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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# GANs (Generative Adversarial Networks)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 정보 엔트로피Information Entropy\n",
+    "<hr/>\n",
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "어떤 확률변수 $X$와 확률분포 $P(X=x)$가 있을 때 확률변수값을 예측하기 위해 고려해야할 정보의 양을 나타내기 위한 개념으로 엔트로피를 사용합니다. 예측을 위해 고려해야할 사항이 많다면, 즉, 불확실성이 크다면 엔트로피는 큰것입니다. 시스템의 질서가 너무 잘 잡혀 있어서 쉽게 예측 가능하다면 무질서도가 낮아 엔트로피가 낮은 것입니다. 정보이론에서 이를 어떻게 정의하는지 실례를 들어 간단하게 알아보도록 하겠습니다. \n",
+    "아래 내용은 <a href=\"https://ko.khanacademy.org/computing/computer-science/informationtheory/moderninfotheory/v/information-entropy\">칸아카데미 정보엔트로피 강의</a> [1]를 참고하여 작성하였습니다. \n",
+    "<br/>\n",
+    "어떤 시스템이 1, 2, 3, 4를 출력하는데 숫자 4개가 아래 그림처럼 배치되어 있고, 한번에 해당 숫자에 불 들어온다고 합시다. 1000번정도 시행해 봤더니 1, 2, 3, 4 모두 딱 250번씩 출력했다고 가정합니다. 이 시스템은 1, 2, 3, 4 라는 실수값에 함수값 0.25를 할당하는 확률질량함수 $P(X)$를 확률 분포로 가지는 이산확률변수 $X$ 라고 할수 있습니다.  1001번째 숫자가 출력 되었을 때 이 숫자가 무엇인지 알아내기 위해 우리는 어떤 것을 고려해야 할까요? 다시 말해 어떤 질문들을 던져야 할까요? 가장 쉽게는 1인가요? 2인가요? 3인가요? 라고 3번 묻는다면 그중 한번은 정답을 줄것입니다. 운이 좋다면 한번에 맞추고 운이 나쁘다면 3번이나 질문을 해야 합니다. 하지만 시스템은 정확히 동일한 확률로 숫자를 출력하므로 이렇게 물어 볼 수 있습니다. \n",
+    "<br/>\n",
+    "<img src=\"1.png\" width=\"200\">\n",
+    "<b>\n",
+    "[1] 지금 출력된 숫자가 위쪽 두개인가요?  \n",
+    "[2] 왼쪽에 있는 숫자인가요?\n",
+    "</b>\n",
+    "<br/><br/>\n",
+    "예를 들어 출력된 숫자가 1이라고 하면 1번 질문에 예라고 대답할 것이고, 이어서 2번 질문에 예라고 답할 것이므로 우리는 1번이 출력되었음을 알 수 있습니다. 4를 출력했다면 1번 질문에 아니오, 2번 질문에 아니오라고 대답할 것이므로 역시 4번이 출력되었음을 알 수 있습니다. 즉, 위와 같이 질문을 하면 1, 2, 3, 4 모든 숫자에 대해 질문 2번만에 현재 출력된 숫자를 정확히 예측할 수 있습니다. 또는 질문을 \"[1] 1 또는 2 입니까?\" [1]에 대해서 예라면 \"[2] 1입니까?\" 아니오라면 \"[2] 3입니까?\"로 하여도 결과는 동일합니다. \n",
+    "<br/>\n",
+    "<img src=\"2.png\" width=\"450\">\n",
+    "<br/><br/>\n",
+    "질문과 결정을 트리 형태로 표현하면 위와 같이 표현할 수 있습니다. 1001번째 나온 숫자가 1인지 알아내는데 필요한 질문수 2개, 2인지 알아내는데 필요한 질문수 2개, 숫자 3, 4 역시 질문수 2개가 필요합니다. 그래서 평균을 내면 숫자를 예측하는데 2번의 질문이 필요함을 알 수 있습니다. 이를 각 숫자에 해당하는 질문수를 $q_i$ 라 두고 식으로 써보면 평균질문수 또는 질문수의 기대값은 다음과 같습니다.\n",
+    "<br/><br/>\n",
+    "$$\n",
+    "\\begin{align}\n",
+    "\\mathbb{E}(q)\n",
+    "&= \\frac{250 \\times q_{1} + 250 \\times q_{2} +250 \\times q_{3}+250 \\times q_{4}}{1000} \\\\\n",
+    "&= \\frac{250}{1000}q_{1}+\\frac{250}{1000}q_{2}+\\frac{250}{1000}q_{3}+\\frac{250}{1000}q_{4}\n",
+    "\\end{align}\n",
+    "$$\n",
+    "<br/>\n",
+    "입니다. 여기에서 $\\frac{250}{1000}$은 각 숫자의 확률이 되므로 다시 쓰면\n",
+    "<br/><br/>\n",
+    "$$\n",
+    "\\mathbb{E}(q) = P(X=1)q_{1}+P(X=2)q_{2}+P(X=3)q_{3}+P(X=4)q_{4}\n",
+    "$$\n",
+    "<br/>\n",
+    "입니다. 여기에서 질문수 $q_{i}$는 위 이진트리에서 얼마나 깊이 내려 갔는가와 일치 합니다. 이진 트리에서 깊이는 $\\log_{2}(노드수)$ 이므로 \n",
+    "다시 쓰면<br/><br/>\n",
+    "$$\n",
+    "\\begin{align}\n",
+    "\\mathbb{E}(q) \n",
+    "&= P(X=1)\\log_{2}4+P(X=2)\\log_{2}4+P(X=3)\\log_{2}4+P(X=4)\\log_{2}4 \\\\\n",
+    "&= \\sum_{i=1}^{4} P(X=x_{i})\\log_{2}4 \\\\\n",
+    "&= -\\sum_{i=1}^{4} P(X=x_{i})\\log_{2}\\frac{1}{4}\n",
+    "\\end{align}\n",
+    "$$\n",
+    "<br/>\n",
+    "마지막 줄에서 $\\frac{1}{4}$는 각 숫자에 대한 확률과 일치하므로 최종적으로 다음과 같이 쓸 수 있습니다.\n",
+    "<br/><br/>\n",
+    "$$H(X)= -\\sum_{i=1}^{4} P(X=x_{i})\\log_{2}P(X=x_{i})$$\n",
+    "<br/>\n",
+    "위 식이 이산 확률변수에 대한 정보 엔트로피의 정의입니다. 출력되는 숫자의 확률이 모두 동일하므로 다음에 무엇이 나올지 예측하기가 정말 어려운 시스템이고, 이는 이 시스템이 우리에게 주는 정보가 많다는 것을 의미합니다. 정보가 많아서 불확실성이 증가하고 곧 엔트로피가 높다는 말이 됩니다.\n",
+    "<br/>\n",
+    "그럼 확률이 서로 다른 경우는 어떻게 될까요? 예를 들어 1이 500번, 2가 125번, 3이 125번, 4가 250번 나온 시스템이라고 가정을 해보겠습니다. 이 시스템은 1, 2, 3, 4 라는 실수값에 함수값 0.5, 0.125, 0.125, 0.25를 할당하는 확률질량함수 $Q(X)$를 확률 분포로 가지는 이산확률변수 $X$ 라고 할수 있습니다. 그렇다면 얼핏 생각해도 1001번째 나올 수는 1이 될것같다는 느낌이 절반 정도는 듭니다. 돈을 건다면 1에 걸면 딸 확률이 50%나 됩니다. 1이 아니라면 4가 될것입니다. 이처럼 확률분포가 불확실성을 떨어트려서 예측이 쉬워졌습니다. 위에서 이야기한 평균 질문수 즉, 엔트로피는 이런 상황을 정량적으로 기술 할 수 있게 해주는 도구입니다. 실제로 계산을 해보도록 하겠습니다.\n",
+    "\n",
+    "<img src=\"3.png\" width=\"320\">\n",
+    "\n",
+    "확률분포에 의해 가장 먼저 1인가를 물어봐야 합니다. 절반 정도는 한번 질문에 1임을 확인할 수 있고, 아니라면 4인가를 물어보는 것이 가장 합리적입니다. 그래도 아니면 그때는 2,3이 나올 확률은 동일하므로 아무것이나 물어봐도 됩니다. 위 계산을 이 시스템에서 다시 반복해보면  $q_{1}=1$, $q_{2}=3$, $q_{3}=3$, $q_{4}=2$ 이므로 아래와 같습니다.\n",
+    "<br/><br/>\n",
+    "$$\n",
+    "\\begin{align}\n",
+    "\\mathbb{E}(q)\n",
+    "&= \\frac{500 \\times q_{1} + 125 \\times q_{2} + 125 \\times q_{3}+ 250 \\times q_{4}}{1000} \\\\\n",
+    "&= \\frac{500}{1000}q_{1}+\\frac{125}{1000}q_{2}+\\frac{125}{1000}q_{3}+\\frac{250}{1000}q_{4} \\\\\n",
+    "&= \\frac{500}{1000}\\times 1+\\frac{125}{1000}\\times 3+\\frac{125}{1000}\\times 3+\\frac{250}{1000}\\times 2 \\\\\n",
+    "&= Q(X=1)\\log_{2}2 + Q(X=2)\\log_{2}8 + Q(X=3)\\log_{2}8 + Q(X=4)\\log_{2}4 \\\\\n",
+    "&= \\left(-Q(X=1)\\log_{2}\\frac{1}{2}\\right) + \\left(-Q(X=2)\\log_{2}\\frac{1}{8}\\right) + \\left(-Q(X=3)\\log_{2}\\frac{1}{8}\\right) + \\left(-Q(X=4)\\log_{2}\\frac{1}{4}\\right) \\\\\n",
+    "&= -Q(X=1)\\log_{2}Q(X=1)-Q(X=2)\\log_{2}Q(X=2)-Q(X=3)\\log_{2}Q(X=3)-Q(X=4)\\log_{2}Q(X=4) \\\\\n",
+    "&= - \\sum_{i=1}^{4} Q(X=x_{i})\\log_{2}Q(X=x_{i}) = 1.75\n",
+    "\\end{align}\n",
+    "$$\n",
+    "<br/>\n",
+    "위 확률이 동일한 경우와 비교해보면 엔트로피가 줄었다는 것을 알 수 있습니다. 예측이 쉬워졌고 이는 불확실성이 떨어졌다는 것을 의미하며 시스템이 주는 정보가 줄었다는 의미입니다.\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 크로스엔트로피Cross Entropy\n",
+    "<hr/>\n",
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "이전까지의 내용을 보면 한가지 이상한 점이 있습니다. 바로 우리가 만든 \"질문 방식\"입니다. $P(X)$를 확률분포로 가지는 시스템에서 적용한 질문 방식과 $Q(X)$에서 사용한 질문 방식이 서로 다릅니다. 무엇을 근거로 우리는 질문 방식을 다르게 했던것일까요? 바로 각 시스템의 확률분포를 보고 질문을 결정했습니다. 각 확률분포에 적합한 질문 방식이 있는것이고 질문을 잘 해야 질문번수를 최대한 줄일 수 있습니다. 그런데 $P(X)$를 확률분포로 가지는 시스템에서 사용한 질문 즉, \"1 또는 2입니까?\"라고 첫 질문을 하는 것은 다분히 감각적이라는 느낌 마져 듭니다. 첫번째 시스템에서 모든 숫자에 똑같은 확률이 분포 되어 있으니 첫 질문을 \"1 또는 2입니까?\"라고 하면 최적으로 질문을 할 수 있겠다는 생각을 하지 못한다면 어떻게 될까요?(이렇게 생각하는게 쉬운가요?) 그냥 우리가 하고 싶은데로 아무렇게나 질문을 했다면 어떻게 될까요? 어떤식의 선택을 하든지 쓸데없는 질문을 한두번 더하게 될것이고 따라서 엔트로피는 증가하게 될것입니다.  \n",
+    "정리하면 시스템이 출력하는 심볼을 식별(identify)하기 위해 질문을 만들어야 하고(coding), 어떤 코딩 방식(coding scheme)을 통해 만들어야 쓸데없는 질문이 들어가지 않는지(code가 길어지지 않는지)는 시스템의 확률분포에 달려 있습니다. 시스템의 실제 확률분포와 다른 확률분포에 의해 만들어진 코딩 방식으로 코딩된 코드의 길이(다르게 말하면 질문의 수)를 실제 확률분포 상에서 평균을 내면 어떻게 될까요? 예를 들어 코딩은 $Q(X)$에서하고 그것을 $P(X)$에서 평균을 내는것입니다.<br/>\n",
+    "<br/>\n",
+    "$$\n",
+    "\\begin{align}\n",
+    "\\mathbb{E}(q) \n",
+    "&= \\frac{250 \\times q_{1} + 250 \\times q_{2} + 250 \\times q_{3}+ 250 \\times q_{4}}{1000} \\\\\n",
+    "&= \\frac{250}{1000}q_{1}+\\frac{250}{1000}q_{2}+\\frac{250}{1000}q_{3}+\\frac{250}{1000}q_{4} \\\\\n",
+    "&= \\frac{250}{1000}\\times 1+\\frac{250}{1000}\\times 3+\\frac{250}{1000}\\times 3+\\frac{250}{1000}\\times 2 \\\\\n",
+    "&= P(X=1)\\log_{2}2 + P(X=2)\\log_{2}8 + P(X=3)\\log_{2}8 + P(X=4)\\log_{2}4 \\\\\n",
+    "&= \\left(-P(X=1)\\log_{2}\\frac{1}{2}\\right) + \\left(-P(X=2)\\log_{2}\\frac{1}{8}\\right) + \\left(-P(X=3)\\log_{2}\\frac{1}{8}\\right) + \\left(-P(X=4)\\log_{2}\\frac{1}{4}\\right) \\\\\n",
+    "&= -P(X=1)\\log_{2}Q(X=1)-P(X=2)\\log_{2}Q(X=2)-P(X=3)\\log_{2}Q(X=3)-P(X=4)\\log_{2}Q(X=4) \\\\\n",
+    "&= - \\sum_{i=1}^{4} P(X=x_{i})\\log_{2}Q(X=x_{i}) = 2.25\n",
+    "\\end{align}\n",
+    "$$\n",
+    "<br/>\n",
+    "엔트로피가 증가함을 확인할 수 있습니다. 아래 표는 이런 상황에 대한 계산을 정리하여 엔트로피를 구한것입니다. 코딩을 위해 가정한 확률분포가 실제 확률분포와 다를 경우 엔트로피는 증가함을 확인할 수 있습니다.\n",
+    "<img src=\"4.png\">  \n",
+    "위와 같이 원래의 확률분포와는 다른 확률분포로 엔트로피를 구한 것을 크로스엔트로피라고 합니다. <a href=\"https://en.wikipedia.org/wiki/Cross_entropy\">위키</a> [2]에는 다음과 같이 되어 있습니다. \n",
+    "</div>\n",
+    "\n",
+    ">\"Cross entropy can be interpreted as the expected message-length per datum when a wrong distribution $Q$ is assumed while the data actually follows a distribution $P$.\"\n",
+    "\n",
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "식은 다음과 같습니다.\n",
+    "<br/><br/>\n",
+    "$$H(P,Q)= -\\sum_{i=1}^{N} P(X=x_{i})\\log_{2}Q(X=x_{i})$$\n",
+    "<br/>\n",
+    "아래는 엔트로피를 구하는 실험 코드입니다. 인위적으로 앞에서 예를 든 $P(X)$, $Q(X)$를 만들고 각 분포에 대해 다른 방식으로 질문을 해서 얻어지는 평균 질문수가 엔트로피 값에 근접해가는지 확인 해보도록 하겠습니다.\n",
+    "\n",
+    "</div>\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H(P(X)) = 2.0\n",
+      "H(Q(X)) = 1.717\n",
+      "H(P(X),Q(X)) = 2.234\n"
+     ]
+    }
+   ],
+   "source": [
+    "import random\n",
+    "\n",
+    "#동일한 비율로 2000개 샘플을 만든다.\n",
+    "P = [1]*500 + [2]*500 + [3]*500 + [4]*500\n",
+    "\n",
+    "#무작위로 섞어 버리고\n",
+    "random.shuffle(P)\n",
+    "q = q2 = 0\n",
+    "\n",
+    "#천개만 뽑아서 질문을 한다.\n",
+    "#H(P)\n",
+    "for x in P[:1000] :\n",
+    "    q2 += 1\n",
+    "    if x == 1 or x == 2: \n",
+    "        q2 += 1\n",
+    "        if x == 1:\n",
+    "            pass #print(q2)\n",
+    "        else :\n",
+    "            pass #print(q2)\n",
+    "    else :\n",
+    "        q2 += 1\n",
+    "        if x == 3:\n",
+    "            pass #print(q2)\n",
+    "        else :\n",
+    "            pass #print(q2)\n",
+    "    q += q2\n",
+    "    q2 = 0\n",
+    "\n",
+    "print(\"H(P(X)) = {}\".format(q / 1000))\n",
+    "\n",
+    "Q = [1]*1000 + [2]*250 + [3]*250 + [4]*500\n",
+    "random.shuffle(Q)\n",
+    "q = q2 = 0\n",
+    "\n",
+    "#H(Q)\n",
+    "for x in Q[:1000] :\n",
+    "    q2 += 1\n",
+    "    if x == 1 :\n",
+    "        pass#print(q2)\n",
+    "    else :\n",
+    "        q2 += 1\n",
+    "        if x == 4 :\n",
+    "            pass#print(q2)\n",
+    "        else :\n",
+    "            q2 += 1\n",
+    "            if x == 3:\n",
+    "                pass#print(q2)\n",
+    "            else :\n",
+    "                pass#print(q2)\n",
+    "    q += q2\n",
+    "    q2 = 0\n",
+    "\n",
+    "print(\"H(Q(X)) = {}\".format(q / 1000))\n",
+    "\n",
+    "q = q2 = 0\n",
+    "\n",
+    "#H(P,Q)\n",
+    "for x in P[:1000] :\n",
+    "    q2 += 1\n",
+    "    if x == 1 :\n",
+    "        pass#print(q2)\n",
+    "    else :\n",
+    "        q2 += 1\n",
+    "        if x == 4 :\n",
+    "            pass#print(q2)\n",
+    "        else :\n",
+    "            q2 += 1\n",
+    "            if x == 3:\n",
+    "                pass#print(q2)\n",
+    "            else :\n",
+    "                pass#print(q2)\n",
+    "    q += q2\n",
+    "    q2 = 0\n",
+    "\n",
+    "print(\"H(P(X),Q(X)) = {}\".format(q / 1000))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "실제 우리의 계산 결과에 수렴하는것을 실험적으로도 확인할 수 있습니다."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 쿨백-라이블러 발산Kullback–Leibler divergence, KLD\n",
+    "<hr/>\n",
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "위에서 엔트로피와 크로스엔트로피를 알아봤습니다. 이 둘을 이용하여 서로 다른 두 이산확률변수의 확률분포 $P$와 $Q$가 있다고 할때 이 둘의 엔트로피 차이를 정의할 수 있습니다.\n",
+    "\n",
+    "즉, $H(P,Q)-H(P)$ 로 정의를 하면 다음과 같고 이를 쿨백-라이블러 발산이라 합니다.\n",
+    "<br/><br/>\n",
+    "$$\n",
+    "\\begin{align}\n",
+    "D_{KL}(P || Q) \n",
+    "&=H(P,Q)-H(P) \\\\\n",
+    "&= -\\sum_{i=1} P(X=x_{i}) \\log Q(X=x_{i}) - \\left( -\\sum_{i=1} P(X=x_{i}) \\log P(X=x_{i}) \\right)\\\\\n",
+    "&= -\\sum_{i=1} \\left( P(X=x_{i}) \\left( \\log Q(X=x_{i}) - \\log P(X=x_{i}) \\right) \\right) \\\\\n",
+    "&= -\\sum_{i=1} P(X=x_{i}) \\frac{\\log Q(X=x_{i})}{\\log P(X=x_{i})} \\\\\n",
+    "&= \\sum_{i=1} P(X=x_{i}) log \\frac{P(X=x_{i})}{Q(X=x_{i})} \\\\\n",
+    "\\end{align}\n",
+    "$$\n",
+    "<br/>\n",
+    "\n",
+    "두 확률분포의 상대적인 엔트로피를 나타내는 $D_{KL}$은 크로스엔트로피에 엔트로피를 뺀 것으로 항상 0보다 같거나 크며, 볼록함수Convex Function인 특징을 가지고 있습니다. 예를 들어 $P(X)$는 평균 6, 표준편차 1.5인 정규분포, $Q(X)$를 평균 0, 표준편차 1인 정규분포라 하면 $P(X)$, $Q(X)$를 확률분포로 가지는 두 확률변수로 부터 $D_{KL}$을 계산하면 0보다 큰 양수가 나오게 됩니다. $Q$가 $P$와 비슷해지면 값은 점점 작아지다 $P$와 동일해 지면 0이 됩니다. \n",
+    "\n",
+    "\n",
+    "\n",
+    "하여튼 이 분포에서 임의로 5개씩 샘플을 추출하면 $P(X)$는 6 근처의 값이, $Q(X)$는 0 근처의 값이 추출될 것입니다. 이것이 GANs과 무슨 상관이 있는지 GANs 관점에서 이야기해보면 $P(X)$가 진짜 실세계의 확률분포라면 $Q(X)$에서 추출된 샘플은 쉽게 진짜가 아니라는 것을 알 수 있습니다. 만약 $Q(X)$의 분포를 조정해서 $P(X)$와 유사하게 만든다면 $Q(X)$에서 추출된 샘플을 $P(X)$에서 추출된 샘플과 구별할 수 없게 될것입니다. GANs의 핵심이 바로 $Q(X)$를 조정해서 $P(X)$와 같게 만드는 과정입니다. 어떻게 조정하는지 구체적인 이야기는 차차 하도록하고 여기서는 $D_{KL}$을 목적함수로 이용하여 확률분포 $P$, $Q$의 차이를 줄이는 최적화 과정을 실습해보겠습니다. 다행스럽게도 $D_{KL}$은 확률분포 $Q(X)$ 도메인에서 볼록함수이므로 꽤 손쉽게 전역 최적점을 찾을 수 있습니다. 볼록성에 대한 증명은 <a href=\"http://homes.cs.washington.edu/~anuprao/pubs/CSE533Autumn2010/lecture3.pdf\" target=\"blink\">CSE 533: Information Theory in Computer Science</a> [3] 세번째 강의 노트에서 확인할 수 있습니다. 기준이 되는 확률분포 $P(X)$를 평균 6, 표준편차 1.5로 두고 평균 $\\mu$와 표준편차 $\\sigma$ 를 설계변수로 하여 최적화를 수행 해보겠습니다. 우선 $D_{KL}$의 볼록성부터 그래프로 확인 해보도록 하겠습니다. \n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "\"\"\"\n",
+    "쿨백-라이블러 발산 그래프 그리기\n",
+    "\"\"\"\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "#A normal continuous random variable.\n",
+    "from scipy.stats import norm\n",
+    "from scipy import stats\n",
+    "\n",
+    "def cost(mu, sigma) :\n",
+    "    P = norm(6, 1.5)\n",
+    "    Q = norm(mu, sigma)\n",
+    "    x = np.linspace(-10, 10, 100)\n",
+    "\n",
+    "    return stats.entropy(P.pdf(x), Q.pdf(x))\n",
+    "    \n",
+    "mus    = np.linspace(4, 8, 100)\n",
+    "sigmas = np.linspace(0.5, 2.0, 100)\n",
+    "MUS, SIGMAS = np.meshgrid(mus, sigmas)\n",
+    "\n",
+    "#X,Y를 순회하면서 cost를 계산해서 cost를 reshape\n",
+    "Z = np.array([cost(mu, sigma) for mu, sigma in zip(MUS.reshape(-1), SIGMAS.reshape(-1))]).reshape(MUS.shape)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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3xTFwfG+lrn/w7dntcvhqgsvnU6mva/hHKHxtWRb+tSt8X19H9PQEV652Pjt+cUEZALY6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\nuMzOU+3WrQ0mGWnC5eknxMSINgSEKXQmaaJNhxa4d+4No1b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caTJ+cLfKdKXa4PB4NP/S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\nCBURDT+EECoiGn4IIVTEfwieYSwvEHaeAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09f73c9470>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "levels1 = np.linspace(0, 0.1, 5)\n",
+    "levels2 = np.linspace(0.2, 2, 10)\n",
+    "\n",
+    "CS = plt.contour(MUS, SIGMAS, Z, levels=np.concatenate((levels1, levels2)))\n",
+    "plt.clabel(CS, inline=1, fontsize=10)\n",
+    "plt.title('Convexity of DKL')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "6, 1.5 에서 최솟점이 생기는 것을 확인할 수 있고 그래프상 볼록함수로 보입니다. 이제 $\\mu$, $\\sigma$에 대해 수치 미분을 하면서 경사하강법을 이용해서 최적화를 하도록 하겠습니다. 즉, $Q(x;\\boldsymbol{\\theta})$ 라는 확률 분포에서 $\\boldsymbol{\\theta}=(\\mu, \\sigma)$를 조정하여 $P(x)$와 최대한 차이가 없게 만들겠습니다. 스탭사이즈(학습률)는 선탐색Line search하지 않고 그냥 0.1로 고정하도록 하겠습니다.(목적함수가 볼록하므로 효율을 위해서는 선탐색을 하여야 합니다. 다만 머신러닝에서는 선탐색이 별 효용이 없으므로 그냥 고정값으로 하겠습니다.) 아래 코드가 있고 자세한 주석이 달려있어 이해하기 어렵지 않을 것으로 생각합니다.\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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w4xVb17fWfkpZ0s9wmdCJ6/N/rWRViSfTOnFj+Z/p7beDjSPLWNLPYFGNDgxx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\nhrd6tetH2bYN9oR4neSAxVX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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09ef438048>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Init. Samples of P(x) : [ 5.55202053  7.32547706  5.77007986  5.29420197  5.56929033]\n",
+      "Init. Samples of Q(x) : [-1.00133037  0.41098088 -1.22261296 -0.19380835  0.29114829]\n",
+      "Entorpy of P(x)  : +3.464382\n",
+      "DKL of P(x),Q(x) : +18.057248\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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ivwPvBkpvNF9K/usMySvX75B0v6R1adqM/hs/ZV62bvWLiJCU23m5kuYB3wDe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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09ef3fa128>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ITER:491, COST:+0.000009, mu:+5.994762, sigma:+1.250326\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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UOAt33nw7aidU5k4L3Fd46w676uZwWekbE0a7d75IV/dpClLGkVtR6TpO3Jh3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\nGGMSyP8Hxo0pyfvIc80AAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09ef3ea6d8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Samples of P(x) : [ 6.08387116  7.72948787  5.73906567  5.14606368  5.671743  ]\n",
+      "Samples of Q(x) : [ 7.41969975  6.05231346  6.73068703  6.02675761  4.28135528]\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "#A normal continuous random variable.\n",
+    "from scipy.stats import norm\n",
+    "from scipy import stats\n",
+    "\n",
+    "h = 0.01          #미분을 위한 작은 구간\n",
+    "epsilon = 1.e-5   #수렴 판단을 위한 매우 작은 수\n",
+    "alpha = 0.1       #step size\n",
+    "\n",
+    "#확률변수의 구간\n",
+    "x = np.linspace(-5, 11, 100)\n",
+    "\n",
+    "#진짜 확률 분포를 가지는 확률변수\n",
+    "P = norm(6, 1.25)\n",
+    "\n",
+    "#params theta = [μ, σ]  확률분포를 조정하는 파라메터는 평균과, 표준편차\n",
+    "mu, sigma = 0, 1.0\n",
+    "\n",
+    "#P와는 많이 다른 확률분포를 가지는 확률변수\n",
+    "Q = norm(mu, sigma)\n",
+    "\n",
+    "plt.plot(x, P.pdf(x), 'r-', lw=2, alpha=0.6, label='P pdf')\n",
+    "plt.plot(x, Q.pdf(x), 'g-', lw=2, alpha=0.6, label='Q pdf')\n",
+    "plt.title('Init. P(x) and Q(x)')\n",
+    "plt.show()\n",
+    "\n",
+    "\"\"\"\n",
+    "두 확률분포는 다르기 때문에 임의로 5개씩 샘플을 추출하면 \n",
+    "p는 0 근처의 값이, q는 5 근처의 값이 추출됨.\n",
+    "\"\"\"\n",
+    "p = P.rvs(size=5)\n",
+    "q = Q.rvs(size=5)\n",
+    "print(\"Init. Samples of P(x) : {}\".format(p))\n",
+    "print(\"Init. Samples of Q(x) : {}\".format(q))\n",
+    "\n",
+    "#P의 확률분포 엔트로피\n",
+    "print(\"Entorpy of P(x)  : {:+f}\".format(stats.entropy(P.pdf(x))))\n",
+    "\n",
+    "#P와 Q의 확률분포 간의 DKL\n",
+    "dkl = stats.entropy(P.pdf(x), Q.pdf(x))\n",
+    "print(\"DKL of P(x),Q(x) : {:+f}\".format(dkl))\n",
+    "dkls = [dkl]\n",
+    "\n",
+    "for i in range(1000):\n",
+    "    #경사 구하기 미분  {f(x+h)-f(x-h)} / 2h\n",
+    "    dmu =    (stats.entropy(P.pdf(x), norm(mu+h, sigma).pdf(x))-stats.entropy(P.pdf(x), norm(mu-h, sigma).pdf(x))) / (h*2)\n",
+    "    dsigma = (stats.entropy(P.pdf(x), norm(mu, sigma+h).pdf(x))-stats.entropy(P.pdf(x), norm(mu, sigma-h).pdf(x))) / (h*2)\n",
+    "    \n",
+    "    #경사하강  w = w - η* ∇f\n",
+    "    mu    -= alpha*dmu\n",
+    "    sigma -= alpha*dsigma\n",
+    "    \n",
+    "    #업데이트된 파라메터로 확률변수를 다시 만든다.\n",
+    "    Q = norm(mu, sigma)\n",
+    "    \n",
+    "    #목적함수를 평가하고 입실론보다 작으면 그만\n",
+    "    dkl = stats.entropy(P.pdf(x),Q.pdf(x))\n",
+    "    dkls.append(dkl)\n",
+    "    \n",
+    "    if dkl < epsilon :\n",
+    "        break;\n",
+    "    \n",
+    "plt.plot(dkls)\n",
+    "plt.title('Objective function')\n",
+    "plt.show()    \n",
+    "print(\"ITER:{}, COST:{:+f}, mu:{:+f}, sigma:{:+f}\".format(i, dkl, mu, sigma))\n",
+    "\n",
+    "plt.plot(x, P.pdf(x), 'r-', lw=2, alpha=0.6, label='P pdf')\n",
+    "plt.plot(x, Q.pdf(x), 'g-', lw=2, alpha=0.6, label='Q pdf')\n",
+    "plt.title('Result')\n",
+    "plt.show()\n",
+    "\n",
+    "\"\"\"\n",
+    "이제 Q에서 뽑은 샘플을 P에서 뽑은 샘플과 구별할 수 없어졌다.\n",
+    "\"\"\"\n",
+    "p = P.rvs(size=5)\n",
+    "q = Q.rvs(size=5)\n",
+    "print(\"Samples of P(x) : {}\".format(p))\n",
+    "print(\"Samples of Q(x) : {}\".format(q))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Keras를 이용한 100줄 짜리 확률분포 모델 GAN  \n",
+    "<hr/>\n",
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "GANs를 살짝 맛보기 위해서 정규분포를 근사하는 문제를 풀어보겠습니다. 인터넷에 이미 시도된 몇몇 글 \n",
+    "<a href=\"https://medium.com/@devnag/generative-adversarial-networks-gans-in-50-lines-of-code-pytorch-e81b79659e3f\">GANs in 50 lines of code (PyTorch)</a>[4], \n",
+    "<a href=\"https://github.com/hwalsuklee/tensorflow-GAN-1d-gaussian-ex\">tensorflow-GAN-1d-gaussian-ex-hwalsuklee</a>[5], \n",
+    "<a href=\"http://blog.naver.com/atelierjpro/220984758512\">아주 간단한 GAN 구현하기-홍정모[6]</a>을 볼 수 있습니다. 해결해야하는 문제는 임의의 평균과 표준편차를 가지는 정규분포로 부터 획득된 학습데이터만을 가지고(평균과 표준편차는 뭔지 모름) 그 데이터의 분포를 흉내내는 모델을 만드는 것입니다. 쿨벡-라이블러 발산을 코스트로한 예제에서는 추정해야하는 모델이 정규분포라는 것을 알고 또 조정하는 설계변수가 평균과 표준편차라는 것을 알고 그것을 조절해서 최적화를 수행하였습니다. 하지만 GANs는 흉내내야하는 모델의 설계변수등 아무런 정보없이 단지 그 모델로 부터 획득된 데이터만 사용하여 그 모델처럼 동작하는 모델을 만들어내는 것입니다. 기본개념은 위 확률분포 최적화 문제와 같지만 훨씬 일반화된 상태로 문제를 풀어나갑니다.  \n",
+    "\n",
+    "GANs를 numpy만으로 구현하기에는 코드양이 꽤 되고 GPU의 힘을 빌리지 않고는 훈련시키기에 많은 인내가 필요하므로 케라스를 쓰도록 하겠습니다. 우선 필요한 모듈을 로딩하고 보조 함수를 만듭니다. GAN은 D와 G를 따로 훈련시키는데 Ian Goodfellow의 최초 GANs 논문[6]에 의하면 G를 훈련할 때 D는 훈련하지 않습니다. 케라스에는 모델과 레이어에 trainable이라는 속성을 제공합니다. 이 속성을 false 또는 true로 만드는 보조함수 make_trainable을 정의합니다.[8] (https://github.com/osh/KerasGAN)\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Using Theano backend.\n",
+      "WARNING (theano.sandbox.cuda): The cuda backend is deprecated and will be removed in the next release (v0.10).  Please switch to the gpuarray backend. You can get more information about how to switch at this URL:\n",
+      " https://github.com/Theano/Theano/wiki/Converting-to-the-new-gpu-back-end%28gpuarray%29\n",
+      "\n",
+      "Using gpu device 0: GeForce GTX 1070 (CNMeM is enabled with initial size: 80.0% of memory, cuDNN 5105)\n"
+     ]
+    }
+   ],
+   "source": [
+    "import sys\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "import matplotlib.mlab as mlab\n",
+    "\n",
+    "from keras.models import Sequential, Model\n",
+    "from keras.layers import Dense, Activation, Input\n",
+    "from keras import optimizers\n",
+    "from keras.utils import np_utils\n",
+    "\n",
+    "#np.random.seed(78)\n",
+    "#np.random.seed(0)\n",
+    "\n",
+    "batch_size = 200\n",
+    "print_interval = 5000\n",
+    "\n",
+    "def make_trainable(net, val):\n",
+    "    \"\"\"\n",
+    "    D의 param.들을 학습안되게 했다가 학습되게 했다가 전환시키기 위한 보조함수\n",
+    "    \"\"\"\n",
+    "    net.trainable = val\n",
+    "    for l in net.layers:\n",
+    "        l.trainable = val"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "그 다음 학습데이터를 생성합니다. 평균 6, 표준편차 1.25인 정규분포에서 원하는 개수만큼 숫자를 생성하여 리턴하는 get_distribution_sampler함수를 정의합니다. 이 때 생성된 숫자는 진짜 데이터이므로 라벨 1을 붙여서 되돌립니다. \n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "################################################################\n",
+    "# 학습 데이터 생성\n",
+    "################################################################\n",
+    "mu, sigma = 6, 1.25\n",
+    "\n",
+    "def get_distribution_sampler(mu, sigma, N):\n",
+    "    \"\"\"\n",
+    "    주어진 평균과 표준편차로 N개의 정규분포 난수를 발생시키고 그 라벨로 1을 붙여서 되돌림\n",
+    "    \"\"\"\n",
+    "    data_xp, data_yp = np.random.normal(mu, sigma, N), np.ones(N)\n",
+    "    data_p = np.vstack((data_xp, data_yp)).T\n",
+    "    \n",
+    "    return data_p"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "이후 모델을 생성합니다. 생성할 모델은 D와 G 그리고 이 둘이 중첩된 모델 GAN을 생성합니다.   \n",
+    "모델 정의를 위해 우선 GAN에 대한 기초 구조를 이야기 하도록 하겠습니다.  \n",
+    "    어떤 확률변수 $\\boldsymbol{X}$가 있어서 이 변수가 어떤 데이터를 나타낸다고 합시다. 쉬운 예로 28x28 픽셀의 사람 얼굴이라면 요소를 784개 가지는 벡터로 생각할 수 있고 $\\boldsymbol{X}$는 그 벡터를 값으로 가지는 확률 변수가 됩니다. 784개의 요소에 아무값이나 집어 넣은 임의의 벡터 $\\boldsymbol{x}$는 사람 얼굴이 아닐 것입니다. 하지만 어떤 규칙에 의해 784개의 값을 적당히 잘 지정하면 벡터 $\\boldsymbol{x}$는 사람얼굴 처럼 보일 수 도 있습니다. 여기서 어떤 규칙 즉, 확률변수 $\\boldsymbol{X}$가 얼굴로 보이는 $\\boldsymbol{x}$를 가질 확률을 나타내는 확률분포 $p(\\boldsymbol{X})$가 있을 수 있습니다. 존재할 수 있는 모든 길이 784짜리 벡터가 모여있는 공간에는 사람 얼굴처럼 보이는 $\\boldsymbol{x}$도 있고 전혀 아닌 $\\boldsymbol{x}$도 있는데 어떤 확률변수 $\\boldsymbol{X}$가 이들 표본을 가질 때 얼굴을 닮은 $\\boldsymbol{x}$에 대해서 높은 확률을 부여하는 $p(\\boldsymbol{X}=\\boldsymbol{x})$가 존재한는 것입니다.  $\\boldsymbol{x}$가 $p(\\boldsymbol{X})$에 따르면 즉, $\\boldsymbol{x} \\sim p(\\boldsymbol{x})$이면 $\\boldsymbol{x}$는 사람 얼굴이 될 것입니다. 문제는 $p(\\boldsymbol{X})$가 무엇인지 전혀 알지 못합니다. 다만 $\\boldsymbol{x} \\sim p(\\boldsymbol{X})$인 $\\boldsymbol{x}$ 여러개는 가질 수 있습니다. 바로 우리가 모은 데이터입니다. 이 데이터를 이용하여 입력된 $\\boldsymbol{x}$가 $p(\\boldsymbol{X})$에서 추출된 것인지 아닌지를 구별하는 D를 만들고, $\\boldsymbol{x}$를 무작위로 만들어 D에게 검사를 받는 G를 만들어 둘을 훈련시키는 네트워크가 GANs입니다. 여기서 $p(\\boldsymbol{X})$가 무엇인지 전혀 알지 못하므로 모아둔 데이터의 분포를 나타내는 $p_{\\text{data}}(\\boldsymbol{X})$를 생각 해볼 수 있습니다. $p_{\\text{data}}(\\boldsymbol{X})$는 $p(\\boldsymbol{X})$와 완전히 같지는 않겠지만 우리가 할 수 있는 최선입니다. 그리고 G도 어떤 규칙으로 데이터를 만들어 낼테니까 G에서 생성되는 데이터의 확률분포 $p_{g}(\\boldsymbol{X})$를 생각해 볼 수 있습니다. 이제 $p_{\\text{data}}(\\boldsymbol{X})$와 최대한 비슷한 $p_{g}(\\boldsymbol{X})$를 만드는것이 우리의 목표입니다.  \n",
+    "우선 D를 훈련 시키기 위한 코스트를 살펴보겠습니다.\n",
+    "<br/><br/>\n",
+    "$$ J^{D} \\left( \\boldsymbol{\\theta}^{(D)} , \\boldsymbol{\\theta}^{(G)} \\right) \n",
+    "= - \\frac{1}{2} \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{data}}} \\log D( \\boldsymbol{x} ) \n",
+    "- \\frac{1}{2} \\mathbb{E}_{\\boldsymbol{z}} \\log \\left(1-D\\left(G(\\boldsymbol{z})\\right)  \\right)\n",
+    "$$\n",
+    "<br/>\n",
+    "위 식은 일반적인 바이너리 크로스엔트로피 식인데 보통의 경우와 약간 다른 점이 있습니다. 아래 그림을 보면 첫째 행에 일반적인 바이너리 크로스엔트로피 식을 적었고 두번째 행에 논문에서 사용하는 형태의 표기로 바꾼 식이 적혀 있습니다. 대응되는 같은 부분을 같은 색으로 표시했습니다. 여기서 두번째 항에 확률분포를 살짝 바꾼식이 세번째 행에 있는 식, 즉 위 식이 됩니다. 이렇게 해놓고 보면 세번째 식의 각 항은 앞서 알아보았던 크로스엔트로피가 된다는 것을 알 수 있습니다. 그리고 그것들이 더해진 형태입니다. NIPS 2016 Tutorial:Generative Adversarial Networks[9]의 설명문을 그림밑에 인용하였습니다.\n",
+    "\n",
+    "<img src=\"7.png\" width=\"550\">\n",
+    "\n",
+    "</div>\n",
+    "\n",
+    ">\"This is just the standard cross-entropy cost that is minimized when training\n",
+    "a standard binary classifier with a sigmoid output. The only difference is that\n",
+    "the classifier is trained on two minibatches of data; one coming from the dataset,\n",
+    "where the label is 1 for all examples, and one coming from the generator, where\n",
+    "the label is 0 for all examples.\"\n",
+    "\n",
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "\n",
+    "위 식에서 $\\boldsymbol{\\theta}^{(D)}$는 $D(x)$를 조정하는 매개변수, $\\boldsymbol{\\theta}^{(G)}$는 $G(z)$를 조정하는 매개변수입니다. 먼저 첫번째 항에 대해 이야기하면 $D(\\boldsymbol{x})$는 데이터 $\\boldsymbol{x}$를 입력받아 0~1을 출력하는 함수입니다. $\\boldsymbol{x} \\sim p_{\\text{data}}$는 우리가 모은 데이터의 확률분포에서 추출한 데이터 $\\boldsymbol{x}$라는 뜻으로 그냥 우리의 데이터셋에서 뽑은 데이터라는 뜻입니다. 즉, 진짜 데이터가 되겠습니다. 이 진짜 데이터에 대한 기대값이란 의미이며 또는 $\\boldsymbol{x}$에 대한 평균으로 생각해도 되겠습니다. 두번째 항에서 $G(\\boldsymbol{z})$는 잠재변수latent variable $\\boldsymbol{z}$를 입력받아 우리가 원하는 데이터를 출력하는 함수입니다. 잠재변수는 보통 노이즈인데 우리 예제에서는 균등분포 난수를 사용하겠습니다. 이는 목표로 하는 확률분포가 정규분포인데 G의 입력을 정규분포로 넣어주는 것보다 균등분포로 넣어주는 것이 문제를 더 어렵게 만들기 때문입니다. 이것이 다시 D에 입력되니 결국 0~1의 값이 되고 D가 똑똑하다면 0 근처의 값을 출력해야 합니다. G를 고정시키고(지금 G는 그냥 열심히 가짜 데이터를 만들기만 하면 됨) $\\boldsymbol{\\theta}^{(D)}$에 대해서 위 식을 최소화 시킵니다. 자세한 상황은 아래 그림과 같습니다.\n",
+    "\n",
+    "<img src=\"6.png\" width=\"650\">  \n",
+    "\n",
+    "즉, 아래 식과 같이 그래디언트를 구하고 $\\boldsymbol{\\theta}^{(D)}$를 업데이트 시켜 나가면 D는 점점 똑똑해집니다. 아래 식은 Goodfellow et al[6]의 Algorithm 1에 나와 있는 식입니다. 각 항의 부호가 바뀐것과 기대값 표시가 평균을 구하는 방법으로 바뀐것만 빼면 위 식과 동일한 식입니다. 부호가 바뀌었으므로 이 경우는 $\\boldsymbol{\\theta}^{(D)}$에 대해 최대화 시켜야 합니다.\n",
+    "<br/><br/>\n",
+    "$$ \n",
+    "\\bigtriangledown_{\\theta^{(D)}} \\frac{1}{m} \\sum_{i=1}^{m} \\left[  \\log D\\left(x^{(i)}\\right) + \\log \\left( 1-D\\left(G(z^{(i)})\\right) \\right)\\right] \n",
+    "$$\n",
+    "<br/>\n",
+    "실제 구현에 있어서 $\\log D\\left(x^{(i)}\\right)$에 대한 함수를 만들고 라벨값으로 1을 넣어주고,\n",
+    "$\\log \\left( 1-D\\left(G(z^{(i)})\\right)\\right)$데 대한 함수를 만들고 라벨값으로 0을 넣어주고, \n",
+    "두 함수를 더하는 방식으로 구현하면 됩니다. 아래는 김남주님의 <a href=\"https://www.slideshare.net/ssuser77ee21/generative-adversarial-networks-70896091\">GAN 슬라이드</a>[10]에 나오는 구현 부분입니다.\n",
+    "</div>\n",
+    "\n",
+    "```python\n",
+    "#loss for discriminator\n",
+    "loss_disc_real = tf.nn.sigmoid_cross_entropy_with_logits(disc_real, targets=tf.ones(batch_size))\n",
+    "loss_disc_fake = tf.nn.sigmoid_cross_entropy_with_logits(disc_fake, targets=tf.zeros(batch_size))\n",
+    "\n",
+    "loss_disc = 0.5 * loss_disc_real + 0.5 * loss_disc_fake\n",
+    "```\n",
+    "\n",
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "텐서플로로 구현되어 있는데 리얼 데이터와 라벨로 1을, 페이크 데이터와 라벨 0을 크로스엔트로피 로스에 넘기고 그 둘을 더해서 수식과 동일하게 처리하고 있습니다. 또는 라벨값은 0 아니면 1이므로 리얼과 페이크를 구별하지 않고 그냥 모두 트레이닝 배치에 집어넣고 아래와 같이 바이너리 크로스엔트로피 식으로 처리해도 됩니다. 우리는 Keras에 있는 binary_crossentropy 함수를 사용하도록 하겠습니다.\n",
+    "<br/><br/>\n",
+    "$$ \\bigtriangledown_{\\theta^{(D)}} \\frac{1}{m} \\sum_{i=1}^{2m} \\left[  y^{(i)}\\log D\\left(x^{(i)}\\right) + (1-y^{(i)})\\log \\left( 1-D\\left(G(z^{(i)})\\right) \\right)\\right] \n",
+    "$$\n",
+    "<br/>\n",
+    "이제 G에 대한 코스트를 살펴보겠습니다. \n",
+    "G에 대한 코스트는 D에 대한 코스트에 - 부호를 붙여서 그것을 최소화 하면 됩니다.\n",
+    "<br/><br/>\n",
+    "$$J^{G} = - J^{D} $$\n",
+    "<br/>\n",
+    "그래서 아래처럼 다시 함수를 정의 하면\n",
+    "<br/><br/>\n",
+    "$$ V \\left( \\boldsymbol{\\theta}^{(D)} , \\boldsymbol{\\theta}^{(G)} \\right) = -J^{(D)} \\left( \\boldsymbol{\\theta}^{(D)} , \\boldsymbol{\\theta}^{(G)} \\right) $$\n",
+    "<br/>\n",
+    "으로 쓸 수 있고 GANs가 해결해야하는 문제를 종합적으로 말하자면 이 벨류펑션을 $\\boldsymbol{\\theta}^{(D)}$에 대해서 최대화,  $\\boldsymbol{\\theta}^{(G)}$에 대해서 최소화하는 문제가 됩니다.\n",
+    "<br/><br/>\n",
+    "$$\n",
+    "\\boldsymbol{\\theta}^{(G)*} = \\underset{\\boldsymbol{\\theta}^{(G)}}{\\text{argmin}} \\, \\underset{\\boldsymbol{\\theta}^{(D)}}{\\text{argmax}}  = \\frac{1}{2} \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{data}}} \\log D( \\boldsymbol{x} ) \n",
+    "+ \\frac{1}{2} \\mathbb{E}_{\\boldsymbol{z}} \\log \\left(1-D \\left( G(\\boldsymbol{z}) \\right)  \\right)\n",
+    "$$\n",
+    "<br/>\n",
+    "위 식에서 $\\log D(\\boldsymbol{x})$ 부분은 G와 아무 상관이 없는 항입니다. 따라서 G는 식의 뒷부분인  $\\frac{1}{2} \\mathbb{E}_{z} \\log \\left(1-D(G(\\boldsymbol{z}) \\right)$를 최소화시키면 됩니다. 그런데 전체 식이 D에 대해서 최대화 되었다는 말은 코스트 함수에서 어느정도 평탄한 부분에 도달했다는 말이 됩니다. 그 상태에서 뒷 부분을 코스트로 해서 그래디언트를 계산하고 이를 다시 최소화 시킨다고 했을 때 기울기 값이 크지 않아 최소화 시키기가 힘들 수 있습니다. D는 최대화된 최적점에 가버리고 거기서 G는 다시 낮은 곳으로 가야하는데 기울기가 없어서 꾸물꾸물 거리게 되는 것입니다. 그래서 논문에서는 식을 약간 변형한 형태인 아래 식으로 코스트 함수를 설정하는 것이 효율적이라 합니다.\n",
+    "<br/><br/>\n",
+    "$$ J^{G} = -\\frac{1}{2} \\mathbb{E}_{z} \\log \\left(D(G(\\boldsymbol{z}) \\right) $$\n",
+    "<br/>\n",
+    "각 형태에 대한 상황을 그림으로 정리했습니다.\n",
+    "\n",
+    "<img src=\"5.png\" width=\"680\">  \n",
+    "\n",
+    "둘 다 최소화 시키는 코스트로 사용 가능한데 우리 실험에서는 아래와 같이 그래디언트를 구하고 G를 업데이트 하도록하겠습니다.\n",
+    "<br/><br/>\n",
+    "$$ \\bigtriangledown_{\\theta^{(G)}} \\left( - \\frac{1}{m}\\sum_{i=1}^{m} \\log D\\left(G(z^{(i)})\\right) \\right)$$\n",
+    "<br/>\n",
+    "Keras에서 제공하는 mean_squared_logarithmic_error 함수를 사용하겠습니다. GANs의 구조는 대충 알아보았으므로 Keras를 이용해서 모델을 만들겠습니다. 특별히 신기술(?)은 적용하지 않고 활성함수로 relu정도만 사용하고 나머지는 평이하게 구성했습니다.\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "_________________________________________________________________\n",
+      "Layer (type)                 Output Shape              Param #   \n",
+      "=================================================================\n",
+      "dense_13 (Dense)             (None, 30)                60        \n",
+      "_________________________________________________________________\n",
+      "dense_14 (Dense)             (None, 30)                930       \n",
+      "_________________________________________________________________\n",
+      "dense_15 (Dense)             (None, 2)                 62        \n",
+      "=================================================================\n",
+      "Total params: 1,052\n",
+      "Trainable params: 1,052\n",
+      "Non-trainable params: 0\n",
+      "_________________________________________________________________\n",
+      "_________________________________________________________________\n",
+      "Layer (type)                 Output Shape              Param #   \n",
+      "=================================================================\n",
+      "dense_16 (Dense)             (None, 20)                40        \n",
+      "_________________________________________________________________\n",
+      "activation_5 (Activation)    (None, 20)                0         \n",
+      "_________________________________________________________________\n",
+      "dense_17 (Dense)             (None, 40)                840       \n",
+      "_________________________________________________________________\n",
+      "activation_6 (Activation)    (None, 40)                0         \n",
+      "_________________________________________________________________\n",
+      "dense_18 (Dense)             (None, 1)                 41        \n",
+      "=================================================================\n",
+      "Total params: 921\n",
+      "Trainable params: 921\n",
+      "Non-trainable params: 0\n",
+      "_________________________________________________________________\n",
+      "_________________________________________________________________\n",
+      "Layer (type)                 Output Shape              Param #   \n",
+      "=================================================================\n",
+      "input_3 (InputLayer)         (None, 1)                 0         \n",
+      "_________________________________________________________________\n",
+      "sequential_6 (Sequential)    (None, 1)                 921       \n",
+      "_________________________________________________________________\n",
+      "sequential_5 (Sequential)    (None, 2)                 1052      \n",
+      "=================================================================\n",
+      "Total params: 1,973\n",
+      "Trainable params: 921\n",
+      "Non-trainable params: 1,052\n",
+      "_________________________________________________________________\n"
+     ]
+    }
+   ],
+   "source": [
+    "################################################################\n",
+    "# 모델 생성\n",
+    "################################################################\n",
+    "\n",
+    "#Discriminator\n",
+    "D = Sequential()\n",
+    "D.add(Dense(30, activation='relu', input_dim=1))\n",
+    "D.add(Dense(30, activation='relu'))\n",
+    "D.add(Dense( 2, activation='softmax'))\n",
+    "D_opt = optimizers.Adam(lr=0.001*1.58, beta_1=0.9, beta_2=0.999, epsilon=1e-08, decay=0.0)\n",
+    "D.compile(loss='binary_crossentropy', optimizer=D_opt, metrics=['accuracy'])\n",
+    "D.summary()\n",
+    "\n",
+    "#Generator\n",
+    "G = Sequential()\n",
+    "G.add(Dense(20, input_dim=1))\n",
+    "G.add(Activation('sigmoid'))\n",
+    "G.add(Dense(40))\n",
+    "G.add(Activation('sigmoid'))\n",
+    "G.add(Dense(1))\n",
+    "#G.add(Activation('linear'))\n",
+    "G.summary()\n",
+    "\n",
+    "#GAN 1 - D(G(z))\n",
+    "# 이 모델을 훈련시킬때 D는 업데이트 되면 안되므로 D의 trainable 을 False로 세팅\n",
+    "make_trainable(D, False)\n",
+    "gan_input = Input(shape=[1])\n",
+    "GAN = Model( gan_input, D(G(gan_input)) )\n",
+    "G_opt = optimizers.Adam(lr=0.001*1.1, beta_1=0.9, beta_2=0.999, epsilon=1e-08, decay=0.0)\n",
+    "GAN.compile(loss='mean_squared_logarithmic_error', optimizer=G_opt )\n",
+    "GAN.summary()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "일단 초기 G가 균등분포 노이즈를 받아서 어떤 값을 출력하는지 그려보도록하겠습니다.\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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VpI0XHyMws1EZ7+sT8qHnayDGl4PArA2UtdJrxRaDL1jrfA4Cs5J02gqx7G/cjdpr5e+k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\nSUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09b65e4e48>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "G가 만들어낸 값 10개\n",
+      "[[ 1.05592656]\n",
+      " [ 1.06276715]\n",
+      " [ 1.0556128 ]\n",
+      " [ 1.07961988]\n",
+      " [ 1.06597352]\n",
+      " [ 1.06071043]\n",
+      " [ 1.0703969 ]\n",
+      " [ 1.08249021]\n",
+      " [ 1.06915987]\n",
+      " [ 1.07442129]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "################################################################\n",
+    "#학습전에 G로 부터 숫자 생성하고 분포를 그려봄\n",
+    "################################################################\n",
+    "Z1 = np.random.uniform(0,1,10000)\n",
+    "fake1 = G.predict(Z1)\n",
+    "n, bins1, patches = plt.hist(Z1, 50, normed=1, facecolor='grey', alpha=0.2)\n",
+    "plt.title('Distribution of Init. P_g(x)')\n",
+    "n, bins, patches = plt.hist(fake1, 50, normed=1, facecolor='red', alpha=0.5)\n",
+    "plt.grid(True)\n",
+    "plt.axis([-1.5, 1.5, 0, 2])\n",
+    "plt.show()\n",
+    "print(\"G가 만들어낸 값 10개\")\n",
+    "print(fake1[:10])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "G가 토해내는 $p_{g}(\\boldsymbol{x})$는 빨간색으로 표시되는데 한마디로 엉망입니다. 이 G를 훈련시켜서 6을 중심으로 종모양으로 퍼지는 모델을 만드는 것이 목표입니다. 경험적으로 알 수 있는 사실이지만 G의 학습보다는 D의 학습이 더 중요하므로 D를 미리 학습을 한번 시킵니다. Ian Goodfellow의 비유처럼 G는 위폐범인데 D가 위폐를 잘 골라내지 못한다면 G가 적당히 만들어도 D 위폐가 아니라고 판단할 것이고 G는 집중적으로 그 위폐만 만들게 됩니다. 실제로 G가 더 잘 훈련이 되면 우리의 문제에서 G는 거의 모든 값을 6근처의 값으로 집중적으로 만드는 모습을 확인할 수 있습니다. 그래서 왠만하면 D가 G의 결과를 잘 판단하도록 훈련시켜야 합니다. 그의 논문에서 정확히 언급하고 있습니다. \n",
+    "</div>\n",
+    "\n",
+    ">\"in particular, G must not be trained too much without updating D, in order to avoid “the Helvetica scenario” in which G collapses too many values of $\\boldsymbol{z}$ to the same value of $\\boldsymbol{x}$ to have enough diversity to model $p_{\\text{data}}$\"\n",
+    "\n",
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "G가 너무 많은 $\\boldsymbol{z}$ 값을 같은 $\\boldsymbol{x}$값으로 몰리게 해서 $p_{data}$를 묘사하기에 충분한 다양성을 가지지 못하는 문제를 피해야한다는 말인데 어떤 결과를 놓고 이야기하는지 아래에서 실험적으로 확인 해보도록 하겠습니다. 먼저 D를 선학습 시킵니다. (여러번 실험해보면 이 과정이 꼭 필요한것 같지는 않은데 왠지 하면 좀 더 잘되는 느낌은 있습니다.;;)\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "*----------------------------------------------------------------\n",
+      "* Discriminator 미리 학습\n",
+      "*----------------------------------------------------------------\n",
+      "- 진짜 샘플 5개\n",
+      "[[ 6.57336939  1.        ]\n",
+      " [ 5.63364694  1.        ]\n",
+      " [ 5.64404928  1.        ]\n",
+      " [ 7.33483853  1.        ]\n",
+      " [ 5.3510401   1.        ]]\n",
+      "\n",
+      "\n",
+      "- 가짜 샘플 5개\n",
+      "[[ 1.06687319  0.        ]\n",
+      " [ 1.05815434  0.        ]\n",
+      " [ 1.0738405   0.        ]\n",
+      " [ 1.07440543  0.        ]\n",
+      " [ 1.05417192  0.        ]]\n",
+      "\n",
+      "\n",
+      "Epoch 1/1\n",
+      "80000/80000 [==============================] - 0s - loss: 0.0690 - acc: 0.9699     \n",
+      "\n",
+      "\n",
+      "*----------------------------------------------------------------\n",
+      "* 선학습된 Discriminator 테스트\n",
+      "*----------------------------------------------------------------\n",
+      "- Discriminator의 예측\n",
+      "    입력             출력1            출력2\n",
+      "[[  6.57336939e+00   3.48270440e-10   1.00000000e+00]\n",
+      " [  5.63364694e+00   3.58078154e-08   1.00000000e+00]\n",
+      " [  5.64404928e+00   3.40177131e-08   1.00000000e+00]\n",
+      " [  7.33483853e+00   8.15678341e-12   1.00000000e+00]\n",
+      " [  5.35104010e+00   1.44235727e-07   9.99999881e-01]\n",
+      " [  1.06687319e+00   9.97244358e-01   2.75568222e-03]\n",
+      " [  1.05815434e+00   9.97232378e-01   2.76764832e-03]\n",
+      " [  1.07384050e+00   9.97253835e-01   2.74615781e-03]\n",
+      " [  1.07440543e+00   9.97254670e-01   2.74538621e-03]\n",
+      " [  1.05417192e+00   9.97226894e-01   2.77313124e-03]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "################################################################\n",
+    "# Discriminator 미리 학습\n",
+    "################################################################\n",
+    "print(\"*----------------------------------------------------------------\")\n",
+    "print(\"* Discriminator 미리 학습\")\n",
+    "print(\"*----------------------------------------------------------------\")\n",
+    "make_trainable(D, True)\n",
+    "k = 200\n",
+    "real_mb = get_distribution_sampler(mu, sigma, batch_size*k)\n",
+    "fake_mb = np.hstack(\n",
+    "            ( G.predict( np.random.uniform(0,1,batch_size*k) ) , \n",
+    "              np.zeros(batch_size*k).reshape(batch_size*k,1) \n",
+    "            )\n",
+    "        )\n",
+    "\n",
+    "print(\"- 진짜 샘플 5개\")\n",
+    "print(real_mb[:5])\n",
+    "\n",
+    "print(\"\\n\")\n",
+    "print(\"- 가짜 샘플 5개\")\n",
+    "print(fake_mb[:5])\n",
+    "print(\"\\n\")\n",
+    "\n",
+    "train_D = np.vstack((real_mb, fake_mb))\n",
+    "train_D = train_D[np.random.permutation(train_D.shape[0]), :]\n",
+    "train_Dx = train_D[:,0]\n",
+    "train_Dy = np_utils.to_categorical(train_D[:,1], 2)\n",
+    "\n",
+    "D.fit(train_Dx, train_Dy, epochs=1, batch_size=batch_size)\n",
+    "\n",
+    "print(\"\\n\")\n",
+    "print(\"*----------------------------------------------------------------\")\n",
+    "print(\"* 선학습된 Discriminator 테스트\")\n",
+    "print(\"*----------------------------------------------------------------\")\n",
+    "Z = np.concatenate((real_mb[:5,0], fake_mb[:5,0]))\n",
+    "detec = D.predict(Z)\n",
+    "\n",
+    "print(\"- Discriminator의 예측\")\n",
+    "print(\"    입력             출력1            출력2\")\n",
+    "print(np.hstack((Z.reshape(10,1), detec)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "D가 선학습되어 트레이닝 데이터에 대해 매우 높은 정확도를 보이게 되었습니다. 이제 본 학습에 들어가는데 GANs에서 제안한 대로 D와 G의 업데이트 비율을 조절하면서 학습합니다. 여기서는 D 3번 업데이트하고 G를 한번 업데이트하는 식으로 학습을 진행하였습니다.\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "*----------------------------------------------------------------\n",
+      "* 본 학습 시작\n",
+      "*----------------------------------------------------------------\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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ONrPDgN8BN4fzDia4heSBwCjg9qpbRDrnMi9/4zN037GWl/YYXe95F3QfTmnuYXx39R8b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\ncy5LeQFwzrks5QXAOeeylBcA55zLUv8ff0Q1xJHoWrUAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09c02f6860>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch : 0, D:[array(0.0017670195084065199, dtype=float32), array(1.0, dtype=float32)], G loss:0.47773754596710205\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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7XgCcaw9//zv07An77590kuTtuGO4DmL69NzzujblZwE51x5qamDUqKRTpMdP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\nYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09d4048a90>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch : 5000, D:[array(0.6975672841072083, dtype=float32), array(0.5, dtype=float32)], G loss:0.1309429556131363\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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C8TxWUXf/bCn7dFlG48X9d9dQ6RwEXg8k7qjsH3ZLi5mtD/+uBuYApzcgn3Mt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\nTh822Cbx+tDuEb0x1yK0Tlg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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09d6d44eb8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch : 10000, D:[array(0.6931429505348206, dtype=float32), array(0.5450000166893005, dtype=float32)], G loss:0.11358608305454254\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09b6a0a080>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch : 15000, D:[array(0.6891288757324219, dtype=float32), array(0.4350000023841858, dtype=float32)], G loss:0.13778629899024963\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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yjV8PkDpZC4CZ7QMmANOBhcDjZrZA0kRJowEknS5pNfBJ4H5JC8LZjwdmS3od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\ndTi8DBhOUBReMbPfhuMfBP5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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09b63dbac8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch : 20000, D:[array(0.6423803567886353, dtype=float32), array(0.5899999737739563, dtype=float32)], G loss:0.16593211889266968\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09b688fef0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch : 25000, D:[array(0.6673904657363892, dtype=float32), array(0.5249999761581421, dtype=float32)], G loss:0.12458962202072144\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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gnJ8NeBvo0TQBRWTOoC6Mv/dfUYfhqpHWGYCkEZIWS1omaXw15WdLmidpX3gT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\nAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09b6b9c8d0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch : 30000, D:[array(0.6931748986244202, dtype=float32), array(0.5, dtype=float32)], G loss:0.1359509825706482\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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zx1OmVQCLgQrgNjN7qprlJgOTAXr37l0wY8aMBr+hdGVlZeTn50e2vqglOT6P\nreFqim/ZpmUxRHOgHnk92Lyv9kdzDz1oaKTbbF1WRsGVV/Lq//5vcEZQg2z9XpNg3LhxC8yssD7L\nNMcTwQaY2RpJg4G/SnrTzFakFjCzacA0gMLCQisqKops43PnziXK9UUtyfF5bA1XU3w3Tb+J/J3l\nXPPrd7j+myNiOSK+IP8CHil7pNYyc86dE/2Gu3WjqEuX4JGRNcjW7zVbZXIReA3QP2W8XzgtI2a2\nJvy7EpgLjKxHfM61OMcv2ULrfTlYHeKtgRInkwQwDxgiaZCktsAkIKPWPJK6S2oXDvcExpJy7cC5\nXDTqzS3MOzo5rX+ajd8PkDh1JgAzqwCmALOBt4HHzKxE0lRJEwAkjZK0GvgycK+kknDxYcB8Sa8D\ncwiuAXgCcLnLjNFvbea1ETnQ/j/diSfCwoWwfXvckbhQRtcAzGwWMCtt2g0pw/MIqobSl/s7cHQj\nY3SuxRiwdheVglWHdow7lObXsSPcckvQL1CXLnFH42iei8DOuVDnXRX88eS+WVP/n3pT2JxLIrgw\n/K1vNX4dLjKeAJxrRm8N6dqyu3+ui1lQDTRypD8oJgH8G3CuuZSX02ZvfF0/J4IEF14IixbFHYnD\nE4BzzeeZZ7jl52/FHUX8zjoLnn467igcngCcaz4zZ/JaLjb/TPfFL3oCSAhPAM41h8pK+NOf+MfI\nnnFHEr+xY6G0FNatizuSnOcJwLkmNm76OP71xkLebb2DtQd3iDuc+LVpE9wUNmtW3WVdk/JWQM41\ng7GLN/F3P/r/xE9+Al1zuDVUQngCcK4Z/O24g9jWuU3cYSTHgAFxR+DwBOBcZFJvmrpxwI0HzHv7\ncD/a/ZTHHgsSwZgxcUeSszwBONcElm1axk3TbwJgxLKtbOvcNuu7f4j8ruB334UXX/QEECO/COxc\nE/vqH96j/4e74g4jeaqag9bxUKrm0mTPRE4wTwDONaH8neUc8e4OFgzPwd4/6zJ8eNAdxOuvxx1J\nzvIqIOea0Jg3NrP4yG7saVfzYxCTqFmOgiU47zz4/e/huOOafns1yKUj/nSeAJxrQp9ftJG/jzwo\n7jCS6/zz4ac/jTuKT4n8ekdCZVQFJKlY0lJJpZKuqWb+iZIWSqoIHyKfOu8SScvD1yVRBe5c0rXa\nV8kxy7bxj2NzJwHUuw69sDBoDdQMcrGOvy51ngFIygPuAU4FVgPzJM1Me7LXB8ClwHfTlu0B3AgU\nAgYsCJeEI1meAAAQTElEQVTdEk34ziVXZV4rLvrpGPa2za7qn0xEfoRcWendQ8cgk098NFBqZivN\nbC8wA5iYWsDM3jOzN4DKtGVPB54zs83hTv85oDiCuJ3LCi1x5x+5FSuC5wMkpDVQLpHV8aGHVTrF\nZnZ5OH4xMMbMplRT9kHgaTN7PBz/LtDezG4Jx38A7Daz29OWmwxMBujdu3fBjBkzGvu+9isrKyM/\nPz+y9UUtyfF5bPWzbNOy/cMH7+3AqB/dyqwffAvLS9aRbY+8Hmzetzmy9Q09aOj+4arPIHVancwY\nc+GFvHXzzXx0yCFN9r2mfj/VxVyT1LJJ/N1VGTdu3AIzK6zPMom4CGxm04BpAIWFhVZUVBTZuufO\nnUuU64takuPz2GpWVQWSWv1RdeMXwA8WDuaDvA38bvejzR5bXS7Iv4BHyh6JbH1zzv30Z5A6LSMX\nX8yo995j7uGH7/9ea6pmamj1U+r3U13MNUktG/fvLmqZJIA1QP+U8X7htEysAYrSlp2b4bLOZa3P\nvDyPh8YcHHcYzaKhF1UP2JGf/7PgSWGnnBJVWJ/ahvu0TBLAPGCIpEEEO/RJwIUZrn828CNJVXfB\nnAZcW+8oncsincvKOfSd5fztinqdjee0cW99l99tWUWnFStgXOMSSiZnBZ4YAnUmADOrkDSFYGee\nB9xvZiWSpgLzzWympFHAH4DuwFmSbjKzo8xss6SbCZIIwFQzi67y0bkEOmHBBlYfM5zdHRJRw5od\nJP7nosM5eu9HfL+anXNNO2zfkTdORr9QM5sFzEqbdkPK8DyC6p3qlr0fuL8RMTqXCJnubHZ0akNJ\ncRGwsEnjyUa1fYb/GNmTgfm9oKzptuEO5IcozjVCdTublwp70S//CCjL3QTQ0Au1PVe8z4CKnbzf\nt1NThOXSeAJwLkL91+1iY7e2kMyWgrGozxH5oUuWcUHpB9x2xbAmjMhVSVYDZeey3HX3LmHE8m1x\nh5G1lp/4WcYu3EinXRVxh5ITPAE4F5Gh726nS1kF80f0iDuUrPVx184sOKo7J7+6Pu5QcoJXATlX\ni/pUX5w1Zx1/PulQrJWaMKKWb9aJh3LpH97jT+P6xB1Ki+cJwLk0DWlF0nF3BSfN38AlPxrVBBHl\nlvkjevCvj6ygx9Y9bO7WLu5wWjRPAM7R+KaDX1i4kYXDu7HFd1iNVtlKfPXWUX4m1Qw8ATgXgWc/\n35u/jewZdxgthrUSmCHDE0ET8ovAzkVBYmdHP56K0renL+Ok+RviDqNF8wTgcloUT4j610dKOb7E\neziJ2uIjuzHhr2vjDqNF80MWl3Oi7Cqg085yil/6kN+deVhk63SB/yvsxeTHVnLEyu0sHdwl7nBa\nJD8DcK4Rznj5Q+aN6M7WLm3jDqXF2de6Fb8/vR+TZq2KO5QWyxOAcw3UZu8+zn9mFTP+yY/+m8qf\nTzqU45Zupc9Hu+IOpUXyBOBcAxW//CEr+uezfGDnuENpsT5u35rrvjmCzV39DKsp+DUA5xpo+cDO\nvDWka9xhtHhLDvfPuKlkdAYgqVjSUkmlkq6pZn47SY+G81+VNDCcPlDSbkmLw9evog3fufi8M7gL\n7/b3bj+bw1HLtzHxhUyfROsyVWcCkJQH3AOcAQwHLpA0PK3Y14AtZnY4cCfwk5R5K8zsuPB1VURx\nOxebVvsq+drjK2lTXhl3KDljc9e2fPUP79Jht/cSGqVMzgBGA6VmttLM9gIzgIlpZSYC08Phx4FT\nJPnte65FOvnVDRyzbBvlrf0n3lzWHdyBBcO7c46fBUQqkwTQF0hth7U6nFZtGTOrALYBB4XzBkla\nJOn/JJ3QyHidi5UqjYuefp/fThgAfozTrO7/0iDOf2YV3bftjTuUFkNmVnsB6Tyg2MwuD8cvBsaY\n2ZSUMm+FZVaH4yuAMcAOIN/MNkkqAJ4CjjKz7WnbmAxMBujdu3fBjBkzonp/lJWVkZ+f3HraJMfX\nUmNbtmlZg7c7dM7fGfbci/zx1v+oNQH0yOvB5n3JvDs4m2MbM/1x2u7azUtfv7jZYhp60ND9w0n+\nnxg3btwCMyuszzKZtAJaA/RPGe8XTquuzGpJrYGuwCYLssseADNbECaGocD81IXNbBowDaCwsNCK\niorq8x5qNXfuXKJcX9SSHF9Lje2m6Tc1aLn8neVM/+1rXPvvR7NsZ+0HKRfkX8AjZY80aDtNLZtj\nm1lczhcWbmR2M8Y/59xPnmmc5P+JhsikCmgeMETSIEltgUnAzLQyM4FLwuHzgL+amUnqFV5ERtJg\nYAiwMprQnWte7fdW8uDZA1k2yLsliMvOTm2YfcKhcYfRYtR5BmBmFZKmALOBPOB+MyuRNBWYb2Yz\ngfuA30oqBTYTJAmAE4GpksqBSuAqM0vmuadzddjYvR1/Ojn98peLw0mvrWdP21a8cpx3wd0YGd0I\nZmazgFlp025IGf4Y+HI1yz0BPNHIGJ2LlSqNyb9fyUNnDfAunxNiR34bvvPAUhYM705527y4w8la\n3hWEc3U488V1jFi+jV3tfUeTFAuHd2fZgM5c8cS7cYeS1TwBOFeLgzd9zGVPvMtd/zLUn0yVMHdc\nOpQT521gzOub4g4la3kCcK4Gbcor+eE9JTx6Rn9WHJbMpn+5bEd+G3505TC+d/9SOu0sjzucrOQJ\nwLkaXPLUe2zo3o5Hz+hfd2EXizeO6MZ3v3cMOzu1iTuUrORXtJyrwZOn9mVP2zy/4zfh3usXnJ3l\n7yynzBNBvfgZgHNpem7ZQ6tKY3O3dt7qJ0u0Ka9k2o0LGLtwY9yhZBVPAM6l6L1hNz+/dREFJVvi\nDsXVQ3mbVvzw6uF854GlFLzltxplyhOAc6E+63dz122Leay4P/OO7hF3OK6elg3qwg3fOIrr732b\no5dujTucrOAJwDmg/7pd3HnbYh4+awBPjfe7fbPVW0O7ccuVw7jp7hIGrNkZdziJ5xWcLue1Ka/k\nx3e8wQPnDOQZ72cm6y0Y0YPrvnU0a3p3iDuUxPMzAJe7wq7Qy9u04hvXjfSdfwvy9me6UNG6FV12\n7OWime/Tap8/va06ngBcTsrfWc6Nv1jCCfM3ALClW7uYI3JNQuLYpVv52e1v+INkquEJwOUWM8Yu\n3Mivb5jPpm5teeUYv9jbkm3Pb8M13zmGt4Z05f7r5/HlZ1b5s5xT+DUAlztefBG+9z2+uvZd7rj0\nCG/pkyMqW4kHvjSI5z97MF9/dAUD1u7k9suOjDusRPAE4Fq23buDuv6OHWHzZvj2t7li1y+9Y7cc\ntKpPJ/7z34+h7d59APT7cBdjXt/Ec2MPYXt+bt5B7FVAruXZvRueew4uuwz69AmGAc4+G77yFd/5\n57i9Kc8POOK9HTz8vVe47ldLKHptPV3KcqtTuYwSgKRiSUsllUq6ppr57SQ9Gs5/VdLAlHnXhtOX\nSjo9utCdAyorYceOYHjHDjjhBOjVC264AUaMgJISmDgx3hhdIq0+pCM/unI4F/7ss5Qc3pXT/vYh\nv/2PV2n/cQUAg1eVcdjanVBREXOkTafOKqDwmb73AKcCq4F5kmaa2ZKUYl8DtpjZ4ZImAT8BviJp\nOMHjIY8C+gDPSxpqZvuifiOuBTGDvXuhrAy2boW8PBg4MJh3113w/vsMX7Qo2OEvXQr/8i/wi19A\nfj7cdBOMHh0MO5eBHflteGp8X54a35dW+yqpzAuOiz+3aBNnvLwObukKQ4bAYYcxuFMnqHoo/MKF\nUF4OBx0EXboEv7kOHbKq88BMrgGMBkrNbCWApBnARCA1AUwEfhgOPw7cLUnh9Blmtgd4N3xm8Gjg\nH9GE77LOmWfChg3BUdW+fcE/0EknwS9/GcwfPBg++CDY6XfsCN26BUfwd90VzN+yBfr2ZWN+Pgef\neSYMGwZduwbzJDj55Hjel2sRqnb+AA9PGMDDEwYw59w/BQcaq1ax89VXPyn86KPw17/Cpk3BwUhZ\nWVDluGJFMP/CC+HVV+GOOxJ7FioLb4apsYB0HlBsZpeH4xcDY8xsSkqZt8Iyq8PxFcAYgqTwipk9\nFE6/D/iLmT2eto3JwORw9AhgaePf2n49gSR3EZjk+Dy2hktyfB5bwyU5viPMrHN9FkhEKyAzmwZM\na4p1S5pvZoVNse4oJDk+j63hkhyfx9ZwSY5P0vz6LpPJReA1QOojkfqF06otI6k10BXYlOGyzjnn\nYpBJApgHDJE0SFJbgou6M9PKzAQuCYfPA/5qQd3STGBS2EpoEDAEeC2a0J1zzjVGnVVAZlYhaQow\nG8gD7jezEklTgflmNhO4D/hteJF3M0GSICz3GMEF4wrg6hhaADVJ1VKEkhyfx9ZwSY7PY2u4JMdX\n79jqvAjsnHOuZfI7gZ1zLkd5AnDOuRyVUwlA0nckmaSeccdSRdLPJL0j6Q1Jf5DULQEx1dr1R5wk\n9Zc0R9ISSSWSvhl3TOkk5UlaJOnpuGNJJ6mbpMfD39zbkj4Xd0xVJP17+J2+JekRSe1jjud+SevD\n+5yqpvWQ9Jyk5eHf7gmKrd77kpxJAJL6A6cBH8QdS5rngBFmdgywDLg2zmBSuv44AxgOXBB26ZEU\nFcB3zGw48Fng6oTFB/BN4O24g6jBfwPPmNmRwLEkJE5JfYF/AwrNbARBg5NJ8UbFg0Bx2rRrgBfM\nbAjwQjgehwf5dGz13pfkTAIA7gS+DyTqqreZPWtmVb1NvUJwr0Sc9nf9YWZ7gaquPxLBzNaZ2cJw\neAfBDiwxT3GX1A84E/hN3LGkk9QVOJGg1R5mttfMtsYb1QFaAx3Ce4k6AmvjDMbMXiRo1ZhqIjA9\nHJ4OnN2sQYWqi60h+5KcSACSJgJrzOz1uGOpw2XAX2KOoS+wKmV8NQnawaYKe50dCbxae8lmdRfB\ngUYSHzs1CNgAPBBWUf1GUqe4gwIwszXA7QRn6OuAbWb2bLxRVau3ma0Lhz8EescZTC0y2pe0mAQg\n6fmw7jD9NRH4T+CGhMZWVeY6guqNh+OKM5tIygeeAL5lZtvjjgdA0heB9Wa2IO5YatAaOB74pZmN\nBHYSXxXGAcK69IkESaoP0EnSP8cbVe3Cm10TVaMA9duXJKIvoCiY2fjqpks6muBH9XrQQSn9gIWS\nRpvZh3HGVkXSpcAXgVMs/hszEt99h6Q2BDv/h83sybjjSTEWmCDpn4D2QBdJD5lZUnZkq4HVZlZ1\nxvQ4CUkAwHjgXTPbACDpSeDzwEOxRvVpH0k61MzWSToUWB93QKnquy9pMWcANTGzN83sYDMbaGYD\nCf4Jjm+unX9dJBUTVBlMMLNdccdDZl1/xCbsZvw+4G0zuyPueFKZ2bVm1i/8nU0i6BIlKTt/wt/8\nKklHhJNO4cBu3eP0AfBZSR3D7/gUEnKBOk1qtzeXAH+MMZYDNGRf0uITQBa4G+gMPCdpsaRfxRlM\neBGpquuPt4HHzKwkzpjSjAUuBk4OP6/F4RG3y8w3gIclvQEcB/wo5ngACM9KHgcWAm8S7Jti7XZB\n0iMEzy45QtJqSV8DbgNOlbSc4KzltgTFVu99iXcF4ZxzOcrPAJxzLkd5AnDOuRzlCcA553KUJwDn\nnMtRngCccy5HeQJwzrkc5QnAOedy1P8Dhs9tZ3dWzL0AAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09c2a19438>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch : 35000, D:[array(0.6922645568847656, dtype=float32), array(0.4950000047683716, dtype=float32)], G loss:0.12878786027431488\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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p9i5wKfDdWhax1cwGRZDVuZbjzTehVy/o0ydz23xXVAQvvhh3CleLbO4INhhY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\nAElTgBFAagEYAfw4fP4QcJs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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09d40de860>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch : 40000, D:[array(0.6848969459533691, dtype=float32), array(0.4925000071525574, dtype=float32)], G loss:0.12272197008132935\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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fPnj22ZwoAMv6d4Zu3fw2kTFUbzdQSa2Bu4GzgdXAXEmzzGxxQrMPgSuA79ew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\nFwDnnMtR/x8fIWb+IRpVGAAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09b9e73470>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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j5/6YaIkoSYjIaBHJEJG5PvUiIs+KyFIRmS0iPYPqLhWRJd7j0mgFbozxV/DDx91i3piy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\n0P4EOO7W8PE27uAeRTXpBGc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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09bf995438>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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RwyDr1lLbe3V3z4CjI48b1K1Fg7q1uO3sxEcenNPlUG44JYNbzzgSgGd+3oPl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\nTwAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09c1c71198>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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K3qZeI7hXIkr7uv4ws11AZdcfsWBmH5nZvPD9VoINWM9oU31G0uHA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\nOeeylBcA55zLUv8fo+QHfj6Y5PIAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09b675dcc0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 7.12918377]\n",
+      " [ 6.34670162]\n",
+      " [ 7.1849947 ]\n",
+      " [ 4.80329943]\n",
+      " [ 6.08930492]\n",
+      " [ 6.52564669]\n",
+      " [ 5.71299791]\n",
+      " [ 4.34062815]\n",
+      " [ 5.82264519]\n",
+      " [ 5.33823776]]\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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k8/DLi403uEXBhujy6C1k5Qzm0Nyn6RHtwz9jhQNK9+htdI/cxoE5LzD6gAEA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\nFAxERAQFAxERQcFARERQMBAREeD/AW5BI3VHxWj5AAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09b6eeaa20>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 0.47562054  0.52437949]\n",
+      " [ 0.49904591  0.50095403]\n",
+      " [ 0.47395247  0.52604753]\n",
+      " [ 0.51996464  0.48003539]\n",
+      " [ 0.50675774  0.49324229]\n",
+      " [ 0.49368471  0.50631535]\n",
+      " [ 0.51802534  0.48197469]\n",
+      " [ 0.50877184  0.49122813]\n",
+      " [ 0.51474357  0.48525646]\n",
+      " [ 0.52922851  0.47077155]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "################################################################\n",
+    "# 본학습\n",
+    "################################################################\n",
+    "print(\"*----------------------------------------------------------------\")\n",
+    "print(\"* 본 학습 시작\")\n",
+    "print(\"*----------------------------------------------------------------\")\n",
+    "\n",
+    "# the histogram of the data\n",
+    "plt.title('Distribution of P_data(x)')    \n",
+    "n, bins1, patches = plt.hist(get_distribution_sampler(mu, sigma, 10000)[:,0], 50, normed=1, facecolor='blue', alpha=0.75)\n",
+    "y = mlab.normpdf(bins1, mu, sigma)\n",
+    "l = plt.plot(bins1, y, 'r--', linewidth=1)\n",
+    "plt.axis([-5, 12, 0, 0.45])\n",
+    "plt.grid(True)\n",
+    "plt.show()\n",
+    "\n",
+    "nb_epoch = 45000\n",
+    "D_losses = []\n",
+    "GAN_losses = []\n",
+    "\n",
+    "for epoch in range(nb_epoch) :\n",
+    "    #train D\n",
+    "    for k in range(3):\n",
+    "        #진짜 데이터를 받아온다.\n",
+    "        real_mb = get_distribution_sampler(mu, sigma, batch_size)\n",
+    "        #가짜 데이터를 받아온다.\n",
+    "        fake_mb = np.hstack(\n",
+    "                        ( G.predict( np.random.uniform(0,1,batch_size) ) , \n",
+    "                          np.zeros(batch_size).reshape(batch_size,1) \n",
+    "                        )\n",
+    "                    )\n",
+    "        #진짜 가짜를 섞어서\n",
+    "        train_D = np.vstack((real_mb, fake_mb))\n",
+    "        train_D = train_D[np.random.permutation(train_D.shape[0]), :]\n",
+    "        train_Dx = train_D[:,0]\n",
+    "        train_DY = np_utils.to_categorical(train_D[:,1], 2)\n",
+    "        #학습을 한다.\n",
+    "        d_loss = D.train_on_batch(train_Dx, train_DY)\n",
+    "        D_losses.append(d_loss)\n",
+    "    \n",
+    "    #train GAN for G  균등분포 난수와 , 라벨 1을 입력으로 학습힌다.\n",
+    "    g_loss = GAN.train_on_batch( np.random.uniform(0,1,batch_size) , np_utils.to_categorical(np.ones(batch_size),2) )\n",
+    "    GAN_losses.append(g_loss)\n",
+    "        \n",
+    "    if epoch % print_interval == 0:\n",
+    "        print( \"Epoch : {}, D:{}, G loss:{}\".format(epoch, d_loss, g_loss) )\n",
+    "\n",
+    "    if epoch % 5000 == 0 :\n",
+    "        fake = G.predict(Z1)\n",
+    "        plt.title('Epoch {} Distribution of P_g(x)'.format(epoch))\n",
+    "        plt.hist(fake, 50, normed=1, facecolor='green', alpha=0.75)\n",
+    "        l = plt.plot(bins1, y, 'r--', linewidth=1)\n",
+    "        plt.axis([-5, 12, 0, 0.45])\n",
+    "        plt.grid(True)\n",
+    "        plt.show()\n",
+    "        \n",
+    "#################################################################\n",
+    "# 그림 그리는 보조 코드들\n",
+    "#################################################################\n",
+    "plt.title('Discriminator loss and accuracy')    \n",
+    "plt.plot(D_losses)\n",
+    "plt.show()\n",
+    "\n",
+    "plt.title('GAN loss')    \n",
+    "plt.plot(GAN_losses)\n",
+    "plt.show()\n",
+    "\n",
+    "fake = G.predict(Z1)\n",
+    "plt.title('Distribution of P_g(x)')\n",
+    "plt.hist(fake, 50, normed=1, facecolor='green', alpha=0.75)\n",
+    "l = plt.plot(bins1, y, 'r--', linewidth=1)\n",
+    "plt.axis([-5, 12, 0, 0.45])\n",
+    "plt.grid(True)\n",
+    "plt.show()\n",
+    "print(fake[:10])\n",
+    "\n",
+    "plt.title('Discriminator prediction to samples from G(z)')\n",
+    "detec = D.predict(fake)\n",
+    "plt.plot(detec)\n",
+    "plt.axis([0, 10000, 0, 1])\n",
+    "plt.show()\n",
+    "print(detec[:10])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "결과를 다시 한번 찍어보면 아래처럼 모양이 그럭저럭 잘 나오는 것을 확인할 수 있습니다."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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z3jwoLo46TvQuusgLQEx4AXCuHajW4LHHgm+/2e6009i+fBkX3/GJqJNkPS8A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\nvZi3Sxct5gAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f09f73c92b0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.title('Distribution of P_g(x)')\n",
+    "plt.hist(G.predict(np.random.uniform(0,1,10000)), 50, normed=1, facecolor='green', alpha=0.75)\n",
+    "l = plt.plot(bins1, y, 'r--', linewidth=1)\n",
+    "plt.axis([-5, 12, 0, 0.45])\n",
+    "plt.grid(True)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "실습을 통해 다음과 같은 사실을 알 수 있습니다.  \n",
+    "\n",
+    "1. 초록색 분포가 100줄짜리 프로그램(주석과 그림 그리는 부분 빼면 얼추 100줄;;;) 치고는 $p_{data}$ 분포를 꽤 잘 따라가고 있습니다.<br/>\n",
+    "2. D의 정밀도가 처음에는 1.0으로 시작했다가(위 주황색 그래프) 점점 0.5 근처로 수렴하고 있습니다. 마지막 부분에 실제 softmax층에서 나온 출력을 보면 두 값 모두 0.5 근처로 뭐가 뭔지 모르겠다고 결과를 내보내고 있습니다.<br/>\n",
+    "3. 하지만 G, D가 평형점을 정확히 찾지 못하고 왔다갔다 진동하고 있는 모습을 보입니다. 이에 대해서는 <a href=\"https://www.facebook.com/groups/TensorFlowKR/permalink/456848987989498/\">TF-KR의 유재준님 논문 발표</a>[11]에서 확인할 수 있습니다. 계속 학습을 진행하면 결과가 오히려 나빠지는 경우도 많이 나타납니다.<br/>\n",
+    "4. 학습이 초기조건에 꽤 민감하게 반응합니다. 위 결과는 한 서너번 반복해서 나온 괜찮은 결과입니다.<br/>\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 약간의 이론\n",
+    "<hr/>\n",
+    "\n",
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "논문에서 GANs의 이론적 논의는 D를 고정한 상태에서 G에 대한 코스트함수가 전역적 최소를 가지고 그것이 $p_{data}=p_{g}$일 때이며 상기 알고리즘으로 그 전역 최소에 도달할 수 있는지 보이는 것입니다. 크게 3가지 부분으로 이 문제를 설명합니다. <a href=\"http://jaejunyoo.blogspot.com/2017/01/generative-adversarial-nets-1.html\">유재준님의 블로그</a>[12]와 TF-KR의 논문 발표를 참고하여 내용을 정리하였습니다.\n",
+    "</div>\n",
+    "\n",
+    "><b> Proposition 1. </b>  *For G fixed, the optimal discriminator D is*\n",
+    "$$\n",
+    "D^{*}_{G}(\\boldsymbol{x}) = \\frac{p_{data}(\\boldsymbol{x})}{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})}\n",
+    "$$\n",
+    "\n",
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "Proposition 1은 G가 고정된 상태에서 최적의 D는 위 식으로 주어진다는 것을 이야기 하며 이를 보이기 위해서는 $\\frac{\\partial V(G,D)}{\\partial D(\\boldsymbol{x})}=0$  또는 ($ V(G,D) = -J^{D}$ 이므로) $\\frac{\\partial J^{D}}{\\partial D(\\boldsymbol{x})}=0$ 인 $D(\\boldsymbol{x})$를 구하면 됩니다.\n",
+    "<br/><br/>\n",
+    "$$\n",
+    "\\begin{align}\n",
+    "\\frac{\\partial V(G,D)}{\\partial D(\\boldsymbol{x})} \n",
+    "&= \\frac{\\partial}{\\partial D(\\boldsymbol{x})} \\int_{\\boldsymbol{x}} p_{x \\sim data}(\\boldsymbol{x}) \\log D(\\boldsymbol{x}) + p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x}) \\log (1-D(\\boldsymbol{x})) d\\boldsymbol{x} \\\\\n",
+    "&= \\int_{\\boldsymbol{x}} \\frac{\\partial}{\\partial D(\\boldsymbol{x})}  \\left[ p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x}) \\log D(\\boldsymbol{x}) + p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x}) \\log (1-D(\\boldsymbol{x})) \\right] d\\boldsymbol{x} \\\\\n",
+    "&= \\int_{\\boldsymbol{x}} p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x}) \\frac{1}{D(\\boldsymbol{x})} - p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x}) \\frac{1}{1-D(\\boldsymbol{x})} d\\boldsymbol{x} \n",
+    "\\end{align}\n",
+    "$$\n",
+    "<br/>\n",
+    "이므로\n",
+    "<br/><br/>\n",
+    "$$\n",
+    "\\int_{x} \\frac{p_{x \\sim data}(x)\\left( 1-D(x) \\right) - p_{x \\sim g}(x)D(x)}{D(x)\\left(1-D(x) \\right)} dx =0\n",
+    "$$\n",
+    "<br/>\n",
+    "입니다.  \n",
+    "위 적분식이 0이 되기 위해서는 Integrand의 분자가 0 인 경우를 생각해 볼 수 있습니다. 그런데 분자는 0보다 크거나 같다는 것을 알지 못하므로 꼭 분자가 0이 아니더라도 적분식이 0이 될 수 가 있습니다.(적당히 +,- 해서 총합이 0)  따라서 $\\frac{\\partial V(G,D)}{\\partial D(\\boldsymbol{x})}=0$를 만족하는 $D(\\boldsymbol{x})$가 지역 최소(또는 지역 최대)나 안장점이 아니기 위해서는 $V(G,D)$가 볼록함을(또는 오목함을) 보여야 합니다. $ V(G,D) = -J^{D}$ 이므로 $J^{D}$가 볼록함수인지를 보여도 되는데 만약 $J^{D}$가 엄격하게 볼록하다면 전역 최소를 가지며 분자가 0인 경우가 $\\frac{\\partial J^{D}}{\\partial D(\\boldsymbol{x})}=0$ 인 유일한 전역 최소라 할 수 있습니다.\n",
+    "<br/><br/>\n",
+    "$$\n",
+    "\\begin{align}\n",
+    "J^{D} &= -\\int_{x} p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x}) \\log D(x) + p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x}) \\log (1-D(x)) dx \\\\\n",
+    "&= \\int_{x} p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x}) \\left(-\\log D(x)\\right) + p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x}) \\left(-\\log (1-D(x))\\right) dx\n",
+    "\\end{align}\n",
+    "$$\n",
+    "<br/>\n",
+    "$J^{D}$는 위 식과 같은데 위 식에서 $p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x})$는 우리가 가진 샘플들에 의해 이미 결정된 확률분포 입니다. 그리고 지금 G가 주어진 상태, 즉, G가 고정된 상태에서 D(x)만 변화 시켜 $J^{D}$의 변화를 보고 있으므로 $p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x}) $ 역시 고정입니다. 결국 $J^{D}$는 독립변수 $D(x)$에 대한 함수  $-\\log D(x)$와 $-\\log \\left(1-D(x)\\right)$의 조합이므로 $-\\log D(x)$와 $-\\log \\left(1-D(x)\\right)$가 볼록함수임을 보이면 $J^{D}$가 볼록함수임을 보일 수 있습니다. 이를 위해 $D(x)$에 대한 이계미분이 음이 아님을 보이면 되므로\n",
+    "<br/><br/>\n",
+    "$$\n",
+    "\\frac{\\partial}{\\partial D(x)}\\left(\\frac{\\partial  \\{-\\log D(x)\\}}{\\partial D(x)}\\right) = \\frac{\\partial}{\\partial D(x)}\\left( -\\frac{1}{D(x)} \\right) = \\frac{1}{D^{2}(x)} \n",
+    "$$\n",
+    "<br/>\n",
+    "$$\n",
+    "\\frac{\\partial}{\\partial D(x)}\\left(\\frac{\\partial  \\{-\\log (1-D(x))\\}}{\\partial D(x)}\\right) = \\frac{\\partial}{\\partial D(x)}\\left( \\frac{1}{1-D(x)} \\right) = \\frac{1}{ (1-D(x))^2 } \n",
+    "$$\n",
+    "<br/>\n",
+    "이고, 두 결과 모두 $D(x) = 0$를 제외하면 항상 양수이므로 두 함수 모두 볼록 함수이며 이 함수들이 0보다 큰 $p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x})$, $p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x}) $와의 곱의 합으로 나타나는 $J^{D}$ 역시 볼록함수임을 알 수 있습니다. \n",
+    "따라서\n",
+    "<br/><br/>\n",
+    "$$ p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x}) \\left( 1-D(\\boldsymbol{x}) \\right) - p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x})D(\\boldsymbol{x}) =0 $$\n",
+    "<br/>\n",
+    "이며 최종적으로\n",
+    "<br/><br/>\n",
+    "$$ D^{*}(\\boldsymbol{x}) = \\frac{p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x})}{p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x})+p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x})}$$\n",
+    "<br/>\n",
+    "임을 확인할 수 있습니다.   \n",
+    "\n",
+    "\n",
+    "마지막으로 $D(\\boldsymbol{x})$는 $p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x})$와 $p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x})$가 0이 아닌 집합에 대해서만 정의되면 되므로(어떤 샘플 $\\boldsymbol{x}$가 일어날 확률이 0인 것에 대해서는 참 거짖을 판별할 필요 없음) $Supp(p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x})) \\cup Supp(p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x}))$ 에서만 정의되면 된다 라고 논문에서 언급합니다.  \n",
+    "논문에서 증명 하기를 $(a,b) \\in \\mathbb{R}^{2} \\backslash \\{0,0\\}$ 인 a, b에 대해서 $a \\log(y) + b \\log(1-y)$라는 함수를 [0,1]에서 y에 대해 미분해서 0인 점을 찾으면 최대값이 $ \\frac{a}{a+b}$에서 나타난다고 하고 이 식에서 a에 해당하는것이 $p_{\\boldsymbol{x} \\sim data}$이고 b에 해당하는 것이 $p_{\\boldsymbol{x} \\sim g}$ 니까 a, b가 0이 아니었듯이 $p_{\\boldsymbol{x} \\sim data}$, $p_{\\boldsymbol{x} \\sim g}$도 0이 아닌 경우에 대해서 생각하기 위해 $Supp(p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x})) \\cup Supp(p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x}))$ 에서만 정의되면 된다고 언급하고 증명을 마무리한 것으로 생각됩니다.\n",
+    "</div>\n",
+    "\n",
+    "<hr/>\n",
+    "\n",
+    "><b>Theorem 1.</b> *The global minimum of the virtual training criterion $C(G)$ is achieved if and only if $p_g = p_{data}$. At that point, $C(G)$ achieves the value $−log4$*. \n",
+    "\n",
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "위 결과에 의해 $V(G,D)$를 최대화 하는 D를 찾았다고 하면 G에 대한 코스트 C(G)를 아래와 같이 쓸 수 있습니다.\n",
+    "<br/><br/>\n",
+    "$$\n",
+    "\\begin{align}\n",
+    "C(G) \n",
+    "& = \\underset{D}{max}V(G,D) \\\\\n",
+    "& = \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{data}}} \\left[ \\log D^{*}_{G}(x) \\right] + \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{g}}} \\left[ \\log (1-D^{*}_{G}(x)) \\right] \\\\\n",
+    "& = \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{data}}} \\left[ \\log \\frac{p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x})}{p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x})+p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x})} \\right] + \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{g}}} \\left[ \\log \\frac{p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x})}{p_{\\boldsymbol{x} \\sim data}(\\boldsymbol{x})+p_{\\boldsymbol{x} \\sim g}(\\boldsymbol{x})} \\right]\n",
+    "\\end{align}\n",
+    "$$\n",
+    "<br/>\n",
+    "만약 $p_g = p_{data}$ 라면 C(G)는 아래와 같습니다.\n",
+    "<br/><br/>\n",
+    "$$\n",
+    "\\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{data}}} \\left[ - \\log 2 \\right] + \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{g}}} \\left[ - \\log 2 \\right]    = -\\log 4\n",
+    "$$\n",
+    "<br/>\n",
+    "이제 $-\\log 4$가 C(G)의 전역 최소라는 것을 보이기 위해 아래처럼 $C(G)=V(D^{*}_{G}, G)$에서 위 식을 빼면\n",
+    "<br/><br/>\n",
+    "$$\n",
+    "\\begin{matrix} \n",
+    "&  & \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{data}}} \\left [ \\log \\frac{p_{data}(\\boldsymbol{x})}{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})} \\right] & + & \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{g}}} \\left [ \\log \\frac{p_{g}(\\boldsymbol{x})}{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})} \\right] & = & C(G) & \\\\\n",
+    "- & ( & \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{data}}} \\left[ - \\log 2 \\right] & + & \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{g}}} \\left[ - \\log 2 \\right]    & = & -\\log 4 & ) \n",
+    "\\end{matrix}\n",
+    "$$\n",
+    "<br/>\n",
+    "$$\n",
+    "\\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{data}}} \\left [ \\log \\frac{p_{data}(\\boldsymbol{x})}{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})} \\right] - \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{data}}} \\left[ - \\log 2 \\right] \n",
+    "+ \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{g}}} \\left [ \\log \\frac{p_{g}(\\boldsymbol{x})}{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})} \\right]-\\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{g}}} \\left[ - \\log 2 \\right]  = C(G)+\\log 4\n",
+    "$$\n",
+    "<br/>\n",
+    "이 됩니다. 기대값 안에 $-\\log 2$에서 $-$를 끄집어 내고 정리하면\n",
+    "<br/><br/>\n",
+    "$$\n",
+    "\\begin{align}\n",
+    "C(G) &= -\\log 4  + \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{data}}} \\left [ \\log \\frac{p_{data}(\\boldsymbol{x})}{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})} \\right] + \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{data}}} \\left[ \\log 2 \\right] \n",
+    "+ \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{g}}} \\left [ \\log \\frac{p_{g}(\\boldsymbol{x})}{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})} \\right]+\\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{g}}} \\left[ \\log 2 \\right] \\\\\n",
+    "&= -\\log 4  + \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{data}}} \\left [ \\log \\frac{p_{data}(\\boldsymbol{x})}{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})} + \\log 2\\right] + \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{g}}} \\left [ \\log \\frac{p_{g}(\\boldsymbol{x})}{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})} + \\log 2\\right] \\\\\n",
+    "&= -\\log 4  + \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{data}}} \\left [ \\log \\frac{ 2\\,p_{data}(\\boldsymbol{x})}{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})} \\right] + \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{g}}} \\left [ \\log \\frac{2\\, p_{g}(\\boldsymbol{x})}{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})} \\right] \\\\\n",
+    "&= -\\log 4  + \\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{data}}} \\left [ \\log \\frac{ p_{data}(\\boldsymbol{x})}\n",
+    "{ \\frac{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})}{2} } \\right] + \n",
+    "\\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text{g}}} \\left [ \\log \\frac{p_{g}(\\boldsymbol{x})}\n",
+    "{ \\frac{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})}{2} } \\right] \\\\\n",
+    "&= -\\log 4  \n",
+    "+ \\int_{\\boldsymbol{x} \\sim p_{\\text{data}}} p_{data}(\\boldsymbol{x}) \\left [ \\log \\frac{ p_{data}(\\boldsymbol{x})}\n",
+    "{ \\frac{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})}{2} } \\right] d\\boldsymbol{x}\n",
+    "+ \n",
+    "\\int_{\\boldsymbol{x} \\sim p_{\\text{g}}} p_{g}(\\boldsymbol{x}) \\left [ \\log \\frac{p_{g}(\\boldsymbol{x})}\n",
+    "{ \\frac{p_{data}(\\boldsymbol{x})+p_{g}(\\boldsymbol{x})}{2} } \\right] d\\boldsymbol{x} \\\\\n",
+    "&= -\\log 4 + KL \\left( p_{data} \\parallel \\frac{p_{data}+p_{g}}{2} \\right) + KL \\left( p_{g} \\parallel \\frac{p_{data}+p_{g}}{2} \\right)\n",
+    "\\end{align} \n",
+    "$$\n",
+    "<br/>\n",
+    "가 됩니다. 마지막 줄은 앞서 살펴보았던 쿨벡-라이블러 발산의 정의를 그대로 이용한 것입니다. 앞서 쿨벡-라이블러 발산은 항상 0보다 크거나 같으며 볼록하다는 것을 확인했습니다. 따라서 위 식으로 부터 $C(G)$는 볼록함수이며 $p_{data}=p_{g}$일 때 전역적 최솟값 $-\\log 4$를 가진다는 것이 증명되었습니다.\n",
+    "\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 참고문헌\n",
+    "<hr/>\n",
+    "<div style=\"line-height:30px;font-size:15px;\">\n",
+    "[1] 칸아카데미 정보엔트로피 (https://ko.khanacademy.org/computing/computer-science/informationtheory/moderninfotheory/v/information-entropy)<br/>\n",
+    "[2] Cross entropy, https://en.wikipedia.org/wiki/Cross_entropy<br/>\n",
+    "[3] CSE 533: Information Theory in Computer Science, https://catalyst.uw.edu/workspace/anuprao/15415/86593<br/>\n",
+    "[4] GANs in 50 lines of code (PyTorch), Dev Nag, https://medium.com/@devnag/generative-adversarial-networks-gans-in-50-lines-of-code-pytorch-e81b79659e3f<br/>\n",
+    "[5] tensorflow-GAN-1d-gaussian-ex, 이활석, https://github.com/hwalsuklee/tensorflow-GAN-1d-gaussian-ex<br/>\n",
+    "[6] 아주 간단한 GAN 구현하기, 홍정모, http://blog.naver.com/atelierjpro/220984758512<br/>\n",
+    "[7] Generative Adversarial Networks, Ian J. Goodfellow et al, arXiv:1406.2661, 2014<br/>\n",
+    "[8] KerasGAN, https://github.com/osh/KerasGAN<br/>\n",
+    "[9] NIPS 2016 Tutorial:Generative Adversarial Networks, Ian J. Goodfellow, arXiv:1701.00160v3, 2017<br/>\n",
+    "[10] Generative adversarial networks , 김남주, https://www.slideshare.net/ssuser77ee21/generative-adversarial-networks-70896091<br/>\n",
+    "[11] PR12와 함께하는 GANs, 유재준, https://www.slideshare.net/thinkingfactory/pr12-intro-to-gans-jaejun-yoo<br/>\n",
+    "[12] 초짜 대학원생 입장에서 이해하는 Generative Adversarial Nets, 유재준, http://jaejunyoo.blogspot.com/2017/01/generative-adversarial-nets-1.html\n",
+    "</div>"
+   ]
+  }
+ ],
+ "metadata": {
+  "anaconda-cloud": {},
+  "kernelspec": {
+   "display_name": "Python 3",
+   "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": "3.5.2"
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+ "nbformat_minor": 2
+}