjFRQUpPbt22vWrFnVmRWAL/vmG7OQ2cGDUteuUkoKIQL4CbdjJD8/X126dNH06dOr9Pw9e/Zo4MCB6tmzpzIyMjRp0iQ98MADSk5OdntYAD5q506zR+TAAemyy0yInH227akA1JMAd18QHx+v+Pj4Kj9/1qxZateunaZOnSpJ6tixo7Zs2aIpU6Zo2LBh7n57AL5m1y6zR+THH6VLL5XWrJFatLA9FYB6VOfnjGzatElxcXFltvXv319btmzRiRMnyn1NQUGBnE5nmRsAH7R7twmRnBzpkkuktWulli1tTwWgntV5jOTk5Cg8PLzMtvDwcBUVFSk3N7fc1yQlJSk0NLT0FhkZWddjAqhv335rQiQ7W+rc2YRIq1a2pwJgQb18msbhcJR57HK5yt1+0sSJE5WXl1d627dvX53PCKAeffedCZGsLOnii02InHOO7akAWOL2OSPuat26tXJycspsO3DggAICAtSygt2xgYGBCgwMrOvRANjw/fcmRP7zH6ljR2ndOikszPZUACyq8z0jMTExSklJKbNt9erV6tatmxo1alTX3x6AJ/nhBxMi+/ZJF11kQuRXh3EB+B+3Y+TYsWPatm2btm3bJsl8dHfbtm3KzMyUZA6xjBw5svT5CQkJ2rt3rxITE7Vjxw7NnTtXc+bM0YQJE2rnJwDgHfbulXr3ljIzpd/+1oRI69a2pwLgAdw+TLNlyxb16dOn9HFiYqIkadSoUZo/f76ys7NLw0SSoqKitHLlSo0fP14zZsxQmzZt9NJLL/GxXsCfZGaaPSJ790oXXiilpkoREbanAuAhHK6TZ5N6MKfTqdDQUOXl5SmEi2UB3mXfPrNH5PvvpfPPl9LTpd/8xvZUAOpBVX9/c20aAHXnP/8xe0S+/15q397sESFEAPwKMQKgbmRlmSXev/tOiooyIcKaQQDKQYwAqH3795sQ2b1bOu88EyLt2tmeCoCHIkYA1K6cHBMi//63CZDUVOncc21PBcCDESMAas+PP5pzRHbtModk0tLMnhEAqAQxAqB2HDhg9ojs3Cm1bWv2iERF2Z4KgBcgRgDU3MGDJkS++cZ8WiY11XyMFwCqgBgBUDO5uVJsrPT112Yhs9RU6YILbE8FwIsQIwCq79Ah6brrpC+/PBUiF15oeyoAXoYYAVA9hw+bENm+3Vzsbt06qUMH21MB8ELECAD3/fSTCZFt26SwMLNH5KKLbE8FwEsRIwDcc+SI1K+flJEhnXOOCZGOHW1PBcCLESMAqu7IESkuTtq6VWrVyhyaufhi21MB8HLECICqycuTBgyQPvtMatnShEjnzranAuADiBEAZ+Z0mhD55z+lFi2ktWulSy6xPRUAH0GMAKjc0aNSfLy0ebN09tkmRLp0sT0VAB9CjACo2LFj0sCB0saNJkTWrJEuu8z2VAB8DDECoHz5+dL110uffio1by6lpEhdu9qeCoAPIkYAnO5kiKxfL4WGSqtXS9HRtqcC4KOIEQBl/fyzNGiQlJ4uhYRIn3wide9ueyoAPowYAXDK8ePSDTeYhcyCg02IXHml7akA+DhiBIBx/Lg0eLD5tEyzZiZErrrK9lQA/AAxAkD65RdpyBBzkmrTptKqVVJMjO2pAPgJYgTwd7/8Ig0dak5SbdpU+vhj6eqrbU8FwI8QI4A/KyiQhg0ze0LOOktauVLq2dP2VAD8DDEC+KuTIbJypdSkibRihdSrl+2pAPghYgTwR4WF0vDhJkCaNJE++kjq3dv2VAD8FDEC+JvCQummm6QPP5SCgsyfffvangqAHyNGAH9y4oR0yy3SsmVSYKC0fLkUG2t7KgB+jhgB/MWJE9Ktt0pLlpgQWbZM6tfP9lQAQIwAfqGoSLrtNik5WWrc2ARJ//62pwIAScQI4PuKiqQRI6T33pMaNZI++ECKj7c9FQCUIkYAX1ZUJI0cKb3zjgmR5GRzNV4A8CDECOCrioulO+6QFi2SAgLMnpFBg2xPBQCnIUYAX1RcLN15p/TWWyZE3n3XXAQPADwQMQL4muJi6e67pTfflBo2NIdohg61PRUAVIgYAXxJSYl0773SG2+YEFm0yCz5DgAejBgBfEVJiXTffdLcuVKDBuYQzfDhtqcCgDMiRgBfUFIijR4tvf66CZGFC6Wbb7Y9FQBUCTECeDuXSxo7Vpo924TIm2+alVYBwEsQI4A3c7mkBx6QZs6UHA5zrsgf/mB7KgBwCzECeCuXS3rwQWn6dBMi8+ZJt99ueyoAcBsxAngjl0saP156+WUTInPmSKNG2Z4KAKqlWjHyyiuvKCoqSkFBQYqOjtaGDRsqfG5aWpocDsdpt507d1Z7aMCvuVzShAnStGnm8WuvmQXOAMBLuR0jixcv1kMPPaTJkycrIyNDPXv2VHx8vDIzMyt93a5du5SdnV16u/DCC6s9NOC3XC7pkUekF14wj2fPNgucAYAXcztGXnjhBd19992655571LFjR02dOlWRkZGaOXNmpa8LCwtT69atS28NGzas9tCAX3K5pIkTpSlTzONZs6Q//tHuTABQC9yKkcLCQm3dulVxcXFltsfFxWnjxo2Vvvbyyy9XRESEYmNjlZqaWulzCwoK5HQ6y9wAv+ZySZMnS3/7m3k8Y4ZZ4AwAfIBbMZKbm6vi4mKFh4eX2R4eHq6cnJxyXxMREaHZs2crOTlZH3zwgTp06KDY2FitX7++wu+TlJSk0NDQ0ltkZKQ7YwK+xeWS/vxnKSnJPJ4+Xbr/frszAUAtCqjOixwOR5nHLpfrtG0ndejQQR06dCh9HBMTo3379mnKlCnq1atXua+ZOHGiEhMTSx87nU6CBP7rySelZ58196dNk8aMsToOANQ2t/aMtGrVSg0bNjxtL8iBAwdO21tSmauuukq7d++u8OuBgYEKCQkpcwP80tNPm5skvfiiWeAMAHyMWzHSuHFjRUdHKyUlpcz2lJQU9ejRo8p/T0ZGhiIiItz51oD/eeYZ6YknzP0pU6SHHrI6DgDUFbcP0yQmJmrEiBHq1q2bYmJiNHv2bGVmZiohIUGSOcSSlZWlBQsWSJKmTp2q8847T506dVJhYaEWLlyo5ORkJScn1+5PAviSv/xFevxxc/9vf5MeftjuPABQh9yOkZtvvlmHDh3S008/rezsbHXu3FkrV67UueeeK0nKzs4us+ZIYWGhJkyYoKysLDVp0kSdOnXSihUrNHDgwNr7KQBf8te/mk/OSOak1UcesTsPANQxh8vlctke4kycTqdCQ0OVl5fH+SPwbc89Jz36qLn/7LPSpEl25wGAGqjq72+uTQN4ir///VSIPPMMIQLAbxAjgCd48UVzvRnJfJT3//7P6jgAUJ+IEcC2adOkk+vqPP74qU/QAICfIEYAm6ZPP/WR3cmTzV4RAPAzxAhgy4wZ0rhx5v5jj5nzRCpYyRgAfBkxAtgwa5Y0dqy5/8gjZl0RQgSAnyJGgPo2e7Y0erS5//DDZl0RQgSAHyNGgPr0+uvSffeZ++PHS88/T4gA8HvECFBf5s6V7r3X3H/wQbOuCCECAMQIUC/mz5fuuUdyucxJqy++SIgAwH8RI0BdW7BAuusuEyL332/WFSFEAKAUMQLUpbfeku64w4RIQoJZV4QQAYAyiBGgrixaJI0caULk3nvNuiKECACchhgB6sLixdLtt0slJeZckZkzpQb8cwOA8vBfR6C2vfeedNttJkTuukt69VVCBAAqwX8hgdqUnCzdeqtUXCyNGiW99hohAgBnwH8lgdqyZIl0yy0mREaMkObMIUQAoAr4LyVQG5Ytk266SSoqModo5s2TGja0PRUAeAViBKipDz+Uhg83IfKHP0hvvEGIAIAbiBGgJj76SBo2TDpxwhyiIUQAwG3ECFBdK1eeCpHhw6U335QCAmxPBQBehxgBqmPVKunGG6XCQhMkb71FiABANREjgLtWr5aGDJEKCqShQ81Kq40a2Z4KALwWMQK4Y80aafBgEyJDhkjvvEOIAEANESNAVa1dKw0aJP3yi3TDDWbJ98aNbU8FAF6PGAGqIjX1VIj87nfSu+8SIgBQS4gR4EzS002AHD8uDRwovf++FBhoeyoA8BnECFCZ9etNgPz8szRggLn2DCECALWKGAEq8umnp0IkLs5ceyYoyPZUAOBziBGgPBs3SvHxUn6+dN110tKlhAgA1BFiBPi1zZvNIZljx6TYWHMRvCZNbE8FAD6LGAH+1z//KfXvLx09KvXpIy1fLp11lu2pAMCnESPASZ99Zs4NcTqla681V+MlRACgzhEjgCRt2SL162dCpFcvacUKqWlT21MBgF8gRoDPPzchkpcnXXMNIQIA9YwYgX/LyDCfljlyROrRQ1q5UmrWzPZUAOBXiBH4r+3bTYj89JMUEyN9/LEUHGx7KgDwO8QI/NMXX5iP7R4+LF1xhQmRkBDbUwGAXyJG4H+++sqEyKFDUrdu0iefSKGhtqcCAL9FjMC/fP211LevlJsrRUdLKSlS8+a2pwIAv0aMwH98840JkYMHpa5dCREA8BDECPzDzp0mRA4ckC67zITI2WfbngoAIGIE/mDXLrO0+48/Sl26SGvWSC1a2J4KAPBf1YqRV155RVFRUQoKClJ0dLQ2bNhQ6fPT09MVHR2toKAgtW/fXrNmzarWsIDb/v1vEyI5OdIll5gQadnS9lQAgP/hdowsXrxYDz30kCZPnqyMjAz17NlT8fHxyszMLPf5e/bs0cCBA9WzZ09lZGRo0qRJeuCBB5ScnFzj4YFK7d5tQiQ7W+rcWVq7VmrVyvZUAIBfcbhcLpc7L7jyyivVtWtXzZw5s3Rbx44dNWTIECUlJZ32/EcffVTLly/Xjh07SrclJCRo+/bt2rRpU5W+p9PpVGhoqPLy8hTCWhCoim+/lXr3lrKypIsvllJTpbAw21MBgF+p6u/vAHf+0sLCQm3dulWPPfZYme1xcXHauHFjua/ZtGmT4uLiymzr37+/5syZoxMnTqhRo0anvaagoEAFBQVlfpg6sWCBuS4JvF9hoVk35PBh8+d335mL3nXsKK1bR4gAgAdzK0Zyc3NVXFys8PDwMtvDw8OVk5NT7mtycnLKfX5RUZFyc3MVERFx2muSkpL01FNPuTNa9axaJS1aVPffB3ZcfLE5NPOr//0BADyLWzFyksPhKPPY5XKdtu1Mzy9v+0kTJ05UYmJi6WOn06nIyMjqjFq5wYOlqKja/3tR/wICzImpLVqc+vPyy6XGjW1PBgA4A7dipFWrVmrYsOFpe0EOHDhw2t6Pk1q3bl3u8wMCAtSygk81BAYGKjAw0J3Rqufmm80NAABY49anaRo3bqzo6GilpKSU2Z6SkqIePXqU+5qYmJjTnr969Wp169at3PNFAACAf3H7o72JiYl6/fXXNXfuXO3YsUPjx49XZmamEhISJJlDLCNHjix9fkJCgvbu3avExETt2LFDc+fO1Zw5czRhwoTa+ykAAIDXcvuckZtvvlmHDh3S008/rezsbHXu3FkrV67UueeeK0nKzs4us+ZIVFSUVq5cqfHjx2vGjBlq06aNXnrpJQ0bNqz2fgoAAOC13F5nxAbWGQEAwPtU9fc316YBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWub0cvA0nF4l1Op2WJwEAAFV18vf2mRZ794oYOXr0qCQpMjLS8iQAAMBdR48eVWhoaIVf94pr05SUlGj//v0KDg6Ww+GwMoPT6VRkZKT27dvH9XE8HO+Vd+H98h68V97FE94vl8ulo0ePqk2bNmrQoOIzQ7xiz0iDBg3Utm1b22NIkkJCQvhH6CV4r7wL75f34L3yLrbfr8r2iJzECawAAMAqYgQAAFhFjFRRYGCgnnjiCQUGBtoeBWfAe+VdeL+8B++Vd/Gm98srTmAFAAC+iz0jAADAKmIEAABYRYwAAACriBEAAGAVMeKmH374QXfffbeioqLUpEkTnX/++XriiSdUWFhoezRU4Nlnn1WPHj101llnqXnz5rbHwf945ZVXFBUVpaCgIEVHR2vDhg22R0I51q9fr0GDBqlNmzZyOBxaunSp7ZFQgaSkJHXv3l3BwcEKCwvTkCFDtGvXLttjnREx4qadO3eqpKREr776qr7++mu9+OKLmjVrliZNmmR7NFSgsLBQw4cP1+jRo22Pgv+xePFiPfTQQ5o8ebIyMjLUs2dPxcfHKzMz0/Zo+JX8/Hx16dJF06dPtz0KziA9PV1jxozR5s2blZKSoqKiIsXFxSk/P9/2aJXio7214Pnnn9fMmTP1/fff2x4FlZg/f74eeughHTlyxPYokHTllVeqa9eumjlzZum2jh07asiQIUpKSrI4GSrjcDi0ZMkSDRkyxPYoqIKDBw8qLCxM6enp6tWrl+1xKsSekVqQl5enFi1a2B4D8BqFhYXaunWr4uLiymyPi4vTxo0bLU0F+J68vDxJ8vjfUcRIDX333Xd6+eWXlZCQYHsUwGvk5uaquLhY4eHhZbaHh4crJyfH0lSAb3G5XEpMTNQ111yjzp072x6nUsTIfz355JNyOByV3rZs2VLmNfv379eAAQM0fPhw3XPPPZYm90/Veb/geRwOR5nHLpfrtG0Aqmfs2LH64osvtGjRItujnFGA7QE8xdixY3XLLbdU+pzzzjuv9P7+/fvVp08fxcTEaPbs2XU8HX7N3fcLnqVVq1Zq2LDhaXtBDhw4cNreEgDuGzdunJYvX67169erbdu2tsc5I2Lkv1q1aqVWrVpV6blZWVnq06ePoqOjNW/ePDVowA6m+ubO+wXP07hxY0VHRyslJUVDhw4t3Z6SkqLBgwdbnAzwbi6XS+PGjdOSJUuUlpamqKgo2yNVCTHipv3796t3795q166dpkyZooMHD5Z+rXXr1hYnQ0UyMzN1+PBhZWZmqri4WNu2bZMkXXDBBWrWrJnd4fxYYmKiRowYoW7dupXuYczMzOT8Kw907Ngxffvtt6WP9+zZo23btqlFixZq166dxcnwa2PGjNHbb7+tZcuWKTg4uHTvY2hoqJo0aWJ5ukq44JZ58+a5JJV7g2caNWpUue9Xamqq7dH83owZM1znnnuuq3Hjxq6uXbu60tPTbY+EcqSmppb7b2jUqFG2R8OvVPT7ad68ebZHqxTrjAAAAKs42QEAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArPr/UG69k2LCHT0AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch.nn.functional as F\n",
    "def relu(m, b, x): return F.relu(m*x + b)\n",
    "plot_function(partial(relu, 1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "499b4fa21f97445999e66c9af40b90df",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.5, description='m', max=4.5, min=-1.5), FloatSlider(value=1.5, descr…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact(m=1.5, b=1.5)\n",
    "def plot_relu(m, b):\n",
    "    plot_function(partial(relu, m, b), ylim=(-1, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "68a2e6fa8e114b60b3c91ed90c3753a0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=-1.5, description='m1', max=1.5, min=-4.5), FloatSlider(value=-1.5, de…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def double_relu(m1, b1, m2, b2, x):\n",
    "    return relu(m1, b1, x) + relu(m2, b2, x)\n",
    "\n",
    "@interact(m1=-1.5, b1=-1.5, m2=1.5, b2=1.5)\n",
    "def plot_double_relu(m1, b1, m2, b2):\n",
    "    plot_function(partial(double_relu, m1, b1, m2, b2), ylim=(-1,6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4e73a94c14c148b2abf07cde3f7fe1bb",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=-1.5, description='m1', max=1.5, min=-4.5), FloatSlider(value=-1.5, de…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def triple_relu(m1, b1, m2, b2, m3, b3, x):\n",
    "    return relu(m1, b1, x) + relu(m2, b2, x) + relu(m3, b3, x)\n",
    "\n",
    "@interact(m1=-1.5, b1=-1.5, m2=1.5, b2=1.5, m3=1.0, b3=1.0)\n",
    "def plot_triple_relu(m1, b1, m2, b2, m3, b3):\n",
    "    plt.scatter(x, y)\n",
    "    f = partial(triple_relu, m1, b1, m2, b2, m3, b3)\n",
    "    loss = mae(f(x), y)\n",
    "    plot_function(f, title=loss.item())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 TensorBase(2.7224, grad_fn=<AliasBackward0>)\n",
      "100 TensorBase(1.8033, grad_fn=<AliasBackward0>)\n",
      "200 TensorBase(1.9979, grad_fn=<AliasBackward0>)\n",
      "300 TensorBase(1.6558, grad_fn=<AliasBackward0>)\n",
      "400 TensorBase(1.6733, grad_fn=<AliasBackward0>)\n",
      "500 TensorBase(1.8834, grad_fn=<AliasBackward0>)\n",
      "600 TensorBase(1.1347, grad_fn=<AliasBackward0>)\n",
      "700 TensorBase(1.7659, grad_fn=<AliasBackward0>)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([-12.7721, -14.0227,   8.9719,  -6.0736,   2.3161, -14.8647],\n",
       "       requires_grad=True)"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "params = torch.tensor([-1.5, -1.5, 1.5, 1.5, 1.0, 1.0], requires_grad=True)\n",
    "for i in range(800):\n",
    "    f = partial(triple_relu, *params)\n",
    "    loss = mae(f(x), y)\n",
    "    loss.backward()\n",
    "    with torch.no_grad(): params -= 0.001*params.grad\n",
    "    if i % 100 == 0: print(i, loss)\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plot_function(partial(triple_relu, *params.detach()), title=loss.item())\n",
    "params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}