Chapter4 - Gradient Descent - Intro to Neural Learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compare: Does our network make good predictions?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.30250000000000005\n"
     ]
    }
   ],
   "source": [
    "knob_weight = 0.5\n",
    "input = 0.5\n",
    "goal_pred = 0.8\n",
    "\n",
    "pred = input * knob_weight\n",
    "error = (pred - goal_pred)^2\n",
    "println(error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What's the Simplest Form of Neural Learning?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Learning using the Hot and Cold Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.022499999999999975\n"
     ]
    }
   ],
   "source": [
    "# 1) An Empty Network\n",
    "\n",
    "weight = 0.1 \n",
    "lr = 0.01\n",
    "\n",
    "function neural_network(input, weight)\n",
    "    prediction = input * weight\n",
    "    return prediction\n",
    "end\n",
    "\n",
    "\n",
    "# 2) PREDICT: Making A Prediction And Evaluating Error\n",
    "\n",
    "number_of_toes = [8.5]\n",
    "win_or_lose_binary = [1] #(won!!!)\n",
    "\n",
    "input = number_of_toes[1]\n",
    "True = win_or_lose_binary[1]\n",
    "\n",
    "pred = neural_network(input,weight)\n",
    "error = (pred - True) ^ 2\n",
    "println(error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.004224999999999993\n"
     ]
    }
   ],
   "source": [
    "# 3) COMPARE: Making A Prediction With a *Higher* Weight And Evaluating Error\n",
    "\n",
    "weight = 0.1 \n",
    "\n",
    "function neural_network(input, weight)\n",
    "    prediction = input * weight\n",
    "    return prediction\n",
    "end\n",
    "\n",
    "number_of_toes = [8.5]\n",
    "win_or_lose_binary = [1] #(won!!!)\n",
    "\n",
    "input = number_of_toes[1]\n",
    "True = win_or_lose_binary[1]\n",
    "\n",
    "lr = 0.01\n",
    "p_up = neural_network(input,weight+lr)\n",
    "e_up = (p_up - True) ^ 2\n",
    "println(e_up)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.05522499999999994\n"
     ]
    }
   ],
   "source": [
    "# 4) COMPARE: Making A Prediction With a *Lower* Weight And Evaluating Error\n",
    "\n",
    "weight = 0.1 \n",
    "\n",
    "function neural_network(input, weight)\n",
    "    prediction = input * weight\n",
    "    return prediction\n",
    "end\n",
    "\n",
    "number_of_toes = [8.5]\n",
    "win_or_lose_binary = [1] #(won!!!)\n",
    "\n",
    "input = number_of_toes[1]\n",
    "True = win_or_lose_binary[1]\n",
    "\n",
    "lr = 0.01\n",
    "p_dn = neural_network(input,weight-lr)\n",
    "e_dn = (p_dn - True) ^ 2\n",
    "println(e_dn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hot and Cold Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error:0.30250000000000005 Prediction:0.25\n",
      "Error:0.3019502500000001 Prediction:0.2505\n",
      "Error:0.30140100000000003 Prediction:0.251\n",
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    {
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     "output_type": "stream",
     "text": [
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      "Error:0.009702250000004338 Prediction:0.701499999999978\n",
      "Error:0.009604000000004326 Prediction:0.701999999999978\n",
      "Error:0.009506250000004315 Prediction:0.7024999999999779\n",
      "Error:0.009409000000004303 Prediction:0.7029999999999779\n",
      "Error:0.009312250000004291 Prediction:0.7034999999999778\n",
      "Error:0.00921600000000428 Prediction:0.7039999999999778\n",
      "Error:0.009120250000004267 Prediction:0.7044999999999777\n",
      "Error:0.009025000000004255 Prediction:0.7049999999999776\n",
      "Error:0.008930250000004244 Prediction:0.7054999999999776\n",
      "Error:0.008836000000004231 Prediction:0.7059999999999775\n",
      "Error:0.008742250000004219 Prediction:0.7064999999999775\n",
      "Error:0.008649000000004207 Prediction:0.7069999999999774\n",
      "Error:0.008556250000004194 Prediction:0.7074999999999774\n",
      "Error:0.008464000000004182 Prediction:0.7079999999999773\n",
      "Error:0.00837225000000417 Prediction:0.7084999999999773\n",
      "Error:0.008281000000004157 Prediction:0.7089999999999772\n",
      "Error:0.008190250000004144 Prediction:0.7094999999999771\n",
      "Error:0.008100000000004132 Prediction:0.7099999999999771\n",
      "Error:0.008010250000004118 Prediction:0.710499999999977\n",
      "Error:0.007921000000004105 Prediction:0.710999999999977\n",
      "Error:0.007832250000004091 Prediction:0.7114999999999769\n",
      "Error:0.007744000000004078 Prediction:0.7119999999999769\n",
      "Error:0.007656250000004064 Prediction:0.7124999999999768\n",
      "Error:0.007569000000004051 Prediction:0.7129999999999768\n",
      "Error:0.007482250000004037 Prediction:0.7134999999999767\n",
      "Error:0.0073960000000040235 Prediction:0.7139999999999767\n",
      "Error:0.00731025000000401 Prediction:0.7144999999999766\n",
      "Error:0.007225000000003996 Prediction:0.7149999999999765\n",
      "Error:0.007140250000003981 Prediction:0.7154999999999765\n",
      "Error:0.007056000000003967 Prediction:0.7159999999999764\n",
      "Error:0.006972250000003953 Prediction:0.7164999999999764\n",
      "Error:0.006889000000003938 Prediction:0.7169999999999763\n",
      "Error:0.006806250000003923 Prediction:0.7174999999999763\n",
      "Error:0.006724000000003908 Prediction:0.7179999999999762\n",
      "Error:0.006642250000003893 Prediction:0.7184999999999762\n",
      "Error:0.006561000000003879 Prediction:0.7189999999999761\n",
      "Error:0.006480250000003863 Prediction:0.719499999999976\n",
      "Error:0.006400000000003848 Prediction:0.719999999999976\n",
      "Error:0.006320250000003833 Prediction:0.7204999999999759\n",
      "Error:0.006241000000003817 Prediction:0.7209999999999759\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error:0.006162250000003802 Prediction:0.7214999999999758\n",
      "Error:0.006084000000003786 Prediction:0.7219999999999758\n",
      "Error:0.006006250000003771 Prediction:0.7224999999999757\n",
      "Error:0.005929000000003755 Prediction:0.7229999999999757\n",
      "Error:0.005852250000003739 Prediction:0.7234999999999756\n",
      "Error:0.005776000000003723 Prediction:0.7239999999999756\n",
      "Error:0.005700250000003707 Prediction:0.7244999999999755\n",
      "Error:0.00562500000000369 Prediction:0.7249999999999754\n",
      "Error:0.005550250000003674 Prediction:0.7254999999999754\n",
      "Error:0.005476000000003658 Prediction:0.7259999999999753\n",
      "Error:0.005402250000003641 Prediction:0.7264999999999753\n",
      "Error:0.005329000000003624 Prediction:0.7269999999999752\n",
      "Error:0.005256250000003607 Prediction:0.7274999999999752\n",
      "Error:0.00518400000000359 Prediction:0.7279999999999751\n",
      "Error:0.005112250000003573 Prediction:0.7284999999999751\n",
      "Error:0.0050410000000035565 Prediction:0.728999999999975\n",
      "Error:0.004970250000003539 Prediction:0.729499999999975\n",
      "Error:0.004900000000003521 Prediction:0.7299999999999749\n",
      "Error:0.004830250000003504 Prediction:0.7304999999999748\n",
      "Error:0.004761000000003486 Prediction:0.7309999999999748\n",
      "Error:0.004692250000003469 Prediction:0.7314999999999747\n",
      "Error:0.004624000000003451 Prediction:0.7319999999999747\n",
      "Error:0.0045562500000034326 Prediction:0.7324999999999746\n",
      "Error:0.004489000000003415 Prediction:0.7329999999999746\n",
      "Error:0.0044222500000033966 Prediction:0.7334999999999745\n",
      "Error:0.004356000000003378 Prediction:0.7339999999999745\n",
      "Error:0.00429025000000336 Prediction:0.7344999999999744\n",
      "Error:0.0042250000000033415 Prediction:0.7349999999999743\n",
      "Error:0.004160250000003323 Prediction:0.7354999999999743\n",
      "Error:0.0040960000000033045 Prediction:0.7359999999999742\n",
      "Error:0.004032250000003285 Prediction:0.7364999999999742\n",
      "Error:0.003969000000003267 Prediction:0.7369999999999741\n",
      "Error:0.003906250000003247 Prediction:0.7374999999999741\n",
      "Error:0.003844000000003228 Prediction:0.737999999999974\n",
      "Error:0.003782250000003209 Prediction:0.738499999999974\n",
      "Error:0.0037210000000031896 Prediction:0.7389999999999739\n",
      "Error:0.00366025000000317 Prediction:0.7394999999999738\n",
      "Error:0.0036000000000031506 Prediction:0.7399999999999738\n",
      "Error:0.0035402500000031307 Prediction:0.7404999999999737\n",
      "Error:0.003481000000003111 Prediction:0.7409999999999737\n",
      "Error:0.0034222500000030912 Prediction:0.7414999999999736\n",
      "Error:0.003364000000003071 Prediction:0.7419999999999736\n",
      "Error:0.003306250000003051 Prediction:0.7424999999999735\n",
      "Error:0.0032490000000030307 Prediction:0.7429999999999735\n",
      "Error:0.0031922500000030104 Prediction:0.7434999999999734\n",
      "Error:0.0031360000000029897 Prediction:0.7439999999999733\n",
      "Error:0.003080250000002969 Prediction:0.7444999999999733\n",
      "Error:0.0030250000000029485 Prediction:0.7449999999999732\n",
      "Error:0.0029702500000029276 Prediction:0.7454999999999732\n",
      "Error:0.0029160000000029067 Prediction:0.7459999999999731\n",
      "Error:0.002862250000002886 Prediction:0.7464999999999731\n",
      "Error:0.0028090000000028648 Prediction:0.746999999999973\n",
      "Error:0.0027562500000028437 Prediction:0.747499999999973\n",
      "Error:0.002704000000002822 Prediction:0.7479999999999729\n",
      "Error:0.002652250000002801 Prediction:0.7484999999999729\n",
      "Error:0.002601000000002779 Prediction:0.7489999999999728\n",
      "Error:0.0025502500000027573 Prediction:0.7494999999999727\n",
      "Error:0.0025000000000027357 Prediction:0.7499999999999727\n",
      "Error:0.0024502500000027137 Prediction:0.7504999999999726\n",
      "Error:0.0024010000000026918 Prediction:0.7509999999999726\n",
      "Error:0.0023522500000026695 Prediction:0.7514999999999725\n",
      "Error:0.0023040000000026472 Prediction:0.7519999999999725\n",
      "Error:0.002256250000002625 Prediction:0.7524999999999724\n",
      "Error:0.0022090000000026025 Prediction:0.7529999999999724\n",
      "Error:0.00216225000000258 Prediction:0.7534999999999723\n",
      "Error:0.0021160000000025572 Prediction:0.7539999999999722\n",
      "Error:0.0020702500000025345 Prediction:0.7544999999999722\n",
      "Error:0.0020250000000025118 Prediction:0.7549999999999721\n",
      "Error:0.0019802500000024887 Prediction:0.7554999999999721\n",
      "Error:0.0019360000000024655 Prediction:0.755999999999972\n",
      "Error:0.0018922500000024423 Prediction:0.756499999999972\n",
      "Error:0.0018490000000024188 Prediction:0.7569999999999719\n",
      "Error:0.0018062500000023956 Prediction:0.7574999999999719\n",
      "Error:0.001764000000002372 Prediction:0.7579999999999718\n",
      "Error:0.0017222500000023482 Prediction:0.7584999999999718\n",
      "Error:0.0016810000000023245 Prediction:0.7589999999999717\n",
      "Error:0.0016402500000023007 Prediction:0.7594999999999716\n",
      "Error:0.0016000000000022767 Prediction:0.7599999999999716\n",
      "Error:0.0015602500000022525 Prediction:0.7604999999999715\n",
      "Error:0.0015210000000022283 Prediction:0.7609999999999715\n",
      "Error:0.001482250000002204 Prediction:0.7614999999999714\n",
      "Error:0.0014440000000021794 Prediction:0.7619999999999714\n",
      "Error:0.001406250000002155 Prediction:0.7624999999999713\n",
      "Error:0.0013690000000021302 Prediction:0.7629999999999713\n",
      "Error:0.0013322500000021056 Prediction:0.7634999999999712\n",
      "Error:0.0012960000000020806 Prediction:0.7639999999999711\n",
      "Error:0.0012602500000020557 Prediction:0.7644999999999711\n",
      "Error:0.0012250000000020305 Prediction:0.764999999999971\n",
      "Error:0.0011902500000020052 Prediction:0.765499999999971\n",
      "Error:0.00115600000000198 Prediction:0.7659999999999709\n",
      "Error:0.0011222500000019546 Prediction:0.7664999999999709\n",
      "Error:0.0010890000000019291 Prediction:0.7669999999999708\n",
      "Error:0.0010562500000019033 Prediction:0.7674999999999708\n",
      "Error:0.0010240000000018776 Prediction:0.7679999999999707\n",
      "Error:0.0009922500000018517 Prediction:0.7684999999999707\n",
      "Error:0.0009610000000018258 Prediction:0.7689999999999706\n",
      "Error:0.0009302500000017998 Prediction:0.7694999999999705\n",
      "Error:0.0009000000000017735 Prediction:0.7699999999999705\n",
      "Error:0.0008702500000017472 Prediction:0.7704999999999704\n",
      "Error:0.0008410000000017208 Prediction:0.7709999999999704\n",
      "Error:0.0008122500000016942 Prediction:0.7714999999999703\n",
      "Error:0.0007840000000016676 Prediction:0.7719999999999703\n",
      "Error:0.0007562500000016409 Prediction:0.7724999999999702\n",
      "Error:0.000729000000001614 Prediction:0.7729999999999702\n",
      "Error:0.000702250000001587 Prediction:0.7734999999999701\n",
      "Error:0.0006760000000015599 Prediction:0.77399999999997\n",
      "Error:0.0006502500000015327 Prediction:0.77449999999997\n",
      "Error:0.0006250000000015054 Prediction:0.7749999999999699\n",
      "Error:0.0006002500000014781 Prediction:0.7754999999999699\n",
      "Error:0.0005760000000014506 Prediction:0.7759999999999698\n",
      "Error:0.0005522500000014229 Prediction:0.7764999999999698\n",
      "Error:0.0005290000000013951 Prediction:0.7769999999999697\n",
      "Error:0.0005062500000013673 Prediction:0.7774999999999697\n",
      "Error:0.00048400000000133937 Prediction:0.7779999999999696\n",
      "Error:0.0004622500000013113 Prediction:0.7784999999999695\n",
      "Error:0.0004410000000012831 Prediction:0.7789999999999695\n",
      "Error:0.0004202500000012548 Prediction:0.7794999999999694\n",
      "Error:0.0004000000000012264 Prediction:0.7799999999999694\n",
      "Error:0.0003802500000011979 Prediction:0.7804999999999693\n",
      "Error:0.00036100000000116925 Prediction:0.7809999999999693\n",
      "Error:0.0003422500000011405 Prediction:0.7814999999999692\n",
      "Error:0.0003240000000011117 Prediction:0.7819999999999692\n",
      "Error:0.00030625000000108273 Prediction:0.7824999999999691\n",
      "Error:0.00028900000000105366 Prediction:0.782999999999969\n",
      "Error:0.0002722500000010245 Prediction:0.783499999999969\n",
      "Error:0.00025600000000099523 Prediction:0.7839999999999689\n",
      "Error:0.00024025000000096582 Prediction:0.7844999999999689\n",
      "Error:0.0002250000000009363 Prediction:0.7849999999999688\n",
      "Error:0.0002102500000009067 Prediction:0.7854999999999688\n",
      "Error:0.00019600000000087698 Prediction:0.7859999999999687\n",
      "Error:0.00018225000000084715 Prediction:0.7864999999999687\n",
      "Error:0.0001690000000008172 Prediction:0.7869999999999686\n",
      "Error:0.00015625000000078716 Prediction:0.7874999999999686\n",
      "Error:0.000144000000000757 Prediction:0.7879999999999685\n",
      "Error:0.0001322500000007267 Prediction:0.7884999999999684\n",
      "Error:0.00012100000000069633 Prediction:0.7889999999999684\n",
      "Error:0.00011025000000066583 Prediction:0.7894999999999683\n",
      "Error:0.00010000000000063523 Prediction:0.7899999999999683\n",
      "Error:9.025000000060451e-5 Prediction:0.7904999999999682\n",
      "Error:8.100000000057368e-5 Prediction:0.7909999999999682\n",
      "Error:7.225000000054275e-5 Prediction:0.7914999999999681\n",
      "Error:6.40000000005117e-5 Prediction:0.7919999999999681\n",
      "Error:5.625000000048055e-5 Prediction:0.792499999999968\n",
      "Error:4.9000000000449285e-5 Prediction:0.792999999999968\n",
      "Error:4.225000000041791e-5 Prediction:0.7934999999999679\n",
      "Error:3.6000000000386424e-5 Prediction:0.7939999999999678\n",
      "Error:3.0250000000354826e-5 Prediction:0.7944999999999678\n",
      "Error:2.500000000032312e-5 Prediction:0.7949999999999677\n",
      "Error:2.0250000000291302e-5 Prediction:0.7954999999999677\n",
      "Error:1.6000000000259378e-5 Prediction:0.7959999999999676\n",
      "Error:1.225000000022734e-5 Prediction:0.7964999999999676\n",
      "Error:9.000000000195194e-6 Prediction:0.7969999999999675\n",
      "Error:6.250000000162936e-6 Prediction:0.7974999999999675\n",
      "Error:4.000000000130569e-6 Prediction:0.7979999999999674\n",
      "Error:2.2500000000980924e-6 Prediction:0.7984999999999673\n",
      "Error:1.000000000065505e-6 Prediction:0.7989999999999673\n",
      "Error:2.5000000003280753e-7 Prediction:0.7994999999999672\n"
     ]
    }
   ],
   "source": [
    "weight = 0.5\n",
    "input = 0.5\n",
    "goal_prediction = 0.8\n",
    "\n",
    "step_amount = 0.001\n",
    "\n",
    "for iteration=1:1100\n",
    "\n",
    "    prediction = input * weight\n",
    "    error = (prediction - goal_prediction) ^ 2\n",
    "\n",
    "    println(\"Error:\" * string(error) * \" Prediction:\" * string(prediction))\n",
    "    \n",
    "    up_prediction = input * (weight + step_amount)\n",
    "    up_error = (goal_prediction - up_prediction) ^ 2\n",
    "\n",
    "    down_prediction = input * (weight - step_amount)\n",
    "    down_error = (goal_prediction - down_prediction) ^ 2\n",
    "\n",
    "    if(down_error < up_error)\n",
    "        weight = weight - step_amount\n",
    "    end\n",
    "        \n",
    "    if(down_error > up_error)\n",
    "        weight = weight + step_amount\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating Both Direction and Amount from Error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error:0.30250000000000005 Prediction:0.25\n",
      "Error:0.17015625000000004 Prediction:0.3875\n",
      "Error:0.095712890625 Prediction:0.49062500000000003\n",
      "Error:0.05383850097656251 Prediction:0.56796875\n",
      "Error:0.03028415679931642 Prediction:0.6259765625\n",
      "Error:0.0170348381996155 Prediction:0.669482421875\n",
      "Error:0.00958209648728372 Prediction:0.70211181640625\n",
      "Error:0.005389929274097089 Prediction:0.7265838623046875\n",
      "Error:0.0030318352166796153 Prediction:0.7449378967285156\n",
      "Error:0.0017054073093822882 Prediction:0.7587034225463867\n",
      "Error:0.0009592916115275371 Prediction:0.76902756690979\n",
      "Error:0.0005396015314842384 Prediction:0.7767706751823426\n",
      "Error:0.000303525861459885 Prediction:0.7825780063867569\n",
      "Error:0.00017073329707118678 Prediction:0.7869335047900676\n",
      "Error:9.603747960254256e-5 Prediction:0.7902001285925507\n",
      "Error:5.402108227642978e-5 Prediction:0.7926500964444131\n",
      "Error:3.038685878049206e-5 Prediction:0.7944875723333098\n",
      "Error:1.7092608064027242e-5 Prediction:0.7958656792499823\n",
      "Error:9.614592036015323e-6 Prediction:0.7968992594374867\n",
      "Error:5.408208020258491e-6 Prediction:0.7976744445781151\n"
     ]
    }
   ],
   "source": [
    "weight = 0.5\n",
    "goal_pred = 0.8\n",
    "input = 0.5\n",
    "\n",
    "for iteration=1:20\n",
    "    pred = input * weight\n",
    "    error = (pred - goal_pred) ^ 2\n",
    "    direction_and_amount = (pred - goal_pred) * input\n",
    "    weight = weight - direction_and_amount\n",
    "\n",
    "    println(\"Error:\" * string(error) * \" Prediction:\" * string(pred))\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# One Iteration of Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 0.8, 0.5)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1) An Empty Network\n",
    "\n",
    "weight = 0.1 \n",
    "alpha = 0.01\n",
    "\n",
    "function neural_network(input, weight)\n",
    "    prediction = input * weight\n",
    "    return prediction\n",
    "end\n",
    "\n",
    "# 2) PREDICT: Making A Prediction And Evaluating Error\n",
    "\n",
    "number_of_toes = [8.5]\n",
    "win_or_lose_binary = [1] # (won!!!)\n",
    "\n",
    "input = number_of_toes[1]\n",
    "goal_pred = win_or_lose_binary[1]\n",
    "\n",
    "pred = neural_network(input,weight)\n",
    "error = (pred - goal_pred) ^ 2\n",
    "\n",
    "# 3) COMPARE: Calculating \"Node Delta\" and Putting it on the Output Node\n",
    "\n",
    "delta = pred - goal_pred\n",
    "\n",
    "# 4) LEARN: Calculating \"Weight Delta\" and Putting it on the Weight\n",
    "\n",
    "weight_delta = input * delta\n",
    "\n",
    "# 5) LEARN: Updating the Weight\n",
    "\n",
    "alpha = 0.01 # fixed before training\n",
    "weight -= weight_delta * alpha\n",
    "\n",
    "weight, goal_pred, input = (0.0, 0.8, 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning is just Reducing Error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error:0.6400000000000001 Prediction:0.0\n",
      "Error:0.3600000000000001 Prediction:0.2\n",
      "Error:0.2025 Prediction:0.35000000000000003\n",
      "Error:0.11390625000000001 Prediction:0.4625\n"
     ]
    }
   ],
   "source": [
    "for iteration=1:4\n",
    "    \n",
    "    pred = input * weight\n",
    "    error = (pred - goal_pred) ^ 2\n",
    "    delta = pred - goal_pred\n",
    "    weight_delta = delta * input\n",
    "    weight = weight - weight_delta\n",
    "    println(\"Error:\" * string(error) * \" Prediction:\" * string(pred))\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's Watch Several Steps of Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----\n",
      "Weight:0.0\n",
      "Error:0.6400000000000001 Prediction:0.0\n",
      "Delta:-0.8 Weight Delta:-0.8800000000000001\n",
      "-----\n",
      "Weight:0.8800000000000001\n",
      "Error:0.02822400000000005 Prediction:0.9680000000000002\n",
      "Delta:0.16800000000000015 Weight Delta:0.1848000000000002\n",
      "-----\n",
      "Weight:0.6951999999999999\n",
      "Error:0.0012446784000000064 Prediction:0.76472\n",
      "Delta:-0.03528000000000009 Weight Delta:-0.0388080000000001\n",
      "-----\n",
      "Weight:0.734008\n",
      "Error:5.4890317439999896e-5 Prediction:0.8074088\n",
      "Delta:0.007408799999999993 Weight Delta:0.008149679999999992\n"
     ]
    }
   ],
   "source": [
    "weight, goal_pred, input = (0.0, 0.8, 1.1)\n",
    "\n",
    "for iteration=1:4\n",
    "    println(\"-----\\nWeight:\" * string(weight))\n",
    "    pred = input * weight\n",
    "    error = (pred - goal_pred) ^ 2\n",
    "    delta = pred - goal_pred\n",
    "    weight_delta = delta * input\n",
    "    weight = weight - weight_delta\n",
    "    println(\"Error:\" * string(error) * \" Prediction:\" * string(pred))\n",
    "    println(\"Delta:\" * string(delta) * \" Weight Delta:\" * string(weight_delta))\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Why does this work? What really is weight_delta?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error:0.30250000000000005 Prediction:0.25\n",
      "Error:0.17015625000000004 Prediction:0.3875\n",
      "Error:0.095712890625 Prediction:0.49062500000000003\n",
      "Error:0.05383850097656251 Prediction:0.56796875\n",
      "Error:0.03028415679931642 Prediction:0.6259765625\n",
      "Error:0.0170348381996155 Prediction:0.669482421875\n",
      "Error:0.00958209648728372 Prediction:0.70211181640625\n",
      "Error:0.005389929274097089 Prediction:0.7265838623046875\n",
      "Error:0.0030318352166796153 Prediction:0.7449378967285156\n",
      "Error:0.0017054073093822882 Prediction:0.7587034225463867\n",
      "Error:0.0009592916115275371 Prediction:0.76902756690979\n",
      "Error:0.0005396015314842384 Prediction:0.7767706751823426\n",
      "Error:0.000303525861459885 Prediction:0.7825780063867569\n",
      "Error:0.00017073329707118678 Prediction:0.7869335047900676\n",
      "Error:9.603747960254256e-5 Prediction:0.7902001285925507\n",
      "Error:5.402108227642978e-5 Prediction:0.7926500964444131\n",
      "Error:3.038685878049206e-5 Prediction:0.7944875723333098\n",
      "Error:1.7092608064027242e-5 Prediction:0.7958656792499823\n",
      "Error:9.614592036015323e-6 Prediction:0.7968992594374867\n",
      "Error:5.408208020258491e-6 Prediction:0.7976744445781151\n"
     ]
    }
   ],
   "source": [
    "weight = 0.5\n",
    "goal_pred = 0.8\n",
    "input = 0.5\n",
    "\n",
    "for iteration = 1:20\n",
    "    pred = input * weight\n",
    "    error = (pred - goal_pred) ^ 2\n",
    "    direction_and_amount = (pred - goal_pred) * input\n",
    "    weight = weight - direction_and_amount\n",
    "\n",
    "    println(\"Error:\" * string(error) * \" Prediction:\" * string(pred))\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to use a Derivative to Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error:0.6400000000000001 Prediction:0.0\n",
      "Error:0.02822400000000005 Prediction:0.9680000000000002\n",
      "Error:0.0012446784000000064 Prediction:0.76472\n",
      "Error:5.4890317439999896e-5 Prediction:0.8074088\n"
     ]
    }
   ],
   "source": [
    "weight = 0.0\n",
    "goal_pred = 0.8\n",
    "input = 1.1\n",
    "\n",
    "for iteration =1:4\n",
    "    pred = input * weight\n",
    "    error = (pred - goal_pred) ^ 2\n",
    "    delta = pred - goal_pred\n",
    "    weight_delta = delta * input\n",
    "    weight = weight - weight_delta\n",
    "\n",
    "    println(\"Error:\" * string(error) * \" Prediction:\" * string(pred))\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Breaking Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error:0.30250000000000005 Prediction:0.25\n",
      "Error:0.17015625000000004 Prediction:0.3875\n",
      "Error:0.095712890625 Prediction:0.49062500000000003\n",
      "Error:0.05383850097656251 Prediction:0.56796875\n",
      "Error:0.03028415679931642 Prediction:0.6259765625\n",
      "Error:0.0170348381996155 Prediction:0.669482421875\n",
      "Error:0.00958209648728372 Prediction:0.70211181640625\n",
      "Error:0.005389929274097089 Prediction:0.7265838623046875\n",
      "Error:0.0030318352166796153 Prediction:0.7449378967285156\n",
      "Error:0.0017054073093822882 Prediction:0.7587034225463867\n",
      "Error:0.0009592916115275371 Prediction:0.76902756690979\n",
      "Error:0.0005396015314842384 Prediction:0.7767706751823426\n",
      "Error:0.000303525861459885 Prediction:0.7825780063867569\n",
      "Error:0.00017073329707118678 Prediction:0.7869335047900676\n",
      "Error:9.603747960254256e-5 Prediction:0.7902001285925507\n",
      "Error:5.402108227642978e-5 Prediction:0.7926500964444131\n",
      "Error:3.038685878049206e-5 Prediction:0.7944875723333098\n",
      "Error:1.7092608064027242e-5 Prediction:0.7958656792499823\n",
      "Error:9.614592036015323e-6 Prediction:0.7968992594374867\n",
      "Error:5.408208020258491e-6 Prediction:0.7976744445781151\n"
     ]
    }
   ],
   "source": [
    "weight = 0.5\n",
    "goal_pred = 0.8\n",
    "input = 0.5\n",
    "\n",
    "for iteration =1:20\n",
    "    pred = input * weight\n",
    "    error = (pred - goal_pred) ^ 2\n",
    "    delta = pred - goal_pred\n",
    "    weight_delta = input * delta\n",
    "    weight = weight - weight_delta\n",
    "    println(\"Error:\" * string(error) * \" Prediction:\" * string(pred))\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error:0.03999999999999998 Prediction:1.0\n",
      "Error:0.3599999999999998 Prediction:0.20000000000000018\n",
      "Error:3.2399999999999984 Prediction:2.5999999999999996\n",
      "Error:29.159999999999986 Prediction:-4.599999999999999\n",
      "Error:262.4399999999999 Prediction:16.999999999999996\n",
      "Error:2361.959999999998 Prediction:-47.79999999999998\n",
      "Error:21257.639999999978 Prediction:146.59999999999994\n",
      "Error:191318.75999999983 Prediction:-436.5999999999998\n",
      "Error:1.721868839999999e6 Prediction:1312.9999999999995\n",
      "Error:1.5496819559999991e7 Prediction:-3935.799999999999\n",
      "Error:1.3947137603999993e8 Prediction:11810.599999999997\n",
      "Error:1.2552423843599997e9 Prediction:-35428.59999999999\n",
      "Error:1.1297181459239996e10 Prediction:106288.99999999999\n",
      "Error:1.0167463313315994e11 Prediction:-318863.79999999993\n",
      "Error:9.150716981984395e11 Prediction:956594.5999999997\n",
      "Error:8.235645283785954e12 Prediction:-2.869780599999999e6\n",
      "Error:7.412080755407356e13 Prediction:8.609344999999996e6\n",
      "Error:6.670872679866621e14 Prediction:-2.5828031799999986e7\n",
      "Error:6.00378541187996e15 Prediction:7.748409859999996e7\n",
      "Error:5.403406870691965e16 Prediction:-2.324522925999999e8\n"
     ]
    }
   ],
   "source": [
    "# Now let's break it:\n",
    "\n",
    "weight = 0.5\n",
    "goal_pred = 0.8\n",
    "input = 2\n",
    "\n",
    "for iteration =1:20\n",
    "    pred = input * weight\n",
    "    error = (pred - goal_pred) ^ 2\n",
    "    delta = pred - goal_pred\n",
    "    weight_delta = input * delta\n",
    "    weight = weight - weight_delta\n",
    "    println(\"Error:\" * string(error) * \" Prediction:\" * string(pred))\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error:0.03999999999999998 Prediction:1.0\n",
      "Error:0.0144 Prediction:0.92\n",
      "Error:0.005183999999999993 Prediction:0.872\n",
      "Error:0.0018662400000000014 Prediction:0.8432000000000001\n",
      "Error:0.0006718464000000028 Prediction:0.8259200000000001\n",
      "Error:0.00024186470400000033 Prediction:0.815552\n",
      "Error:8.70712934399997e-5 Prediction:0.8093312\n",
      "Error:3.134566563839939e-5 Prediction:0.80559872\n",
      "Error:1.1284439629823931e-5 Prediction:0.803359232\n",
      "Error:4.062398266736526e-6 Prediction:0.8020155392\n",
      "Error:1.4624633760252567e-6 Prediction:0.8012093235200001\n",
      "Error:5.264868153690924e-7 Prediction:0.8007255941120001\n",
      "Error:1.8953525353291194e-7 Prediction:0.8004353564672001\n",
      "Error:6.82326912718715e-8 Prediction:0.8002612138803201\n",
      "Error:2.456376885786678e-8 Prediction:0.8001567283281921\n",
      "Error:8.842956788836216e-9 Prediction:0.8000940369969153\n",
      "Error:3.1834644439835434e-9 Prediction:0.8000564221981492\n",
      "Error:1.1460471998340758e-9 Prediction:0.8000338533188895\n",
      "Error:4.125769919393652e-10 Prediction:0.8000203119913337\n",
      "Error:1.485277170987127e-10 Prediction:0.8000121871948003\n"
     ]
    }
   ],
   "source": [
    "weight = 0.5\n",
    "goal_pred = 0.8\n",
    "input = 2\n",
    "alpha = 0.1\n",
    "\n",
    "for iteration =1:20\n",
    "    pred  = input * weight\n",
    "    error = (pred - goal_pred) ^ 2\n",
    "    derivative = input * (pred - goal_pred)\n",
    "    weight = weight - (alpha * derivative)\n",
    "    println(\"Error:\" * string(error) * \" Prediction:\" * string(pred))\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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