ニューラルネットワークの学習.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ニューラルネットワークの学習\n",
    "## 損失関数\n",
    "### 2乗和誤差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def mean_squared_error(y, t):\n",
    "    return 0.5 * np.sum((y-t)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = [0.1, 0.05, 0.6, 0.0, 0.05, 0.1, 0.0, 0.1, 0.0, 0.0]\n",
    "t = [0, 0, 1, 0, 0, 0, 0, 0, 0, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.097500000000000031"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(np.array(y), np.array(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 交差エントロピー誤差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def cross_entropy_error(y, t):\n",
    "    delta = 1e-7\n",
    "    return -np.sum(t * np.log(y + delta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.51082545709933802"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_entropy_error(np.array(y), np.array(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ミニバッチ学習"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 784)\n",
      "(60000, 10)\n"
     ]
    }
   ],
   "source": [
    "from mymodule.mnist import load_mnist\n",
    "(x_train, t_train), (x_test, t_test)= load_mnist(normalize=True, one_hot_label=True)\n",
    "print(x_train.shape)\n",
    "print(t_train.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[12725 15614  4447 22004 41049 44449 58596 21660 47599  7767]\n"
     ]
    }
   ],
   "source": [
    "train_size = x_train.shape[0]\n",
    "batch_size = 10\n",
    "batch_mask = np.random.choice(train_size, batch_size)\n",
    "x_batch = x_train[batch_mask]\n",
    "t_batch = t_train[batch_mask]\n",
    "print(batch_mask)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def cross_entropy_error(y, t): #バッチ対応版\n",
    "    if y.ndim == 1:\n",
    "        t = t.reshape(1, t.size)\n",
    "        y = y.reshape(1, y.size)\n",
    "        \n",
    "    # 教師データがone-hot-vectorの場合、正解ラベルのインデックスに変換\n",
    "    if t.size == y.size:\n",
    "        t = t.argmax(axis=1)\n",
    "             \n",
    "    batch_size = y.shape[0]\n",
    "    return -np.sum(np.log(y[np.arange(batch_size), t])) / batch_size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.51082545709933802"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_entropy_error(np.array(y), np.array(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 数値微分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def numerical_diff(f, x):\n",
    "    h = 1e-4 # 0.0001\n",
    "    return (f(x+h) - f(x-h)) / (2*h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1999999999990898\n"
     ]
    },
    {
     "data": {
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u5Z0V29j75StcU/ARo8N2U1y/EWFDJkD8FMLb9PG6RBGpwPPAN8ZMBaYCxMTE\neFyNnEp2fjHzlyzDrpzJNWWLaWaOkdusJ2XnPknkYDVhRQKZ54FvrZ0GTAOIi4uzHpcjVdibkcuy\nj+fSecccxpl1lBDO0djLsRf+jOjYc9WEFQkCnge+BC5rLeu3bmfnZ88zPPM9xppMsiNbkj74/9Hm\ngp/Sqkl7r0sUkRpw87bMecCFQCtjzD7gUWvtTLfGk9pTUlLK8mWfUfy/aYwsWMpgU8LepkPJOu9x\nmg+9QU1YkSDl5l06Y9z63uKOnNxs1i6YSZstsznX7uQ4UeyO+TExV9xLTEctpRAJdprSEXamrOfA\nwmcYmD6f880xUiNiSB74O3pdNoXeDZp4XZ6I1BIFfogqLi5m3ZI3iUiayZDCVcTYMDY1vYDoc++k\n2/DL1YQVqYMU+CEm89ABUj5+lq673yCOdDJpzqrYqfS48h4Gt9VtsSJ1mQI/BNiyMpKTlpD31QsM\nzl7MOaaY5PqDyBz6MP1HjaVVZD2vSxQRP1Dg12FZR7NZ/+ks2qW8Sr+y7RyzUaxrfS3tLrmbvn2G\neV2eiPiZAr+Osdayet1qjn75PMOOfMQF5hh7w2NY3f9hel8+mfgmLbwuUUQ8osCvIzKyj7Ny4Ru0\n2Pwy8SVrKDOGlOYXkHPeXcQMvYwYNWFFQp4CP4gVl5bx9foUjnw1i7jD73GVSedIWAtSet9F18t/\nRv+Wnb0uUUQCiAI/yFhr2XQgh/999RntU2Zzadk31DfF7I4+i7SRf6Bdwk200EpYEamEAj9IpOcU\n8GHSDrJWvM6lxz5kSthOCkwD0nvcRLtLfk5se62EFZGTU+AHsPyiUhYmH+KrxJX02Ps6N4V/SXOT\nx9Hobhw/+680jBtH5yithBWR6lHgB5iikjKWbs3gw7WpFG75jJvtp/w1fB1EhHG82+Vw3l00iz1P\nK2FFpMYU+AGgtMyyfOdhPlh7gG82buXK4oU8ELmITmHpFDVoDcMfICzuDho36eB1qSISxBT4Hikr\ns6xJzeLDdQeZv/4gHY5tZmK9hfwp7H9ERhZRFjMS4v9KvT7XQoRWworImVPg+1FJaRkrdh3hk01p\nfLopjaM5uVwfuZy3Gi4htn4KNrIRZvCtMHwyYW37e12uiNQxCnyXFRSX8vX2TD7ZmMbC5ENkHS+m\nR2QGf2z5DRfaT6hXnA3RvWDU3zGDfwJRTb0uWUTqKAW+C3ILilm6NZNPNqWxZEs6eYUlNIkK4+7O\ne7i+eAHSYFTAAAAJ7ElEQVSt05ZissOgz9UwfDJ0PV9NWBFxnQK/luzKPMbiLeks3nKIFbuOUFxq\nadmoHj/p35Cx9ZbSbffrmNQ90KgNnP8ADJsATTt6XbaIhBAF/mkqLi1j5e4jLE5OZ/GWdHZmHgOg\nZ5vGTDy3K9e2PEi//W8StukdKCmAmJFwyaOgJqyIeESBXwMHjuazbFsmX27NYOnWDHILS6gXHsaI\n7i0ZPzKWUT2a0PnAJ7Di95C4GiIbweAxzrRNO62EFRFvKfBPIq+whOU7DrNseyZfbctgR4ZzFd8m\nuj5XD2rPqD5tOKdHKxod3wcrZ8KLr0L+EWjVC658AgbfoiasiAQMBX45JaVlbNifzVfbMlm2LZPV\ne7MoKbNERYaR0LUlY+JjOK9na3q1bYyxFnYsgremw7bPwIRBn6t8TdgL1IQVkYAT0oFf7Av4xJ1H\nSNx1mFW7s8grLMEY6N+hCVPO78Z5PVoxLLY59SPCnScdPwLf/AdWzYSs3b4m7K9g2B1qwopIQHM1\n8I0xVwBPAeHADGvtX90c71QKS0pZvy+bxJ2HSdx1hKQ9WRwvKgWgR5vGXDekA2d3a8k5PVrRolGF\nxur+1c60zca3fE3Ys2HUI9D3OjVhRSQouBb4xphw4FngUmAfsNIY84G1drNbY1aUmVfI6j1ZrEk9\nyuo9WaxNPUphSRkAfdpFc9OwTiR0a0l81xa0alz/h9+guAA2vQsrp8P+JIhs6GvCToJ2A/31nyEi\nUivcvMKPB7Zba3cCGGNeA0YDrgR+cWkZyQdzvgv4vVmkHskHICLM0L9DE8YldCGhWwviY1vQvOIV\nfHlZu2HVLFg922nCtuwJV/wNhoxRE1ZEgpabgd8RSC33+T4gobYHKSwp5bYZK1i377ur97ZN6jM0\npjm3jejC0JjmDOjYlKjI8JN/o7Iypwm7cgZs/dRpuva+CuKnqAkrInWC501bY8xUYCpATExMjZ9f\nPyKcVtH1GJfQhaFdmjE0pjntm0ZhqhvQx4/A2jnO/HzWrnJN2AnQtFON6xERCVRuBv5+oPy7aHfy\nfe17rLXTgGkAcXFx9nQGem7csJo/6cAaWDGjQhP2t2rCikid5WbgrwR6GmO64gT9LcBYF8c7teIC\n2PwerJgO+1f5mrC3+FbCqgkrInWba4FvrS0xxtwNfIpzW+Ysa+0mt8Y7qaw9ThN2zWw4fvi7Juzg\nW6BBM09KEhHxN1fn8K21C4AFbo5RpbIy2LHY14T95Lsm7PDJ0O1CNWFFJOR43rStdcePwNq5zkrY\nIzuhUWs475cQd4easCIS0upO4B9Y6yyQ2vA2lORD5xFw4W+g33UQUcmiKhGREBP8gV+YC7NvgH0r\nnSbsoJudaZv2g7yuTEQkoAR/4NePhuZdYcCPnW0P1IQVEalU8Ac+wI+ne12BiEjAC/O6ABER8Q8F\nvohIiFDgi4iECAW+iEiIUOCLiIQIBb6ISIhQ4IuIhAgFvohIiDDWntZ7jrjCGJMB7DnNp7cCMmux\nnNqiumouUGtTXTWjumrudGrrYq1tXZ0DAyrwz4QxZpW1Ns7rOipSXTUXqLWprppRXTXndm2a0hER\nCREKfBGREFGXAn+a1wVUQXXVXKDWprpqRnXVnKu11Zk5fBERObm6dIUvIiInEVSBb4y5whiTYozZ\nbox5qJLHjTHmad/j640xQ/1UV2djzBJjzGZjzCZjzH2VHHOhMSbbGLPW9+d3fqpttzFmg2/MVZU8\n7vdzZozpXe48rDXG5Bhj7q9wjN/OlzFmljEm3RizsdzXWhhjPjfGbPP93byK5570NelCXX83xmzx\n/azeNcZU+o4/p/q5u1DX740x+8v9vK6q4rn+Pl+vl6tptzFmbRXPdfN8VZoPnrzGrLVB8QcIB3YA\n3YB6wDqgX4VjrgI+BgwwAkj0U23tgaG+j6OBrZXUdiEw34PzthtodZLHPTlnFX6uaTj3EntyvoDz\ngaHAxnJfewJ4yPfxQ8Dfqqj9pK9JF+q6DIjwffy3yuqqzs/dhbp+D/yqGj9rv56vCo8/CfzOg/NV\naT548RoLpiv8eGC7tXantbYIeA0YXeGY0cAr1rEcaGaMae92Ydbag9ba1b6Pc4FkoKPb49YST85Z\nORcDO6y1p7vg7oxZa5cCRyp8eTTwsu/jl4HrK3lqdV6TtVqXtfYza22J79PlQKfaGu9M6qomv5+v\nE4wxBrgZmFdb41XXSfLB76+xYAr8jkBquc/38cNQrc4xrjLGxAJnAYmVPDzS96v4x8aY/n4qyQIL\njTFJxpiplTzu9Tm7har/J/TifJ3Q1lp70PdxGtC2kmO8PncTcX47q8ypfu5uuMf385pVxfSEl+fr\nPOCQtXZbFY/75XxVyAe/v8aCKfADnjGmMfA2cL+1NqfCw6uBGGvtIOA/wHt+Kutca+0Q4Erg58aY\n8/007ikZY+oB1wFvVvKwV+frB6zzu3VA3c5mjHkYKAHmVHGIv3/u/8WZdhgCHMSZPgkkYzj51b3r\n5+tk+eCv11gwBf5+oHO5zzv5vlbTY1xhjInE+WHOsda+U/Fxa22OtTbP9/ECINIY08rtuqy1+31/\npwPv4vyKWJ5n5wznf67V1tpDFR/w6nyVc+jE1Jbv7/RKjvHk3BljJgDXAON8QfED1fi51ypr7SFr\nbam1tgyYXsV4Xp2vCOBHwOtVHeP2+aoiH/z+GgumwF8J9DTGdPVdGd4CfFDhmA+A2313nowAssv9\nyuQa3/zgTCDZWvvPKo5p5zsOY0w8zrk/7HJdjYwx0Sc+xmn4baxwmCfnzKfKqy4vzlcFHwDjfR+P\nB96v5JjqvCZrlTHmCuBB4Dpr7fEqjqnOz7226yrf97mhivH8fr58LgG2WGv3Vfag2+frJPng/9eY\nG11pt/7g3FGyFadr/bDva3cCd/o+NsCzvsc3AHF+qutcnF/H1gNrfX+uqlDb3cAmnC77cmCkH+rq\n5htvnW/sQDpnjXACvGm5r3lyvnD+0TkIFOPMkU4CWgKLgG3AQqCF79gOwIKTvSZdrms7zpzuidfZ\n8xXrqurn7nJds32vn/U4gdQ+EM6X7+svnXhdlTvWn+erqnzw+2tMK21FREJEME3piIjIGVDgi4iE\nCAW+iEiIUOCLiIQIBb6ISIhQ4IuIhAgFvohIiFDgi1TBGDPctxlYlG815iZjzACv6xI5XVp4JXIS\nxpg/AVFAA2CftfZxj0sSOW0KfJGT8O1fshIowNneodTjkkROm6Z0RE6uJdAY552KojyuReSM6Apf\n5CSMMR/gvMtQV5wNwe72uCSR0xbhdQEigcoYcztQbK2da4wJB74xxoyy1i72ujaR06ErfBGREKE5\nfBGREKHAFxEJEQp8EZEQocAXEQkRCnwRkRChwBcRCREKfBGREKHAFxEJEf8fIXGIsnFlxMQAAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1174cb8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# coding: utf-8\n",
    "import matplotlib.pylab as plt\n",
    "%matplotlib inline\n",
    "\n",
    "def function_1(x):\n",
    "    return 0.01*x**2 + 0.1*x \n",
    "\n",
    "def tangent_line(f, x):\n",
    "    d = numerical_diff(f, x)\n",
    "    print(d)\n",
    "    y = f(x) - d*x\n",
    "    return lambda t: d*t + y\n",
    "     \n",
    "x = np.arange(0.0, 20.0, 0.1)\n",
    "y = function_1(x)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "\n",
    "tf = tangent_line(function_1, 5)\n",
    "y2 = tf(x)\n",
    "\n",
    "plt.plot(x, y)\n",
    "plt.plot(x, y2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 勾配"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def _numerical_gradient_no_batch(f, x):\n",
    "    h = 1e-4 # 0.0001\n",
    "    grad = np.zeros_like(x)\n",
    "    \n",
    "    for idx in range(x.size):\n",
    "        tmp_val = x[idx]\n",
    "        x[idx] = float(tmp_val) + h\n",
    "        fxh1 = f(x) # f(x+h)\n",
    "        \n",
    "        x[idx] = tmp_val - h \n",
    "        fxh2 = f(x) # f(x-h)\n",
    "        grad[idx] = (fxh1 - fxh2) / (2*h)\n",
    "        \n",
    "        x[idx] = tmp_val # 値を元に戻す\n",
    "        \n",
    "    return grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def function_2(x):\n",
    "    if x.ndim == 1:\n",
    "        return np.sum(x**2)\n",
    "    else:\n",
    "        return np.sum(x**2, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6.,  8.])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_numerical_gradient_no_batch(function_2, np.array([3.0, 4.0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def numerical_gradient(f, X):\n",
    "    if X.ndim == 1:\n",
    "        return _numerical_gradient_no_batch(f, X)\n",
    "    else:\n",
    "        grad = np.zeros_like(X)\n",
    "        \n",
    "        for idx, x in enumerate(X):\n",
    "            grad[idx] = _numerical_gradient_no_batch(f, x)\n",
    "        \n",
    "        return grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def tangent_line(f, x):\n",
    "    d = numerical_gradient(f, x)\n",
    "    print(d)\n",
    "    y = f(x) - d*x\n",
    "    return lambda t: d*t + y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kot/miniconda2/envs/python3/lib/python3.6/site-packages/matplotlib/axes/_axes.py:545: UserWarning: No labelled objects found. Use label='...' kwarg on individual plots.\n",
      "  warnings.warn(\"No labelled objects found. \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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QWHgJNbUfV65coUOHDqostU1MTKSiooKysjKGDBnCyZMnFemdPn2a+vXrs3fv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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12d538b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# coding: utf-8\n",
    "# cf.http://d.hatena.ne.jp/white_wheels/20100327/p3\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "%matplotlib inline\n",
    "\n",
    "x0 = np.arange(-2, 2.5, 0.25)\n",
    "x1 = np.arange(-2, 2.5, 0.25)\n",
    "X, Y = np.meshgrid(x0, x1)\n",
    "\n",
    "X = X.flatten()\n",
    "Y = Y.flatten()\n",
    "\n",
    "grad = numerical_gradient(function_2, np.array([X, Y]) )\n",
    "\n",
    "plt.figure()\n",
    "plt.quiver(X, Y, -grad[0], -grad[1],  angles=\"xy\",color=\"#666666\")#,headwidth=10,scale=40,color=\"#444444\")\n",
    "plt.xlim([-2, 2])\n",
    "plt.ylim([-2, 2])\n",
    "plt.xlabel('x0')\n",
    "plt.ylabel('x1')\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.draw()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 勾配法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def gradient_descent(f, init_x, lr=0.01, step_num=100):\n",
    "    x = init_x\n",
    "    x_history = []\n",
    "\n",
    "    for i in range(step_num):\n",
    "        x_history.append( x.copy() )\n",
    "\n",
    "        grad = numerical_gradient(f, x)\n",
    "        x -= lr * grad\n",
    "\n",
    "    return x, np.array(x_history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TfQjqi6aBkOQVSSrJqS3rkCQ1DIQkZwIvAD7bqgZJ0hEtRwhvBK4AqmENkqROk0BIcilw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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x130947320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# coding: utf-8\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "#from gradient_2d import numerical_gradient\n",
    "%matplotlib inline\n",
    "\n",
    "def function_2(x):\n",
    "    return x[0]**2 + x[1]**2\n",
    "\n",
    "init_x = np.array([-3.0, 4.0])    \n",
    "\n",
    "lr = 0.1\n",
    "step_num = 20\n",
    "x, x_history = gradient_descent(function_2, init_x, lr=lr, step_num=step_num)\n",
    "\n",
    "plt.plot( [-5, 5], [0,0], '--b')\n",
    "plt.plot( [0,0], [-5, 5], '--b')\n",
    "plt.plot(x_history[:,0], x_history[:,1], 'o')\n",
    "\n",
    "plt.xlim(-3.5, 3.5)\n",
    "plt.ylim(-4.5, 4.5)\n",
    "plt.xlabel(\"X0\")\n",
    "plt.ylabel(\"X1\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ニューラルネットワークに対する勾配"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "class simpleNet:\n",
    "    def __init__(self):\n",
    "        self.W = np.random.randn(2,3)\n",
    "\n",
    "    def predict(self, x):\n",
    "        return np.dot(x, self.W)\n",
    "\n",
    "    def loss(self, x, t):\n",
    "        z = self.predict(x)\n",
    "        y = softmax(z)\n",
    "        loss = cross_entropy_error(y, t)\n",
    "        return loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.31623088  0.04891163 -0.36514251]\n",
      " [ 0.47434632  0.07336744 -0.54771376]]\n"
     ]
    }
   ],
   "source": [
    "# coding: utf-8\n",
    "import sys, os\n",
    "sys.path.append(os.pardir)  # 親ディレクトリのファイルをインポートするための設定\n",
    "import numpy as np\n",
    "from mymodule.functions import softmax, cross_entropy_error\n",
    "from mymodule.gradient import numerical_gradient\n",
    "\n",
    "x = np.array([0.6, 0.9])\n",
    "t = np.array([0, 0, 1])\n",
    "\n",
    "net = simpleNet()\n",
    "\n",
    "f = lambda w: net.loss(x, t)\n",
    "dW = numerical_gradient(f, net.W)\n",
    "\n",
    "print(dW)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2層ニューラルネットワークのクラス"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# coding: utf-8\n",
    "import sys, os\n",
    "sys.path.append(os.pardir)  # 親ディレクトリのファイルをインポートするための設定\n",
    "from mymodule.functions import *\n",
    "from mymodule.gradient import numerical_gradient\n",
    "\n",
    "\n",
    "class TwoLayerNet:\n",
    "\n",
    "    def __init__(self, input_size, hidden_size, output_size, weight_init_std=0.01):\n",
    "        # 重みの初期化\n",
    "        self.params = {}\n",
    "        self.params['W1'] = weight_init_std * np.random.randn(input_size, hidden_size)\n",
    "        self.params['b1'] = np.zeros(hidden_size)\n",
    "        self.params['W2'] = weight_init_std * np.random.randn(hidden_size, output_size)\n",
    "        self.params['b2'] = np.zeros(output_size)\n",
    "\n",
    "    def predict(self, x):\n",
    "        W1, W2 = self.params['W1'], self.params['W2']\n",
    "        b1, b2 = self.params['b1'], self.params['b2']\n",
    "    \n",
    "        a1 = np.dot(x, W1) + b1\n",
    "        z1 = sigmoid(a1)\n",
    "        a2 = np.dot(z1, W2) + b2\n",
    "        y = softmax(a2)\n",
    "        \n",
    "        return y\n",
    "        \n",
    "    # x:入力データ, t:教師データ\n",
    "    def loss(self, x, t):\n",
    "        y = self.predict(x)\n",
    "        \n",
    "        return cross_entropy_error(y, t)\n",
    "    \n",
    "    def accuracy(self, x, t):\n",
    "        y = self.predict(x)\n",
    "        y = np.argmax(y, axis=1)\n",
    "        t = np.argmax(t, axis=1)\n",
    "        \n",
    "        accuracy = np.sum(y == t) / float(x.shape[0])\n",
    "        return accuracy\n",
    "        \n",
    "    # x:入力データ, t:教師データ\n",
    "    def numerical_gradient(self, x, t):\n",
    "        loss_W = lambda W: self.loss(x, t)\n",
    "        \n",
    "        grads = {}\n",
    "        grads['W1'] = numerical_gradient(loss_W, self.params['W1'])\n",
    "        grads['b1'] = numerical_gradient(loss_W, self.params['b1'])\n",
    "        grads['W2'] = numerical_gradient(loss_W, self.params['W2'])\n",
    "        grads['b2'] = numerical_gradient(loss_W, self.params['b2'])\n",
    "        \n",
    "        return grads\n",
    "        \n",
    "    def gradient(self, x, t):\n",
    "        W1, W2 = self.params['W1'], self.params['W2']\n",
    "        b1, b2 = self.params['b1'], self.params['b2']\n",
    "        grads = {}\n",
    "        \n",
    "        batch_num = x.shape[0]\n",
    "        \n",
    "        # forward\n",
    "        a1 = np.dot(x, W1) + b1\n",
    "        z1 = sigmoid(a1)\n",
    "        a2 = np.dot(z1, W2) + b2\n",
    "        y = softmax(a2)\n",
    "        \n",
    "        # backward\n",
    "        dy = (y - t) / batch_num\n",
    "        grads['W2'] = np.dot(z1.T, dy)\n",
    "        grads['b2'] = np.sum(dy, axis=0)\n",
    "        \n",
    "        da1 = np.dot(dy, W2.T)\n",
    "        dz1 = sigmoid_grad(a1) * da1\n",
    "        grads['W1'] = np.dot(x.T, dz1)\n",
    "        grads['b1'] = np.sum(dz1, axis=0)\n",
    "\n",
    "        return grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.10367082  0.09479027  0.09646175  0.0976099   0.09643014  0.10534564\n",
      "   0.11351447  0.09714606  0.09772518  0.09730575]\n",
      " [ 0.10370514  0.09551623  0.09629093  0.09727947  0.09620149  0.10544123\n",
      "   0.11376555  0.09732914  0.09752802  0.09694279]\n",
      " [ 0.10354438  0.094939    0.09638792  0.0974336   0.09647522  0.10560926\n",
      "   0.11352656  0.09747596  0.09753358  0.09707453]\n",
      " [ 0.10325765  0.09473589  0.09619979  0.09781487  0.09625612  0.10613874\n",
      "   0.11360267  0.09727314  0.09754611  0.09717503]\n",
      " [ 0.10336792  0.09490557  0.09612918  0.0974013   0.09657672  0.10587389\n",
      "   0.11353339  0.09716664  0.09804558  0.09699981]\n",
      " [ 0.1034402   0.09517651  0.09613979  0.09748063  0.09639921  0.10576113\n",
      "   0.11371928  0.097294    0.09749499  0.09709426]\n",
      " [ 0.10340416  0.09491995  0.09612156  0.09781727  0.09637837  0.10582093\n",
      "   0.11315641  0.09729886  0.09782377  0.09725872]\n",
      " [ 0.1035974   0.09518469  0.09615298  0.09735027  0.09623511  0.10570848\n",
      "   0.11384599  0.09747316  0.0976472   0.09680472]\n",
      " [ 0.10353392  0.09507303  0.09626424  0.09744944  0.09638031  0.10613693\n",
      "   0.11338786  0.09747755  0.09734934  0.09694738]\n",
      " [ 0.10338468  0.09470548  0.09648883  0.09785831  0.09615428  0.10559057\n",
      "   0.11400998  0.09732413  0.09772884  0.09675488]\n",
      " [ 0.10360109  0.09515098  0.09616628  0.09759359  0.09642112  0.10568466\n",
      "   0.11329511  0.09738794  0.09786947  0.09682977]\n",
      " [ 0.10340375  0.09483135  0.09666576  0.09746198  0.09629309  0.10541206\n",
      "   0.11347598  0.09755973  0.09785035  0.09704596]\n",
      " [ 0.10361427  0.09490067  0.0966257   0.09728309  0.09601373  0.10595918\n",
      "   0.11370983  0.09698813  0.09787718  0.09702822]\n",
      " [ 0.10348479  0.09472268  0.09630097  0.09754206  0.09658455  0.10542256\n",
      "   0.11384967  0.09740465  0.09770777  0.09698029]\n",
      " [ 0.10357714  0.09510523  0.09603122  0.09762087  0.09649619  0.10575999\n",
      "   0.11364116  0.09711378  0.09760841  0.09704601]\n",
      " [ 0.10336456  0.09476365  0.09660215  0.09759952  0.09591588  0.10524624\n",
      "   0.11430279  0.09716405  0.09778399  0.09725717]\n",
      " [ 0.10356384  0.09498307  0.09626227  0.09734968  0.09639528  0.10571604\n",
      "   0.11351518  0.09724702  0.09796428  0.09700333]\n",
      " [ 0.10294609  0.09452934  0.09629462  0.09758262  0.0963543   0.10602685\n",
      "   0.11400695  0.09734129  0.09784658  0.09707136]\n",
      " [ 0.10354164  0.09477884  0.09651979  0.09744512  0.09584932  0.10561321\n",
      "   0.11404843  0.09754357  0.09750497  0.0971551 ]\n",
      " [ 0.1036714   0.09492617  0.09647864  0.09744065  0.09616188  0.10598962\n",
      "   0.11361011  0.09705935  0.09761079  0.09705139]\n",
      " [ 0.1032295   0.09454921  0.09617835  0.09764098  0.09636909  0.10639753\n",
      "   0.11352477  0.09700204  0.09783706  0.09727146]\n",
      " [ 0.10387642  0.09464837  0.09649467  0.09764721  0.09658126  0.1055753\n",
      "   0.11311828  0.09724764  0.09778955  0.09702129]\n",
      " [ 0.10365923  0.09482296  0.09643405  0.09758713  0.09606482  0.10544325\n",
      "   0.11391418  0.09729236  0.09796254  0.09681947]\n",
      " [ 0.10319734  0.09495189  0.09637599  0.09749677  0.09609444  0.10552326\n",
      "   0.11385384  0.0972906   0.0979108   0.09730508]\n",
      " [ 0.10343785  0.09516412  0.09640186  0.09723803  0.09618114  0.10590221\n",
      "   0.11357532  0.09717002  0.09792725  0.0970022 ]\n",
      " [ 0.10315931  0.09498711  0.09625506  0.09727253  0.09645229  0.10603379\n",
      "   0.11370511  0.09738983  0.09785441  0.09689056]\n",
      " [ 0.10350202  0.09496208  0.09640557  0.09725681  0.09648072  0.10584358\n",
      "   0.11379059  0.09731626  0.09765679  0.09678558]\n",
      " [ 0.10341538  0.0948994   0.09627071  0.09779746  0.09609296  0.10576032\n",
      "   0.11336566  0.09744026  0.09769157  0.09726627]\n",
      " [ 0.10349762  0.09469195  0.09652979  0.09743318  0.09611361  0.10588134\n",
      "   0.11392444  0.09731908  0.09749386  0.09711512]\n",
      " [ 0.10338629  0.09479871  0.096444    0.09751646  0.09667524  0.10558961\n",
      "   0.11371138  0.09706655  0.09781694  0.09699483]\n",
      " [ 0.10327229  0.0948389   0.09616683  0.09742139  0.0960045   0.10611934\n",
      "   0.11387717  0.09735791  0.09785796  0.09708371]\n",
      " [ 0.1038353   0.09477209  0.09645835  0.09747089  0.09605933  0.10558803\n",
      "   0.11348905  0.09735937  0.09779245  0.09717514]\n",
      " [ 0.10320789  0.09485175  0.0963211   0.09753573  0.09611724  0.10573106\n",
      "   0.11342218  0.09743097  0.09812749  0.0972546 ]\n",
      " [ 0.10369861  0.09508061  0.09623248  0.09768131  0.09601444  0.10564451\n",
      "   0.11343973  0.09737424  0.09751739  0.09731668]\n",
      " [ 0.10324542  0.09487752  0.09581459  0.09759     0.09684731  0.10626929\n",
      "   0.11365564  0.09716781  0.09763532  0.0968971 ]\n",
      " [ 0.10311246  0.09492267  0.09609107  0.09730746  0.09650677  0.10619844\n",
      "   0.11369789  0.09695014  0.09804874  0.09716436]\n",
      " [ 0.10349557  0.09476622  0.09639998  0.09745626  0.09615033  0.10584448\n",
      "   0.11387774  0.0972914   0.09772466  0.09699336]\n",
      " [ 0.10349094  0.09509643  0.09623526  0.09770724  0.09643429  0.10598776\n",
      "   0.11320778  0.09707076  0.09762132  0.09714821]\n",
      " [ 0.10376536  0.09512676  0.09636964  0.09727872  0.0962042   0.10555427\n",
      "   0.11376841  0.09712984  0.09772269  0.09708011]\n",
      " [ 0.10349381  0.09489317  0.09649171  0.09737264  0.09642755  0.10584646\n",
      "   0.11390865  0.09717209  0.0975431   0.09685082]\n",
      " [ 0.10333053  0.09478807  0.09624852  0.09779008  0.09621812  0.10609636\n",
      "   0.11368551  0.09706436  0.09773103  0.09704743]\n",
      " [ 0.1036127   0.09498321  0.09645975  0.09758257  0.0960892   0.10534037\n",
      "   0.11345525  0.09723384  0.09788105  0.09736207]\n",
      " [ 0.10344113  0.09460839  0.09652612  0.09742494  0.09679146  0.10562607\n",
      "   0.11371631  0.09725209  0.097624    0.09698949]\n",
      " [ 0.1034596   0.09486862  0.09615301  0.09756254  0.09634269  0.10614634\n",
      "   0.113479    0.09700646  0.0977238   0.09725794]\n",
      " [ 0.10312288  0.09492344  0.0963062   0.09753016  0.09638465  0.10548096\n",
      "   0.11348128  0.09736087  0.09788821  0.09752136]\n",
      " [ 0.10349264  0.09507148  0.09633969  0.09759861  0.0965389   0.10541007\n",
      "   0.11358626  0.09737106  0.0974675   0.09712379]\n",
      " [ 0.1033773   0.09476423  0.09628093  0.09758793  0.09606628  0.10526225\n",
      "   0.11420288  0.09767378  0.09780916  0.09697528]\n",
      " [ 0.10336973  0.09486639  0.09655025  0.09768554  0.09692578  0.10525455\n",
      "   0.1133887   0.09686335  0.0980172   0.09707851]\n",
      " [ 0.10342562  0.09502738  0.09621989  0.0972588   0.09632021  0.1059962\n",
      "   0.1133399   0.09720664  0.09809828  0.09710707]\n",
      " [ 0.10341537  0.09498616  0.09622123  0.09736885  0.09609007  0.10583516\n",
      "   0.11366317  0.09747833  0.09798774  0.09695392]\n",
      " [ 0.10315584  0.09478486  0.09623069  0.09743434  0.09637473  0.10606327\n",
      "   0.11361294  0.09738823  0.0978391   0.097116  ]\n",
      " [ 0.10383353  0.09479182  0.09628422  0.09749407  0.09633608  0.10530841\n",
      "   0.11381501  0.09744567  0.09786254  0.09682865]\n",
      " [ 0.10325796  0.09504546  0.09655409  0.09740719  0.09625337  0.10567375\n",
      "   0.11342283  0.09742217  0.09771626  0.09724693]\n",
      " [ 0.10355474  0.09499022  0.09642584  0.09741508  0.0962711   0.10568786\n",
      "   0.11340847  0.09704245  0.09831978  0.09688447]\n",
      " [ 0.10367996  0.09515579  0.09609429  0.0976486   0.09623629  0.10571961\n",
      "   0.11363696  0.09698581  0.09775637  0.09708634]\n",
      " [ 0.10322208  0.09530825  0.09652657  0.09728007  0.09624246  0.10591789\n",
      "   0.11335445  0.09693941  0.09791559  0.09729322]\n",
      " [ 0.1030599   0.09485522  0.09632159  0.0975402   0.09621876  0.1064606\n",
      "   0.11352251  0.09720691  0.09765498  0.09715932]\n",
      " [ 0.10376064  0.09501073  0.09633641  0.09754959  0.09612713  0.10548621\n",
      "   0.11320968  0.09738981  0.09775903  0.09737077]\n",
      " [ 0.10346409  0.09487982  0.09630544  0.09748226  0.09666193  0.10564112\n",
      "   0.11354367  0.09734161  0.09803292  0.09664716]\n",
      " [ 0.10335378  0.09478458  0.09648526  0.09769955  0.09627725  0.10562057\n",
      "   0.11397851  0.09712441  0.09772556  0.09695052]\n",
      " [ 0.10345836  0.09500874  0.09644083  0.09732909  0.09637779  0.106219\n",
      "   0.11338509  0.09694109  0.09759298  0.09724703]\n",
      " [ 0.10347906  0.09514347  0.09607919  0.09770782  0.09630105  0.106161\n",
      "   0.11344711  0.09704503  0.09766069  0.09697558]\n",
      " [ 0.10337142  0.09489003  0.09637319  0.09757253  0.09596185  0.10588921\n",
      "   0.11377502  0.09720734  0.097917    0.09704241]\n",
      " [ 0.10330472  0.09481179  0.09635099  0.09778429  0.09616546  0.10571504\n",
      "   0.11371405  0.09739848  0.09754902  0.09720615]\n",
      " [ 0.10337298  0.09469182  0.09645229  0.09773187  0.09598046  0.10553668\n",
      "   0.11375764  0.09721081  0.09815399  0.09711145]\n",
      " [ 0.1034032   0.09493167  0.09648999  0.09758202  0.09611973  0.10528555\n",
      "   0.11382616  0.09730647  0.09795515  0.09710006]\n",
      " [ 0.10346023  0.09502214  0.09652107  0.09725638  0.09600719  0.10527969\n",
      "   0.11391226  0.09738794  0.09790715  0.09724594]\n",
      " [ 0.10339058  0.09478134  0.09626293  0.09770721  0.09624394  0.10602452\n",
      "   0.1137558   0.09739568  0.09756598  0.09687201]\n",
      " [ 0.10327832  0.09504485  0.09641109  0.09749443  0.09658213  0.10547431\n",
      "   0.11361574  0.09714095  0.09755088  0.09740731]\n",
      " [ 0.10305818  0.0947249   0.09646573  0.09780568  0.09616814  0.10583149\n",
      "   0.11355371  0.09744565  0.09781027  0.09713626]\n",
      " [ 0.10353495  0.09481374  0.09640271  0.09754861  0.09638774  0.1059661\n",
      "   0.11337743  0.09713818  0.0979343   0.09689623]\n",
      " [ 0.10355293  0.09471916  0.09642364  0.09748893  0.09618247  0.10592444\n",
      "   0.11344193  0.09704662  0.09765868  0.09756121]\n",
      " [ 0.10351238  0.09471753  0.09632352  0.09747202  0.09645437  0.1057288\n",
      "   0.1137237   0.0973746   0.09749527  0.09719781]\n",
      " [ 0.10331111  0.09491301  0.09648866  0.09734429  0.09642937  0.10586373\n",
      "   0.11381208  0.09722813  0.0975545   0.09705512]\n",
      " [ 0.10360451  0.09528556  0.09613623  0.09750235  0.09641937  0.10490654\n",
      "   0.11350991  0.09746855  0.09779232  0.09737467]\n",
      " [ 0.1032128   0.09487487  0.0963583   0.09739142  0.09638361  0.10597095\n",
      "   0.11367006  0.09720337  0.09789432  0.0970403 ]\n",
      " [ 0.10349844  0.09461495  0.09654407  0.0974198   0.09648971  0.10552912\n",
      "   0.11362251  0.09723959  0.09796137  0.09708044]\n",
      " [ 0.10347654  0.09479432  0.09634505  0.09756813  0.09607421  0.10580021\n",
      "   0.11356293  0.09742828  0.09780443  0.09714589]\n",
      " [ 0.10341529  0.09480483  0.09642966  0.0974578   0.09606317  0.10591811\n",
      "   0.11384227  0.09748034  0.09761369  0.09697483]\n",
      " [ 0.10377319  0.09499628  0.0960313   0.09764188  0.09595742  0.10575969\n",
      "   0.11400118  0.09725531  0.09785787  0.09672588]\n",
      " [ 0.10353852  0.09492572  0.09621956  0.09748627  0.09647797  0.10557523\n",
      "   0.11371262  0.09758104  0.09776953  0.09671354]\n",
      " [ 0.10308612  0.09495033  0.09638194  0.0975346   0.09622243  0.10569586\n",
      "   0.11358889  0.09723681  0.09779139  0.09751163]\n",
      " [ 0.10330882  0.0947151   0.09628401  0.09754497  0.09653746  0.10605866\n",
      "   0.11334427  0.09709477  0.09793274  0.0971792 ]\n",
      " [ 0.10354408  0.09469209  0.09657276  0.09775958  0.09642098  0.10516106\n",
      "   0.11385738  0.09694187  0.09784235  0.09720785]\n",
      " [ 0.10347216  0.09493807  0.09641996  0.09731468  0.09645172  0.10582042\n",
      "   0.11366587  0.09698864  0.09762004  0.09730846]\n",
      " [ 0.10376497  0.09498735  0.09631985  0.09759573  0.09651505  0.10532649\n",
      "   0.11315531  0.0975482   0.0978958   0.09689124]\n",
      " [ 0.10363001  0.09471302  0.09623423  0.09763708  0.09670594  0.10586162\n",
      "   0.11335767  0.09743186  0.09773125  0.09669732]\n",
      " [ 0.10375791  0.09470236  0.0963705   0.09738316  0.09663371  0.10559649\n",
      "   0.11363719  0.09716954  0.09769884  0.0970503 ]\n",
      " [ 0.10362858  0.0948281   0.09629959  0.09745992  0.09633315  0.10519324\n",
      "   0.11393622  0.09749798  0.09764786  0.09717534]\n",
      " [ 0.10339347  0.09491055  0.09655345  0.09740026  0.09627538  0.10590578\n",
      "   0.11332334  0.09702015  0.09813027  0.09708735]\n",
      " [ 0.10329989  0.09515331  0.09585586  0.09760662  0.09636141  0.10596281\n",
      "   0.11316471  0.0975304   0.09772504  0.09733995]\n",
      " [ 0.10314086  0.09460419  0.09645057  0.09768193  0.09622171  0.10573139\n",
      "   0.1139367   0.09727201  0.09769445  0.09726619]\n",
      " [ 0.10355443  0.09465076  0.09627149  0.09767112  0.09647642  0.10565983\n",
      "   0.1136114   0.09716158  0.09774738  0.09719559]\n",
      " [ 0.10338706  0.09465473  0.0964109   0.09772361  0.09627296  0.10572771\n",
      "   0.11389154  0.09736289  0.09774936  0.09681923]\n",
      " [ 0.10373324  0.09493804  0.0963682   0.09727249  0.09654144  0.10577225\n",
      "   0.11384533  0.09704652  0.0976372   0.09684531]\n",
      " [ 0.10367002  0.09484681  0.09638485  0.09759012  0.0959509   0.10584492\n",
      "   0.11376335  0.09753206  0.09760135  0.09681562]\n",
      " [ 0.10359829  0.0949266   0.09615354  0.09755351  0.09632394  0.10528007\n",
      "   0.11366501  0.09745908  0.09790845  0.0971315 ]\n",
      " [ 0.10354437  0.09469433  0.09623923  0.0975579   0.09628636  0.10600591\n",
      "   0.11356786  0.09741278  0.09780217  0.09688908]\n",
      " [ 0.10345099  0.09521102  0.09632521  0.09757825  0.09617071  0.10587436\n",
      "   0.11371838  0.09729772  0.09751392  0.09685944]\n",
      " [ 0.10338018  0.09507883  0.09649727  0.09723977  0.0963523   0.10577775\n",
      "   0.1135283   0.09720346  0.09767714  0.097265  ]]\n"
     ]
    }
   ],
   "source": [
    "net = TwoLayerNet(input_size=784, hidden_size=100, output_size=10)\n",
    "x = np.random.rand(100, 784)\n",
    "y = net.predict(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.random.rand(100, 784)\n",
    "t = np.random.rand(100, 10)\n",
    "grads = net.numerical_gradient(x, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'W1': array([[  1.61360778e-04,   1.20043919e-04,   6.89253987e-05, ...,\n",
      "          3.23179750e-05,  -3.51339979e-05,   1.25530821e-04],\n",
      "       [  5.82171023e-05,   2.22927945e-04,   1.72836723e-05, ...,\n",
      "         -6.01102079e-05,  -1.67789582e-05,   1.79360786e-04],\n",
      "       [  7.19693194e-05,   1.24935289e-04,   4.59431737e-05, ...,\n",
      "         -1.20054715e-04,  -1.75628645e-05,   1.29623725e-04],\n",
      "       ..., \n",
      "       [  1.71491237e-04,   1.42138374e-04,   7.33165240e-05, ...,\n",
      "         -5.84959436e-05,  -1.82599513e-05,   1.02064832e-04],\n",
      "       [  4.22377977e-05,   1.97750258e-04,   5.48633383e-05, ...,\n",
      "         -8.78759243e-05,   1.50891566e-05,   2.29489372e-04],\n",
      "       [  1.76003505e-04,   5.01910957e-05,   1.11402585e-04, ...,\n",
      "         -4.23339319e-05,  -5.50190982e-05,   1.33508946e-04]]), 'b1': array([  2.24106820e-04,   3.18442770e-04,   8.50670867e-05,\n",
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      "        -7.19458626e-05,  -5.69749137e-05,   2.79938210e-04,\n",
      "        -1.04844533e-05,  -2.59335096e-04,  -8.71692873e-05,\n",
      "         1.79807595e-04,   1.90870608e-04,   4.01982112e-04,\n",
      "         6.79056811e-08,   2.16687521e-04,   4.76192845e-04,\n",
      "         4.47310593e-04,   6.97533764e-05,   7.34495109e-05,\n",
      "        -6.56053523e-05,  -1.90512670e-04,  -1.72305248e-04,\n",
      "         1.85869302e-04,   3.43615036e-04,   1.49049997e-04,\n",
      "        -2.86456894e-04,  -1.62983658e-04,  -2.78321299e-05,\n",
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      "         1.05170168e-04,  -2.32367834e-04,  -2.22743086e-04,\n",
      "        -1.46212309e-05,  -6.71095712e-05,   1.10315799e-04,\n",
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      "        -9.05753561e-05,  -2.79382717e-05,   2.60483277e-04,\n",
      "        -1.33093734e-04,  -4.91282925e-05,   1.92187377e-06,\n",
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      "        -2.99454479e-04,  -1.71571917e-04,   2.14879501e-04,\n",
      "        -5.76984793e-05,   9.46916323e-05,  -5.60583913e-05,\n",
      "         1.62453717e-04,  -3.77032472e-05,   2.44215359e-05,\n",
      "         3.72522380e-04,   4.19225141e-04,  -2.15701255e-04,\n",
      "         3.44129469e-04,   3.04946757e-05,   2.32703325e-04,\n",
      "         9.55515311e-05,  -1.93453327e-04,   7.32164551e-05,\n",
      "         2.75084733e-05,  -8.79287843e-05,  -5.56448909e-05,\n",
      "         2.72366791e-04]), 'W2': array([[ 0.00737691, -0.00234876, -0.00712771, -0.01242792, -0.01708929,\n",
      "         0.01348764,  0.01770026, -0.02264042,  0.00969058,  0.01337871],\n",
      "       [ 0.0057193 , -0.00224286, -0.00596033, -0.01074008, -0.01631053,\n",
      "         0.01217038,  0.01539342, -0.01932411,  0.00830708,  0.01298773],\n",
      "       [ 0.00652714, -0.00206584, -0.00808272, -0.01176395, -0.01723458,\n",
      "         0.01355534,  0.01790998, -0.02236431,  0.00867283,  0.01484611],\n",
      "       [ 0.00648029, -0.00303633, -0.00700587, -0.01155075, -0.01634792,\n",
      "         0.01311982,  0.01715591, -0.02257925,  0.00908888,  0.01467522],\n",
      "       [ 0.00580638, -0.0030603 , -0.00580772, -0.01026981, -0.01536475,\n",
      "         0.01089204,  0.01605352, -0.02009735,  0.0083534 ,  0.0134946 ],\n",
      "       [ 0.00679003, -0.00346891, -0.00664362, -0.01137419, -0.01727166,\n",
      "         0.0133839 ,  0.01825546, -0.02292853,  0.00948767,  0.01376986],\n",
      "       [ 0.00716354, -0.00300631, -0.0067067 , -0.01218126, -0.01761017,\n",
      "         0.01367184,  0.01786411, -0.02184053,  0.00838641,  0.01425907],\n",
      "       [ 0.00678094, -0.00308018, -0.00745565, -0.01250181, -0.01795605,\n",
      "         0.01359541,  0.01943786, -0.02280459,  0.01003884,  0.01394525],\n",
      "       [ 0.00686315, -0.00282591, -0.00617882, -0.01134636, -0.01590928,\n",
      "         0.01226682,  0.0165885 , -0.02079243,  0.0083209 ,  0.01301344],\n",
      "       [ 0.00605012, -0.00177943, -0.0064378 , -0.01100167, -0.01439341,\n",
      "         0.01262643,  0.0152999 , -0.01887849,  0.00741275,  0.0111016 ],\n",
      "       [ 0.007876  , -0.00203673, -0.00879865, -0.01168777, -0.01833277,\n",
      "         0.0148216 ,  0.01917927, -0.0247063 ,  0.00893194,  0.01475342],\n",
      "       [ 0.00791362, -0.00307924, -0.00787885, -0.01255228, -0.01911973,\n",
      "         0.01396693,  0.01818769, -0.02260883,  0.01043137,  0.01473932],\n",
      "       [ 0.00639648, -0.00338863, -0.00616536, -0.01104833, -0.01614581,\n",
      "         0.01253176,  0.01746579, -0.02076832,  0.00853864,  0.01258379],\n",
      "       [ 0.00625309, -0.00350742, -0.00638378, -0.01153453, -0.01527341,\n",
      "         0.01310967,  0.01628827, -0.02110963,  0.00907467,  0.01308308],\n",
      "       [ 0.00598906, -0.00244463, -0.00517122, -0.01090397, -0.01612932,\n",
      "         0.01194564,  0.01649642, -0.01981781,  0.00777653,  0.01225929],\n",
      "       [ 0.00702585, -0.00372564, -0.00687548, -0.01016654, -0.01741897,\n",
      "         0.01251118,  0.01753639, -0.02154513,  0.00911786,  0.01354048],\n",
      "       [ 0.00742588, -0.00331273, -0.00677166, -0.01113657, -0.01787326,\n",
      "         0.0134557 ,  0.01757056, -0.0223652 ,  0.00836697,  0.01464031],\n",
      "       [ 0.00703009, -0.0029443 , -0.00721406, -0.01166616, -0.01701717,\n",
      "         0.01333955,  0.01754151, -0.02130358,  0.00859176,  0.01364234],\n",
      "       [ 0.00661208, -0.00277842, -0.00710611, -0.01225373, -0.01715511,\n",
      "         0.01341866,  0.01778235, -0.02210998,  0.00919634,  0.01439391],\n",
      "       [ 0.0067802 , -0.00273368, -0.00646756, -0.01063647, -0.01724484,\n",
      "         0.01265014,  0.01582056, -0.02158993,  0.00996504,  0.01345654],\n",
      "       [ 0.00685267, -0.00265121, -0.00708384, -0.00897855, -0.01648806,\n",
      "         0.01219267,  0.01464518, -0.02089057,  0.00967543,  0.01272628],\n",
      "       [ 0.00638067, -0.00301055, -0.00609944, -0.01174783, -0.01805306,\n",
      "         0.0133887 ,  0.01767998, -0.02224342,  0.00963508,  0.01406986],\n",
      "       [ 0.00703004, -0.00322611, -0.00702881, -0.01058146, -0.0172983 ,\n",
      "         0.01252921,  0.0164896 , -0.02115302,  0.00909777,  0.01414106],\n",
      "       [ 0.00707961, -0.00277506, -0.00822435, -0.012061  , -0.01905253,\n",
      "         0.01425118,  0.01821697, -0.02286081,  0.00977358,  0.0156524 ],\n",
      "       [ 0.00743417, -0.00349867, -0.00674274, -0.01121005, -0.01663972,\n",
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      "         0.01380847,  0.01807671, -0.023117  ,  0.00940545,  0.01350168],\n",
      "       [ 0.00762534, -0.00292024, -0.00618219, -0.01144542, -0.01739811,\n",
      "         0.01283356,  0.01715162, -0.02179941,  0.00850297,  0.01363187],\n",
      "       [ 0.00633381, -0.00285126, -0.00788731, -0.01244748, -0.01820611,\n",
      "         0.01285803,  0.01839828, -0.02255801,  0.01036778,  0.01599226],\n",
      "       [ 0.0063688 , -0.00264735, -0.00612585, -0.01024647, -0.0142428 ,\n",
      "         0.01111668,  0.01447214, -0.01960347,  0.00815543,  0.01275289],\n",
      "       [ 0.00744093, -0.00281287, -0.00659018, -0.01315726, -0.01916646,\n",
      "         0.01439983,  0.01806754, -0.02301537,  0.00978759,  0.01504624],\n",
      "       [ 0.00593614, -0.00279319, -0.00624032, -0.00996988, -0.01737705,\n",
      "         0.01254924,  0.01642216, -0.02028641,  0.00830488,  0.01345443],\n",
      "       [ 0.00696972, -0.00305455, -0.00741149, -0.01162382, -0.01752938,\n",
      "         0.01311472,  0.01729446, -0.02192618,  0.00940019,  0.01476633],\n",
      "       [ 0.00745429, -0.00262863, -0.00622225, -0.01084687, -0.01693095,\n",
      "         0.01216336,  0.01625168, -0.02227478,  0.00914495,  0.0138892 ],\n",
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      "         0.01286794,  0.01796497, -0.02240907,  0.00910239,  0.01371176],\n",
      "       [ 0.00782254, -0.00268519, -0.00630606, -0.01091048, -0.0163355 ,\n",
      "         0.01223613,  0.01621302, -0.02204224,  0.00883432,  0.01317347],\n",
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      "         0.01399843,  0.01687553, -0.02283437,  0.01030335,  0.01375138],\n",
      "       [ 0.00829657, -0.00342154, -0.00658943, -0.0127997 , -0.01871837,\n",
      "         0.01318246,  0.01916038, -0.02424938,  0.00984068,  0.01529832],\n",
      "       [ 0.0066726 , -0.00167694, -0.00735458, -0.01173536, -0.01731281,\n",
      "         0.01316773,  0.01759515, -0.02214079,  0.00837935,  0.01440566],\n",
      "       [ 0.00619801, -0.00199221, -0.00707425, -0.01127906, -0.01684923,\n",
      "         0.01245846,  0.01671182, -0.01964692,  0.00840533,  0.01306804],\n",
      "       [ 0.00678763, -0.00337781, -0.00621812, -0.01055075, -0.01545997,\n",
      "         0.01227739,  0.01632501, -0.02172236,  0.00911671,  0.01282227],\n",
      "       [ 0.00685344, -0.00227337, -0.00751917, -0.0117559 , -0.01680292,\n",
      "         0.01273094,  0.01759321, -0.02127769,  0.00887113,  0.01358032],\n",
      "       [ 0.00722871, -0.00352505, -0.00706737, -0.01064067, -0.01757935,\n",
      "         0.0123686 ,  0.01774125, -0.02139753,  0.00918537,  0.01368604],\n",
      "       [ 0.00753048, -0.00197503, -0.00693526, -0.01205653, -0.01671394,\n",
      "         0.0129217 ,  0.01535214, -0.0196623 ,  0.00872553,  0.0128132 ],\n",
      "       [ 0.00676293, -0.00253889, -0.00632378, -0.01294212, -0.01833538,\n",
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      "       [ 0.00803351, -0.00298502, -0.00662095, -0.01268296, -0.01989259,\n",
      "         0.01447088,  0.01859461, -0.02581396,  0.010352  ,  0.01654448],\n",
      "       [ 0.00620658, -0.00232938, -0.00659535, -0.01141569, -0.0150393 ,\n",
      "         0.01259878,  0.01684573, -0.02081385,  0.00820497,  0.01233753],\n",
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      "         0.01467843,  0.02037617, -0.02394397,  0.00919651,  0.0149063 ],\n",
      "       [ 0.00651039, -0.003366  , -0.00644906, -0.01123773, -0.0176999 ,\n",
      "         0.01303137,  0.01696386, -0.02137365,  0.00925646,  0.01436425],\n",
      "       [ 0.00778053, -0.00276953, -0.00799891, -0.01354465, -0.01866871,\n",
      "         0.01547232,  0.01940784, -0.02551665,  0.01047816,  0.01535959],\n",
      "       [ 0.00773522, -0.00301676, -0.00567059, -0.00978723, -0.01652495,\n",
      "         0.01183022,  0.0154958 , -0.01970014,  0.00734566,  0.01229276],\n",
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      "       [ 0.00667914, -0.00271727, -0.00787535, -0.01095794, -0.01641298,\n",
      "         0.01315007,  0.0159249 , -0.02175046,  0.00968734,  0.01427256],\n",
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      "         0.01297721,  0.01848351, -0.02329603,  0.00964381,  0.014988  ],\n",
      "       [ 0.00644917, -0.00314232, -0.00640677, -0.0106822 , -0.01555569,\n",
      "         0.01265284,  0.01721033, -0.02121489,  0.0082403 ,  0.01244924],\n",
      "       [ 0.00760946, -0.00233169, -0.00687916, -0.01288937, -0.01888642,\n",
      "         0.01453506,  0.01833869, -0.0235078 ,  0.00919876,  0.01481246],\n",
      "       [ 0.00594407, -0.00183362, -0.00706494, -0.01123643, -0.01718361,\n",
      "         0.01454499,  0.01707111, -0.0214884 ,  0.00723888,  0.01400795],\n",
      "       [ 0.00619733, -0.00257773, -0.00721291, -0.01048336, -0.01525531,\n",
      "         0.01235008,  0.01659489, -0.02012533,  0.00798495,  0.0125274 ],\n",
      "       [ 0.00606657, -0.00203242, -0.0067406 , -0.01151133, -0.01640535,\n",
      "         0.01316657,  0.01689653, -0.02080129,  0.0083133 ,  0.01304803],\n",
      "       [ 0.00658241, -0.00309002, -0.00578851, -0.0125082 , -0.0165096 ,\n",
      "         0.01313102,  0.01800215, -0.02263804,  0.00828599,  0.0145328 ],\n",
      "       [ 0.00721863, -0.00253089, -0.00760832, -0.01219673, -0.01729639,\n",
      "         0.01354151,  0.01789652, -0.02174683,  0.00910849,  0.01361401],\n",
      "       [ 0.00739029, -0.0026003 , -0.00682274, -0.01233208, -0.01847157,\n",
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      "       [ 0.0066208 , -0.00190203, -0.00580189, -0.01161505, -0.01752498,\n",
      "         0.01386346,  0.01756235, -0.02369631,  0.00920909,  0.01328456],\n",
      "       [ 0.00569988, -0.00233706, -0.00638336, -0.0098777 , -0.01587379,\n",
      "         0.01140474,  0.01531575, -0.01850868,  0.00853003,  0.0120302 ],\n",
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      "         0.01335745,  0.01657973, -0.02112766,  0.00966946,  0.01385802],\n",
      "       [ 0.00616539, -0.00259266, -0.00626645, -0.01026493, -0.0160082 ,\n",
      "         0.01176927,  0.01559857, -0.01995238,  0.00863871,  0.01291269],\n",
      "       [ 0.00579846, -0.00265793, -0.00778687, -0.01141013, -0.01793622,\n",
      "         0.01399278,  0.0180803 , -0.02069128,  0.00918905,  0.01342183],\n",
      "       [ 0.00658597, -0.00227076, -0.00661027, -0.01039896, -0.01654789,\n",
      "         0.01209247,  0.01602801, -0.01991769,  0.00788264,  0.01315648],\n",
      "       [ 0.00503831, -0.0032357 , -0.0059146 , -0.00967524, -0.01648853,\n",
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      "         0.01153475,  0.01637804, -0.02010757,  0.00806969,  0.0131332 ],\n",
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      "       [ 0.00678711, -0.00243385, -0.00695318, -0.01173005, -0.01752496,\n",
      "         0.0147561 ,  0.01705073, -0.02304314,  0.00925115,  0.0138401 ],\n",
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      "       [ 0.00513117, -0.00086564, -0.00571698, -0.01136569, -0.01473881,\n",
      "         0.01229891,  0.01388429, -0.01773186,  0.00750747,  0.01159714],\n",
      "       [ 0.00708204, -0.00235589, -0.00772639, -0.01181306, -0.01874615,\n",
      "         0.01480686,  0.01704496, -0.02202492,  0.00962315,  0.01410941],\n",
      "       [ 0.00581206, -0.0015337 , -0.00560499, -0.01168892, -0.01520383,\n",
      "         0.01119929,  0.01601909, -0.02095507,  0.00871162,  0.01324445],\n",
      "       [ 0.00681396, -0.00271553, -0.00766214, -0.01055913, -0.0156273 ,\n",
      "         0.01240939,  0.01654221, -0.02048838,  0.00908928,  0.01219764],\n",
      "       [ 0.00589835, -0.00186738, -0.00667325, -0.01126853, -0.0186047 ,\n",
      "         0.01478683,  0.0179681 , -0.02284593,  0.00912367,  0.01348284],\n",
      "       [ 0.00758701, -0.00187084, -0.00659176, -0.01354558, -0.01767312,\n",
      "         0.01315451,  0.01801194, -0.02373303,  0.0101775 ,  0.01448337],\n",
      "       [ 0.00624654, -0.0030489 , -0.00709974, -0.01110273, -0.0171586 ,\n",
      "         0.01336342,  0.01722309, -0.02084729,  0.00863516,  0.01378904],\n",
      "       [ 0.00661563, -0.00336753, -0.00699037, -0.01308796, -0.01901668,\n",
      "         0.01518163,  0.01905076, -0.02342177,  0.00938174,  0.01565457],\n",
      "       [ 0.00643186, -0.0027529 , -0.00682291, -0.01223604, -0.01773754,\n",
      "         0.01390935,  0.0165292 , -0.02097263,  0.00940504,  0.01424658],\n",
      "       [ 0.00694553, -0.0031564 , -0.0063375 , -0.01211942, -0.01644379,\n",
      "         0.01165001,  0.01754997, -0.019914  ,  0.00902677,  0.01279883],\n",
      "       [ 0.00633283, -0.00238536, -0.00626402, -0.01099482, -0.01640751,\n",
      "         0.01241742,  0.01668449, -0.02054633,  0.00840588,  0.01275741],\n",
      "       [ 0.00759695, -0.00228049, -0.00570196, -0.01181649, -0.01798147,\n",
      "         0.01314141,  0.01644045, -0.02063274,  0.00786479,  0.01336953],\n",
      "       [ 0.00611332, -0.00298459, -0.00737046, -0.01092826, -0.01666005,\n",
      "         0.01312359,  0.01544784, -0.01920816,  0.00824926,  0.01421751],\n",
      "       [ 0.00640914, -0.00166262, -0.00573378, -0.01172273, -0.01657923,\n",
      "         0.01248359,  0.01663657, -0.0221241 ,  0.00882959,  0.01346354],\n",
      "       [ 0.00687829, -0.00179952, -0.00613484, -0.01069485, -0.01508977,\n",
      "         0.01161157,  0.01494313, -0.01996936,  0.00757321,  0.01268215],\n",
      "       [ 0.00673551, -0.00299859, -0.00650711, -0.01276192, -0.01657454,\n",
      "         0.01431217,  0.01698134, -0.02177343,  0.00855272,  0.01403384],\n",
      "       [ 0.0071481 , -0.00240756, -0.00695551, -0.01128112, -0.01855657,\n",
      "         0.01374595,  0.01792691, -0.02349617,  0.009356  ,  0.01451997],\n",
      "       [ 0.00627825, -0.00282215, -0.00783109, -0.01224586, -0.01811497,\n",
      "         0.01464971,  0.0187777 , -0.02321358,  0.0094544 ,  0.0150676 ],\n",
      "       [ 0.00736569, -0.00393931, -0.00698537, -0.01152828, -0.0173578 ,\n",
      "         0.01357202,  0.01679939, -0.02187521,  0.00919141,  0.01475746],\n",
      "       [ 0.00714259, -0.00252889, -0.00710874, -0.011057  , -0.01673003,\n",
      "         0.01237125,  0.01753978, -0.02282367,  0.00839725,  0.01479746],\n",
      "       [ 0.00805957, -0.00187179, -0.00809836, -0.01108546, -0.01682495,\n",
      "         0.0125567 ,  0.01615512, -0.02060704,  0.0084233 ,  0.01329291],\n",
      "       [ 0.00617416, -0.00290558, -0.00658438, -0.01030441, -0.0164438 ,\n",
      "         0.01275353,  0.01665908, -0.02119893,  0.00904894,  0.01280138],\n",
      "       [ 0.00786255, -0.00271548, -0.00635867, -0.01291163, -0.01801447,\n",
      "         0.01335777,  0.01767563, -0.02392931,  0.01021092,  0.0148227 ],\n",
      "       [ 0.0064042 , -0.00244696, -0.00642891, -0.01020994, -0.0141846 ,\n",
      "         0.01070054,  0.01393827, -0.01733988,  0.00767004,  0.01189725],\n",
      "       [ 0.00613616, -0.00292821, -0.00602306, -0.01002506, -0.01572601,\n",
      "         0.01198624,  0.01773106, -0.02257479,  0.00782919,  0.01359448],\n",
      "       [ 0.00682311, -0.00234542, -0.00762326, -0.01086547, -0.01625764,\n",
      "         0.01273666,  0.01597129, -0.02010301,  0.00792418,  0.01373957]]), 'b2': array([ 0.01346497, -0.00513228, -0.01366098, -0.02247379, -0.03373059,\n",
      "        0.0258257 ,  0.0335714 , -0.04273316,  0.01776345,  0.02710529])}\n"
     ]
    }
   ],
   "source": [
    "print(grads)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ミニバッチ学習の実装\n",
    "\n",
    "__numerical_gradient を使った低速版__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fri Feb  3 13:39:00 JST 2017\n",
      "0 2.29433450806 2017/02/03 13:39:38\n",
      "10 2.30151019526 2017/02/03 13:47:42\n",
      "20 2.29443076567 2017/02/03 13:58:31\n",
      "Fri Feb  3 14:07:49 JST 2017\n"
     ]
    }
   ],
   "source": [
    "!date\n",
    "# coding: utf-8\n",
    "import sys, os\n",
    "sys.path.append(os.pardir)  # 親ディレクトリのファイルをインポートするための設定\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from dataset.mnist import load_mnist\n",
    "#from two_layer_net import TwoLayerNet\n",
    "%matplotlib inline\n",
    "from datetime import datetime\n",
    "\n",
    "# データの読み込み\n",
    "(x_train, t_train), (x_test, t_test) = load_mnist(normalize=True, one_hot_label=True)\n",
    "\n",
    "train_loss_list = []\n",
    "\n",
    "# ハイパーパラメータ\n",
    "iters_num = 30\n",
    "train_size = x_train.shape[0]\n",
    "batch_size = 100\n",
    "learning_rate = 0.1\n",
    "\n",
    "network = TwoLayerNet(input_size=784, hidden_size=50, output_size=10)\n",
    "\n",
    "for i in range(iters_num):\n",
    "    # ミニバッチの取得\n",
    "    batch_mask = np.random.choice(train_size, batch_size)\n",
    "    x_batch = x_train[batch_mask]\n",
    "    t_batch = t_train[batch_mask]\n",
    "    \n",
    "    # 勾配の計算\n",
    "    grad = network.numerical_gradient(x_batch, t_batch)\n",
    "    #grad = network.gradient(x_batch, t_batch) # 高速版!\n",
    "    \n",
    "    # パラメータの更新\n",
    "    for key in ('W1', 'b1', 'W2', 'b2'):\n",
    "        network.params[key] -= learning_rate * grad[key]\n",
    "        \n",
    "    # 学習経過の記録\n",
    "    loss = network.loss(x_batch, t_batch)\n",
    "    if i%10 == 0: print(i, loss, datetime.now().strftime(\"%Y/%m/%d %H:%M:%S\"))\n",
    "    train_loss_list.append(loss)\n",
    "!date"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4GcHncZ1T+9/S7KTN5axIL8KxwDSxeLIkHgKk8giRuSTPHB0vyes1EunBOMt4CN1tLhwy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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1291d8160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(train_loss_list)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__gradient を使った高速版__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fri Feb  3 14:11:27 JST 2017\n",
      "0 2.29596964637 2017/02/03 14:11:28\n",
      "1000 0.590789722964 2017/02/03 14:11:30\n",
      "2000 0.286607804041 2017/02/03 14:11:32\n",
      "3000 0.298551722558 2017/02/03 14:11:35\n",
      "4000 0.289130595618 2017/02/03 14:11:39\n",
      "5000 0.226502528465 2017/02/03 14:11:42\n",
      "6000 0.340328112376 2017/02/03 14:11:44\n",
      "7000 0.248002214471 2017/02/03 14:11:47\n",
      "8000 0.158586735178 2017/02/03 14:11:50\n",
      "9000 0.212563041588 2017/02/03 14:11:53\n",
      "Fri Feb  3 14:11:55 JST 2017\n"
     ]
    }
   ],
   "source": [
    "!date\n",
    "# coding: utf-8\n",
    "import sys, os\n",
    "sys.path.append(os.pardir)  # 親ディレクトリのファイルをインポートするための設定\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from dataset.mnist import load_mnist\n",
    "#from two_layer_net import TwoLayerNet\n",
    "%matplotlib inline\n",
    "from datetime import datetime\n",
    "\n",
    "# データの読み込み\n",
    "(x_train, t_train), (x_test, t_test) = load_mnist(normalize=True, one_hot_label=True)\n",
    "\n",
    "train_loss_list = []\n",
    "\n",
    "# ハイパーパラメータ\n",
    "iters_num = 10000\n",
    "train_size = x_train.shape[0]\n",
    "batch_size = 100\n",
    "learning_rate = 0.1\n",
    "\n",
    "network = TwoLayerNet(input_size=784, hidden_size=50, output_size=10)\n",
    "\n",
    "for i in range(iters_num):\n",
    "    # ミニバッチの取得\n",
    "    batch_mask = np.random.choice(train_size, batch_size)\n",
    "    x_batch = x_train[batch_mask]\n",
    "    t_batch = t_train[batch_mask]\n",
    "    \n",
    "    # 勾配の計算\n",
    "    #grad = network.numerical_gradient(x_batch, t_batch)\n",
    "    grad = network.gradient(x_batch, t_batch) # 高速版!\n",
    "    \n",
    "    # パラメータの更新\n",
    "    for key in ('W1', 'b1', 'W2', 'b2'):\n",
    "        network.params[key] -= learning_rate * grad[key]\n",
    "        \n",
    "    # 学習経過の記録\n",
    "    loss = network.loss(x_batch, t_batch)\n",
    "    if i%1000 == 0: print(i, loss, datetime.now().strftime(\"%Y/%m/%d %H:%M:%S\"))\n",
    "    train_loss_list.append(loss)\n",
    "!date"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x13096f898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(train_loss_list)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### テストデータで評価"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train acc, test acc | 0.112366666667, 0.1135\n",
      "train acc, test acc | 0.778966666667, 0.7822\n",
      "train acc, test acc | 0.874666666667, 0.8781\n",
      "train acc, test acc | 0.8979, 0.9006\n",
      "train acc, test acc | 0.90875, 0.912\n",
      "train acc, test acc | 0.91475, 0.9173\n",
      "train acc, test acc | 0.919766666667, 0.9215\n",
      "train acc, test acc | 0.923966666667, 0.9252\n",
      "train acc, test acc | 0.92745, 0.929\n",
      "train acc, test acc | 0.931683333333, 0.9332\n",
      "train acc, test acc | 0.934216666667, 0.9342\n",
      "train acc, test acc | 0.936783333333, 0.9356\n",
      "train acc, test acc | 0.93955, 0.9385\n",
      "train acc, test acc | 0.9422, 0.9388\n",
      "train acc, test acc | 0.944066666667, 0.9412\n",
      "train acc, test acc | 0.945466666667, 0.9421\n",
      "train acc, test acc | 0.947266666667, 0.9446\n"
     ]
    },
    {
     "data": {
      "image/png": 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BI07pitWJiHQraTv9xjkXNbNrgFcAPzDTObfEzK5Ozn8IuA0oBX6RHJgu6pwb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\nItLq/wOXkpKDoWdiJwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117fdef60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# coding: utf-8\n",
    "import sys, os\n",
    "sys.path.append(os.pardir)  # 親ディレクトリのファイルをインポートするための設定\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from dataset.mnist import load_mnist\n",
    "#from two_layer_net import TwoLayerNet\n",
    "%matplotlib inline\n",
    "\n",
    "# データの読み込み\n",
    "(x_train, t_train), (x_test, t_test) = load_mnist(normalize=True, one_hot_label=True)\n",
    "\n",
    "network = TwoLayerNet(input_size=784, hidden_size=50, output_size=10)\n",
    "\n",
    "iters_num = 10000  # 繰り返しの回数を適宜設定する\n",
    "train_size = x_train.shape[0]\n",
    "batch_size = 100\n",
    "learning_rate = 0.1\n",
    "\n",
    "train_loss_list = []\n",
    "train_acc_list = []\n",
    "test_acc_list = []\n",
    "\n",
    "iter_per_epoch = max(train_size / batch_size, 1)\n",
    "\n",
    "for i in range(iters_num):\n",
    "    batch_mask = np.random.choice(train_size, batch_size)\n",
    "    x_batch = x_train[batch_mask]\n",
    "    t_batch = t_train[batch_mask]\n",
    "    \n",
    "    # 勾配の計算\n",
    "    #grad = network.numerical_gradient(x_batch, t_batch)\n",
    "    grad = network.gradient(x_batch, t_batch)\n",
    "    \n",
    "    # パラメータの更新\n",
    "    for key in ('W1', 'b1', 'W2', 'b2'):\n",
    "        network.params[key] -= learning_rate * grad[key]\n",
    "    \n",
    "    loss = network.loss(x_batch, t_batch)\n",
    "    train_loss_list.append(loss)\n",
    "    \n",
    "    if i % iter_per_epoch == 0:\n",
    "        train_acc = network.accuracy(x_train, t_train)\n",
    "        test_acc = network.accuracy(x_test, t_test)\n",
    "        train_acc_list.append(train_acc)\n",
    "        test_acc_list.append(test_acc)\n",
    "        print(\"train acc, test acc | \" + str(train_acc) + \", \" + str(test_acc))\n",
    "\n",
    "# グラフの描画\n",
    "markers = {'train': 'o', 'test': 's'}\n",
    "x = np.arange(len(train_acc_list))\n",
    "plt.plot(x, train_acc_list, label='train acc')\n",
    "plt.plot(x, test_acc_list, label='test acc', linestyle='--')\n",
    "plt.xlabel(\"epochs\")\n",
    "plt.ylabel(\"accuracy\")\n",
    "plt.ylim(0, 1.0)\n",
    "plt.legend(loc='lower right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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