rnn toy code - korean comment

rnn_tutorial-Copy2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Anyone Can Learn To Code an LSTM-RNN in Python (Part 1: RNN)\n",
    "\n",
    "원문링크: https://iamtrask.github.io/2015/11/15/anyone-can-code-lstm/ \n",
    "- 간단한 toy code를 통해 RNN을 이해해본다.\n",
    "- 바이트 연산 - 더하기를 구하는 것이다. \n",
    "\n",
    "바이트 연산으로 3 + 4 = 7 이 되는 것을 RNN으로 해볼 것이다.\n",
    "각 2진수의 자리 연산마다 **carry** 값이 있을 것인데, carry는 결국 이전의 연산 결과들 정보들 묶음이다. \n",
    "이것이 바로 **hidden memory**라 보면 된다. \n",
    "\n",
    "   0000 0011(b) + 0000 0100(b) = 0000 0111(b) 이다. \n",
    "\n",
    "    각 time step에 input은 두개이다. 가장 낮은 자리수 부터 1개씩\n",
    "\t가장 낮은 자리수인 맨 오른쪽부터 더해갈 것이며, carry 값을 기억할 것이다. \n",
    "\t\n",
    "\t두개의 input은 forward propagation 되어 hidden layer로 들어갈 것이고,\n",
    "\thidden layer는 carry 값이 있는지 없는지를 기억할 것이다. \n",
    "\t\n",
    "    prediction은 이 모든 정보들을 바탕으로 각 자릿수 (= time step)의 값을 예측할 것이다. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# numpy와 copy를 import 하고 random 값의 seed를 심는다\n",
    "# copy는 object를 복제하는데 쓰인다 https://pymotw.com/2/copy/\n",
    "import copy, numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "np.random.seed(0)\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# utility 함수들 구현\n",
    "# 시그모이드 함수 구현\n",
    "def sigmoid(x):\n",
    "    output = 1 / (1 + np.exp(-x))\n",
    "    return output\n",
    "\n",
    "# convert output of sigmoid function to its derivative\n",
    "# 시그모이드 함수의 미분\n",
    "# http://math.stackexchange.com/questions/78575/derivative-of-sigmoid-function-sigma-x-frac11e-x\n",
    "def sigmoid_output_to_derivative(output):\n",
    "    return output * (1 - output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## train set을 만들자\n",
    "\n",
    "- 랜덤한 값 2개를 만들고 더한 값을 train set으로 한다. \n",
    "- 이렇게 계속 랜덤하게 생성하도록 한다"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# train set을 위한 lookup table을 만든다. dictionary로 1:00000001 이런 식으로 미리 만들어두는 것\n",
    "int2binary = {}  # lookup table 이다.\n",
    "binary_dim = 8  # 이진수는 최대 8자리. 이걸 넘어가진 않는다고 제한해두자. toy code 잖아?\n",
    "largest_number = pow(2, binary_dim)  # 따라서 최대값은 2^8 -1 이 되겠지? 1 0000 0000 - 1 = 1111 1111\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 이제 lookup table을 채워넣자\n",
    "\n",
    "우선 binary에 2진수 값을 만들어서 넣어주자\n",
    "    - numpy.unpackbits 는 숫자를 2진수 리스트로 만들어준다. 예를 들어 [7] 을 [ 0,0,0,0,1,1,1,1]로 바꿔준다.\n",
    "    - https://docs.scipy.org/doc/numpy/reference/generated/numpy.unpackbits.html\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 1 1 1 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "# numpy.unpackbits 테스트\n",
    "print(np.unpackbits(np.array([63], dtype=np.uint8)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1. Just range()\n",
      "(256,) [  0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17\n",
      "  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35\n",
      "  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53\n",
      "  54  55  56  57  58  59  60  61  62  63  64  65  66  67  68  69  70  71\n",
      "  72  73  74  75  76  77  78  79  80  81  82  83  84  85  86  87  88  89\n",
      "  90  91  92  93  94  95  96  97  98  99 100 101 102 103 104 105 106 107\n",
      " 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125\n",
      " 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143\n",
      " 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161\n",
      " 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179\n",
      " 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197\n",
      " 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215\n",
      " 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233\n",
      " 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251\n",
      " 252 253 254 255]\n",
      "2. 2-d list\n",
      "(1, 256) [[  0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17\n",
      "   18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35\n",
      "   36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53\n",
      "   54  55  56  57  58  59  60  61  62  63  64  65  66  67  68  69  70  71\n",
      "   72  73  74  75  76  77  78  79  80  81  82  83  84  85  86  87  88  89\n",
      "   90  91  92  93  94  95  96  97  98  99 100 101 102 103 104 105 106 107\n",
      "  108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125\n",
      "  126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143\n",
      "  144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161\n",
      "  162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179\n",
      "  180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197\n",
      "  198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215\n",
      "  216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233\n",
      "  234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251\n",
      "  252 253 254 255]]\n",
      "transpose\n",
      "(256, 1) [[  0]\n",
      " [  1]\n",
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      " [254]\n",
      " [255]]\n",
      "np.unpackbits\n",
      "(256, 8) [[0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 1]\n",
      " [0 0 0 ..., 0 1 0]\n",
      " ..., \n",
      " [1 1 1 ..., 1 0 1]\n",
      " [1 1 1 ..., 1 1 0]\n",
      " [1 1 1 ..., 1 1 1]]\n"
     ]
    }
   ],
   "source": [
    "# 0 부터 우리가 다룰 최대값(largest_number-1)까지의 숫자를 2진수의 리스트로 변환해두자\n",
    "# 눈으로 알아보기 쉽게 단계별로 본다\n",
    "\n",
    "# range만 해도 리스트를 만든다\n",
    "binary = np.array(range(largest_number), dtype = np.uint8)\n",
    "print(\"1. Just range()\")\n",
    "print(binary.shape, binary)\n",
    "\n",
    "# range만 해도 리스트를 만드는데 다시 []를 먹였으니 리스트가 2개인게 보인다.\n",
    "binary = np.array([range(largest_number)], dtype = np.uint8)\n",
    "print(\"2. 2-d list\")\n",
    "print(binary.shape, binary)\n",
    "\n",
    "# 이걸 transpose 해준다. \n",
    "binary = binary.T\n",
    "print('transpose')\n",
    "print(binary.shape, binary)\n",
    "\n",
    "# 마지막으로 np.unpackbits 를 먹인다. \n",
    "print('np.unpackbits')\n",
    "binary = np.unpackbits(np.array([range(largest_number)], dtype = np.uint8).T, axis=1)\n",
    "print(binary.shape, binary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 이제 딕셔너리에 넣어주자\n",
    "\n",
    "    - 이러면 int2binary[2] 라고 하면 2의 binary 모양인 [0,0,0,0,0,0,1,0] 를 토해내게 된다.\n",
    "    - 애써 이렇게 할 필요는 없는데 편의, 잘 보여지게 하려고 이렇게 구현함\n",
    "    \n",
    "    - 위에서 (256,8) 형태의 list를 만들었고 이걸 딕셔너리에 넣어보자"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{}\n",
      "[0 0 0 0 0 0 1 1]\n",
      "[0 0 0 0 0 0 1 1]\n"
     ]
    }
   ],
   "source": [
    "int2binary = {}\n",
    "print(int2binary)  # 초기에는 아무것도 없는 딕셔너리\n",
    "print(binary[3])\n",
    "\n",
    "# 값을 채우고\n",
    "for i in range(largest_number):\n",
    "    int2binary[i] = binary[i]\n",
    "\n",
    "print(int2binary[3]) # 테스트 삼아 출력해보자"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 하이퍼 파라미터들\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 32) (32, 1) (32, 32)\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.1 # learning_rate\n",
    "input_node_num = 2 # 우리는 이진수 두 개의 같은 자리 값을 입력으로 넣는다\n",
    "\n",
    "# hidden 계층의 노드는 16개로 하였다. 이것이 carry 정보를 저장할 것이다. \n",
    "# 현재 8자리의 이진수를 다루니 hidden 계층이 16개면 충분할듯 하다. 이 값을 변경해가며 \n",
    "# 얼마나 빨리 최종값을 찾아가는지 테스트 해보자\n",
    "\n",
    "hidden_node_num = 32\n",
    "output_node_num = 1  # 각 자리수의 결과값이 여기에 온다\n",
    "\n",
    "# ------------------------------------------------------------\n",
    "# initialize neural network weights\n",
    "# weight 값들을 정해 준다. \n",
    "# [0.0, 1.0) 사이의 랜덤으로 만든 값들에 2를 곱해주고 1을 빼준다. 따라서 [-1, 1.0) 값이 생성된다. \n",
    "# http://terms.naver.com/entry.nhn?docId=3404970&cid=47324&categoryId=47324\n",
    "# np.random.random은 [0,0, 1.0) 의 값을 생성해준다. half open interval 이라 하는데 간단히 0.0 <= y < 1.0 이다.\n",
    "# 값들을 여러개 생성하면 continueous uniform하게 만들어준다.\n",
    "w0 = 2 * np.random.random((input_node_num, hidden_node_num)) - 1\n",
    "w1 = 2 * np.random.random((hidden_node_num, output_node_num)) - 1\n",
    "wh = 2 * np.random.random((hidden_node_num, hidden_node_num)) - 1\n",
    "\n",
    "print (w0.shape, w1.shape, wh.shape )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# wieght를 업데이트 하기 위한 용도의 공간도 잡아둔다. shape는 똑같겠지?\n",
    "w0_update = np.zeros_like(w0)\n",
    "w1_update = np.zeros_like(w1)\n",
    "wh_update = np.zeros_like(wh)\n",
    "\n",
    "# display 용도\n",
    "overallError_history = list()\n",
    "accuracy = list()\n",
    "accuracy_history = list()\n",
    "accuracy_count = 0\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 드디어 train 시작\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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b5LS9gFfijr0MjE7pJsqGSKqGDq2dEQkhcSCyzTZeM6JAREQkbUURiJjZEDNb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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7bace10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2Bzp7aP9j4ZjUtLxTR5LKkzecLAO26qF9a3re/0RqCsU7dXY3oktSbnnDyT3A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\n2x74Etn08GVkw9vXRMSylNI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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb4c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w0\n",
      "[[ -5.97219869e-01  -6.93597312e-02  -2.57455491e+00  -3.38378563e-01\n",
      "   -1.75749040e-01  -5.82257908e-01   3.88239564e-01   2.03845153e+00\n",
      "    1.33880856e+00  -2.08366535e-01   8.32917253e-01  -4.08539232e-01\n",
      "    2.82378048e-01   1.51573543e+00  -2.43849466e+00  -1.23134703e+00\n",
      "   -1.92579965e+00   6.65879843e-01   4.87520755e-01   7.37217805e-01\n",
      "    4.03825849e+00   6.34330343e-01   5.43585756e-01   6.94832806e+00\n",
      "   -1.27649075e+00   6.18754173e-01  -1.65014761e+00   8.48479058e-01\n",
      "   -1.09173990e-01   3.31809878e+00  -1.01095355e+00   3.79923857e-01]\n",
      " [ -4.92614010e-01  -6.17747884e-01  -3.10070668e+00   6.71369599e-02\n",
      "   -1.69272036e-02  -1.14028929e-02   6.83258110e-01   2.37409066e+00\n",
      "   -1.59791426e+00  -5.19008430e-01   7.41306391e-01  -1.58697401e+00\n",
      "    1.34308990e+00   1.89399687e+00  -2.12704082e+00  -1.15843902e+00\n",
      "   -1.39411472e+00  -7.44535016e-01   4.69992808e-03  -8.94550615e-01\n",
      "    3.68999419e+00  -1.52946971e+00   4.12465184e-01  -4.77673016e+00\n",
      "    4.79399958e-01  -1.22110097e+00  -4.46814352e-01  -1.07264996e+00\n",
      "   -7.78655194e-02  -5.34434513e+00   9.94657729e-01  -5.35011563e-01]]\n",
      "w1\n",
      "[[-0.40203081]\n",
      " [-0.20858175]\n",
      " [ 2.00193935]\n",
      " [-0.64166139]\n",
      " [ 0.14068508]\n",
      " [-0.92960608]\n",
      " [ 0.90596415]\n",
      " [-1.30554002]\n",
      " [ 1.44947462]\n",
      " [-0.023537  ]\n",
      " [ 0.87768472]\n",
      " [-0.87518944]\n",
      " [-0.79981158]\n",
      " [-1.36386235]\n",
      " [-3.4657257 ]\n",
      " [-0.90771114]\n",
      " [-2.18094468]\n",
      " [ 0.35250633]\n",
      " [-0.61857497]\n",
      " [ 0.98407444]\n",
      " [ 7.28277928]\n",
      " [ 0.22230544]\n",
      " [ 0.02060729]\n",
      " [-8.7460741 ]\n",
      " [-0.18035806]\n",
      " [ 0.56899046]\n",
      " [-0.71097144]\n",
      " [ 0.27254687]\n",
      " [-0.63771425]\n",
      " [ 5.7176397 ]\n",
      " [-1.24998507]\n",
      " [ 0.01120062]]\n",
      "wh\n",
      "[[ 0.00430491 -1.0803049   0.96438529 ..., -0.26030016 -1.07330931\n",
      "  -0.43713244]\n",
      " [ 0.16542268 -0.58333964  0.6072552  ..., -0.38021943 -0.28907004\n",
      "  -0.91605346]\n",
      " [ 0.32570138 -0.0763639   1.10606754 ..., -1.36006557 -0.22646215\n",
      "  -0.58308475]\n",
      " ..., \n",
      " [ 0.5573387   0.71178216  0.97842055 ..., -0.85758885  0.61467915\n",
      "  -0.55362447]\n",
      " [-0.57556552  0.28414698  0.98473092 ..., -0.04423211 -0.85713938\n",
      "   0.3047269 ]\n",
      " [ 0.76408938  0.01895369  0.12118621 ..., -1.27924919  0.64584885\n",
      "   0.62476619]]\n"
     ]
    }
   ],
   "source": [
    "for j in range(10000): # 10000번 돌린다\n",
    "    \n",
    "    # a, b를 생성하고 두 값을 더한 c를 계산한다.\n",
    "    # 복잡성을 줄이기 위해(=우리는 toy code를 짜고 있잖아?) \n",
    "    # a, b는 largest_number 의 절반 - 1 크기의 랜덤 정수값이다. 따라서 a + b < largest_number\n",
    "\n",
    "    a_int = np.random.randint(largest_number / 2)\n",
    "    a = int2binary[a_int]\n",
    "\n",
    "    b_int = np.random.randint(largest_number / 2)\n",
    "    b = int2binary[b_int]\n",
    "\n",
    "    # 입력값 a, b를 임의 생성했으니  정답인 c도 확보해두자(=label. 따라서 우리는 supervised learning 중이다)\n",
    "    c_int = a_int + b_int\n",
    "    c = int2binary[c_int]\n",
    "\n",
    "    # c에는 정답이 들어있고, predict_binary에는 우리 네트워크가 예측한 값을 넣어두자.\n",
    "    d = np.zeros_like(c)\n",
    "\n",
    "    overallError = 0  # 에러값을 저장할 공간\n",
    "\n",
    "    # 각 time step마다 output_layer의 미분값과 hidden_layer의 값을 추적할 리스트이다.\n",
    "    output_layer_deltas = list()\n",
    "    hidden_layer_values = list()\n",
    "\n",
    "    # output_layer_deltas 에는 생성한 값을 넣으면 되지만\n",
    "    # hidden_layer_values 처음에는 이전 hidden이 없으니 0으로 한다\n",
    "    hidden_layer_values.append(np.zeros(hidden_node_num))\n",
    "\n",
    "    # forward propagation 부터\n",
    "    #---------------------------------------------------------------\n",
    "    # 여기서부터 각 자리수별로 NN을 돌린다\n",
    "    #---------------------------------------------------------------\n",
    "    # 낮은 자리수부터 각 자리수별로 for 문을 돌면서 수행한다.\n",
    "    for position in range(binary_dim):\n",
    "\n",
    "        # 입력값과 정답(=label)을 각각 X와 y에 써넣자\n",
    "        X = np.array([[a[binary_dim - position-1], b[binary_dim - position-1]]])\n",
    "        y = np.array([[c[binary_dim - position-1]]]).T\n",
    "        \n",
    "     \n",
    "        # hidden layer 연산부 (input ~+ prev_hidden) 이 부분이 RNN의 매우 중요한 부분이다\n",
    "        # hidden layer 연산이다. input X와 weight_input_hidden(=W0) 을 곱해주고,\n",
    "        # 이전의(= -1 = 가장 마지막의) hidden layer 값과 Wweight_hidden_hidden(=Wh)를 곱해준다.\n",
    "        # 그리고 두 값을 더한뒤 sigmoid 먹여준다. 더해준다는 것이 중요하다\n",
    "        hidden_layer = sigmoid(np.dot(X, w0) + np.dot(hidden_layer_values[-1], wh))\n",
    "\n",
    "        # output layer (new binary representation)\n",
    "        # output layer는 이렇게 나온 hidden_layer 값과 weight_hidden_output(= W1) 값을 곱해준뒤 sigmoid 해준다\n",
    "        output_layer = sigmoid(np.dot(hidden_layer, w1))\n",
    "\n",
    "        # 정답과 예측값을 비교해서 loss를 계산해보자\n",
    "        # 일치하면 0, 틀리면 절대값이 1일 것이다. \n",
    "        output_layer_error = y - output_layer  \n",
    "\n",
    "        # 우선 sigmoid에 대한 미분값만을 계산하고 저장하자. \n",
    "        output_layer_deltas.append((output_layer_error) * sigmoid_output_to_derivative(output_layer))\n",
    "\n",
    "        # 에러율 저장\n",
    "        overallError += np.abs(output_layer_error[0])\n",
    "\n",
    "        # 예측값 저장하기. sigmoid 결과값이니 \n",
    "        d[binary_dim - position - 1] = np.round(output_layer[0][0])\n",
    "\n",
    "        '''\n",
    "        if (j == 9999):\n",
    "            print (\"hidden_layer.shape: \", hidden_layer.shape)\n",
    "            print (\"output_layer_error.shape: \", output_layer_error.shape)\n",
    "            print (\"output_layer.shape: \", output_layer.shape)\n",
    "            print (\"output_layer: \", output_layer)\n",
    "            print (\"-------------------------------\")\n",
    "        '''\n",
    "        \n",
    "        # 계산한 hidden_layer는 다음 자리수 계산을 위해 보관해두자\n",
    "        hidden_layer_values.append(copy.deepcopy(hidden_layer))\n",
    "\n",
    "        # 루프를 다 돌면 모든 자리수에 대한 forward propagation 완료된 것\n",
    "\n",
    "    # 미분을 위해서는 그 다음 상위 hidden_layer에서의 미분값이 필요한데 없으므로 0을 채워놓음\n",
    "    future_hidden_layer_delta = np.zeros(hidden_node_num)\n",
    "    \n",
    "    # display 용도\n",
    "    if (j % 100 == 0):\n",
    "        overallError_history.append(overallError[0])\n",
    "        \n",
    "    # 이제 backward propagation\n",
    "    \n",
    "    for position in range(binary_dim):\n",
    "\n",
    "        ##################################################################################\n",
    "        #일단 보관해뒀던 값들을 다 꺼낸다\n",
    "\n",
    "        X = np.array([[a[position], b[position]]])  # 이번엔 맨 왼쪽의 가장 높은 자리수부터 계산해야겠지?\n",
    "        hidden_layer = hidden_layer_values[-position - 1]  # 가장 나중 time step의 hidden layer의 값을 꺼내고\n",
    "        prev_hidden_layer = hidden_layer_values[-position - 2] # 그 하나전의 prev hidden layer의 값도 꺼낸다\n",
    "\n",
    "        # error at output layer\n",
    "        # 현재 자릿수의 output layer의 미분한 값값\n",
    "        output_layer_delta = output_layer_deltas[-position - 1]\n",
    "\n",
    "        ##################################################################################\n",
    "        # error at hidden layer\n",
    "        # 이제 현재 자리수의(=현재 time step)의 hidden layer의 미분값을 계산한다\n",
    "\n",
    "        # 다음 layer에서 내려오는 값과 weight_hidden_(=Wh) 값을 곱하고\n",
    "        # output layer의 미분값과 synapse_1(=W1)값을 곱한 값을 다시 layer_1의 미분값과 곱해준다.\n",
    "        # 이부분은 어렵다. 차근히 봐야겠다\n",
    "        hidden_layer_delta = (future_hidden_layer_delta.dot(wh.T) \\\n",
    "                              + output_layer_delta.dot(w1.T)) * sigmoid_output_to_derivative(hidden_layer)\n",
    "\n",
    "        # let's update all our weights so we can try again\n",
    "        # 이제 weight 값들을 업데이트 해줄 시간이다.\n",
    "        w1_update += np.atleast_2d(hidden_layer).T.dot(output_layer_delta)\n",
    "        wh_update += np.atleast_2d(prev_hidden_layer).T.dot(hidden_layer_delta)\n",
    "        w0_update += X.T.dot(hidden_layer_delta)\n",
    "\n",
    "        future_hidden_layer_delta = hidden_layer_delta\n",
    "\n",
    "    # 모두 다 업데이트 해준다. alpha 라는 learning_rate에 맞춰서 update\n",
    "    # 이렇게 모든 자리수의 backpropagation이 끝난뒤에 update 하는 것이다.\n",
    "\n",
    "    w1 += w1_update * alpha\n",
    "    w0 += w0_update * alpha\n",
    "    wh += wh_update * alpha\n",
    "\n",
    "    # 그리고 다시 초기화\n",
    "    w1_update *= 0\n",
    "    w0_update *= 0\n",
    "    wh_update *= 0\n",
    "\n",
    "    ##################################################################################\n",
    "    #  진행사항 저장\n",
    "    #  참인지 저깃인지를 계속 체크\n",
    "    check = np.equal(d,c)\n",
    "    #print(\"check:\", np.sum(check), binary_dim)\n",
    "    if (np.sum(check) == binary_dim):  # 같은 것 개수가 8개면 참이다\n",
    "        accuracy_count += 1\n",
    "    \n",
    "    # 100번마다 accuracy에서 값을 찾는다. \n",
    "    if (j % 100 == 0):\n",
    "        #print(\"accuracy_count\", accuracy_count)\n",
    "        accuracy_history.append(accuracy_count)\n",
    "        accuracy_count = 0\n",
    "    \n",
    "    ##################################################################################\n",
    "    #  print out progress\n",
    "    #  1000번마다 중간 진행 사항을 update 하자\n",
    "    '''\n",
    "    if (j % 1000 == 0):\n",
    "        print (\"Error:\" + str(overallError))\n",
    "        print (\"Pred:\" + str(d))  # 예측값\n",
    "        print (\"True:\" + str(c))  # 실제값\n",
    "\n",
    "        final_check = np.equal(d,c)\n",
    "        print (np.sum(final_check) == binary_dim)\n",
    "\n",
    "        out = 0\n",
    "\n",
    "        for index, x in enumerate(reversed(d)):\n",
    "            out += x * pow(2, index)\n",
    "        print (str(a_int) + \" + \" + str(b_int) + \" = \" + str(out))\n",
    "        print (\"------------\")\n",
    "    '''\n",
    "    \n",
    "    \n",
    "x_range = range(100)\n",
    "plt.plot(x_range, overallError_history, 'r-')\n",
    "plt.ylabel('overallError')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.plot(x_range, accuracy_history, 'b-')\n",
    "plt.ylabel('accuracy_history')\n",
    "plt.show()\n",
    "\n",
    "print(\"w0\")\n",
    "print(w0)\n",
    "print(\"w1\")\n",
    "print(w1)\n",
    "print(\"wh\")\n",
    "print(wh)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
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