3장. 2절. 경사 소실 - 2.2. 활성화 함수.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 활성화 함수"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-12-01T03:00:31.011014Z",
     "start_time": "2021-12-01T03:00:30.798585Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sigmoid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-12-01T03:00:31.240622Z",
     "start_time": "2021-12-01T03:00:31.027163Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(start=-6, stop=6, num=50)\n",
    "y = 1/(1+np.exp(-x))\n",
    "plt.plot(x, y, c=\"blue\", lw=8)\n",
    "plt.axvline(0, c=\"grey\")\n",
    "plt.axhline(0, c=\"grey\")\n",
    "plt.title(r\"$sigmoid$\", fontsize=20)\n",
    "plt.text(-5, 0.8, r\"$f(x)=\\frac{1}{1+e^{-x}}$\", fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## tanh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-12-01T03:00:31.335820Z",
     "start_time": "2021-12-01T03:00:31.241857Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(start=-3.5, stop=3.5, num=50)\n",
    "y = np.tanh(x)\n",
    "plt.plot(x, y, c=\"blue\", lw=8)\n",
    "plt.axvline(0, c=\"grey\")\n",
    "plt.axhline(0, c=\"grey\")\n",
    "plt.title(r\"$tanh$\", fontsize=20)\n",
    "plt.text(-3.2, 0.75, r\"$f(x)=\\frac{2}{1+e^{-2x}}-1$\", fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ReLU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-12-01T03:00:31.429082Z",
     "start_time": "2021-12-01T03:00:31.336930Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(start=-6, stop=6, num=50)\n",
    "y = [ data if data>=0 else 0 for data in x]\n",
    "plt.plot(x, y, c=\"blue\", lw=8)\n",
    "plt.axvline(0, c=\"grey\")\n",
    "plt.axhline(0, c=\"grey\")\n",
    "plt.title(r\"$ReLU$\", fontsize=20)\n",
    "plt.text(-5, 5, r\"$f(x)=\\{ \\genfrac{}{}{0}{}{0 \\/\\/ for \\/\\/ x<0}{x \\/\\/ for \\/\\/ x\\geq0 } $\", \n",
    "         fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-12-01T03:00:31.514263Z",
     "start_time": "2021-12-01T03:00:31.430298Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(start=-4, stop=4, num=50)\n",
    "y = np.exp(-(x**2))\n",
    "plt.plot(x, y, c=\"blue\", lw=8)\n",
    "# plt.ylim(-0.5,2)\n",
    "plt.axvline(0, c=\"grey\")\n",
    "plt.axhline(0, c=\"grey\")\n",
    "plt.title(r\"$Gaussian$\", fontsize=20)\n",
    "plt.text(-4, 0.8, r\"$f(x)=e^{-x^2 }$\", fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binary Step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-12-01T03:00:31.606882Z",
     "start_time": "2021-12-01T03:00:31.515102Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(start=-4, stop=4, num=1000)\n",
    "y = [ 1 if data>=0 else 0 for data in x]\n",
    "plt.plot(x, y, c=\"blue\", lw=8)\n",
    "plt.axvline(0, c=\"grey\")\n",
    "plt.axhline(0, c=\"grey\")\n",
    "plt.title(r\"$Binary\\/step$\", fontsize=20)\n",
    "plt.text(-4, 0.8, r\"$f(x)=\\{ \\genfrac{}{}{0}{}{0 \\/\\/ for \\/\\/ x<0}{1 \\/\\/ for \\/\\/ x \\geq 0}}$\", \n",
    "         fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## softmax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-12-01T03:00:31.712858Z",
     "start_time": "2021-12-01T03:00:31.607636Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(start=0, stop=10, num=10)\n",
    "def softmax(input):\n",
    "    return np.exp(input) / (np.sum(np.exp(input)))\n",
    "y = softmax(x)\n",
    "plt.plot(x, y, c=\"blue\", lw=8)\n",
    "plt.ylim(-0.1, 1)\n",
    "plt.axvline(0, c=\"grey\")\n",
    "plt.axhline(0, c=\"grey\")\n",
    "plt.title(r\"$softmax$\", fontsize=20)\n",
    "plt.text(2, 0.8, \n",
    "         r\"$f(x)=\\frac{e^{x_i}}{\\sum_{j=1}^J e^x_i}\\/\\/ \\/\\/ for\\/ i=1,\\/\\/...,\\/\\/j$\", \n",
    "         fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LeakyReLU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-12-01T03:00:31.806427Z",
     "start_time": "2021-12-01T03:00:31.715058Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(start=-6, stop=6, num=50)\n",
    "y = [ data if data>=0 else 0.1*data for data in x]\n",
    "plt.plot(x, y, c=\"blue\", lw=8)\n",
    "plt.axvline(0, c=\"grey\")\n",
    "plt.axhline(0, c=\"grey\")\n",
    "plt.title(r\"$LeakyReLU(\\alpha=0.1)$\", fontsize=20)\n",
    "plt.text(-5, 5, \n",
    "         r\"$f(\\alpha,x)=\\{ \\genfrac{}{}{0}{}{\\alpha x \\/\\/ for \\/\\/ x<0}{x \\/\\/ for \\/\\/ x \\geq 0 }}$\", \n",
    "         fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ELU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-12-01T03:00:31.900560Z",
     "start_time": "2021-12-01T03:00:31.807967Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(start=-6, stop=6, num=50)\n",
    "y = [ data if data>=0 else 1*(np.e**data-1) for data in x]\n",
    "plt.plot(x, y, c=\"blue\", lw=8)\n",
    "plt.axvline(0, c=\"grey\")\n",
    "plt.axhline(0, c=\"grey\")\n",
    "plt.title(r\"$ELU(\\alpha=(e^x -1))$\", fontsize=20)\n",
    "plt.text(-5, 5, \n",
    "         r\"$f(\\alpha,x)=\\{\\genfrac{}{}{0}{}{\\alpha (e^x -1) \\/\\/ for \\/\\/ x<0}{x \\/\\/ for \\/\\/ x \\geq 0 }}$\", \n",
    "         fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 케라스에서 활성화 함수 사용"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{\"class_name\": \"Sequential\", \"config\": {\"name\": \"sequential\", \"layers\": [{\"module\": \"keras.layers\", \"class_name\": \"InputLayer\", \"config\": {\"batch_input_shape\": [null, 4], \"dtype\": \"float32\", \"sparse\": false, \"ragged\": false, \"name\": \"input_1\"}, \"registered_name\": null}, {\"module\": \"keras.layers\", \"class_name\": \"Dense\", \"config\": {\"name\": \"dense\", \"trainable\": true, \"dtype\": \"float32\", \"units\": 50, \"activation\": \"sigmoid\", \"use_bias\": true, \"kernel_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"GlorotUniform\", \"config\": {\"seed\": null}, \"registered_name\": null}, \"bias_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Zeros\", \"config\": {}, \"registered_name\": null}, \"kernel_regularizer\": null, \"bias_regularizer\": null, \"activity_regularizer\": null, \"kernel_constraint\": null, \"bias_constraint\": null}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 4]}}, {\"module\": \"keras.layers\", \"class_name\": \"Dense\", \"config\": {\"name\": \"dense_1\", \"trainable\": true, \"dtype\": \"float32\", \"units\": 50, \"activation\": {\"module\": \"keras.layers\", \"class_name\": \"PReLU\", \"config\": {\"name\": \"p_re_lu\", \"trainable\": true, \"dtype\": \"float32\", \"alpha_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Zeros\", \"config\": {}, \"registered_name\": null}, \"alpha_regularizer\": null, \"alpha_constraint\": null, \"shared_axes\": null}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 50]}}, \"use_bias\": true, \"kernel_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"GlorotUniform\", \"config\": {\"seed\": null}, \"registered_name\": null}, \"bias_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Zeros\", \"config\": {}, \"registered_name\": null}, \"kernel_regularizer\": null, \"bias_regularizer\": null, \"activity_regularizer\": null, \"kernel_constraint\": null, \"bias_constraint\": null}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 50]}}, {\"module\": \"keras.layers\", \"class_name\": \"Dense\", \"config\": {\"name\": \"dense_2\", \"trainable\": true, \"dtype\": \"float32\", \"units\": 30, \"activation\": {\"module\": \"keras.layers\", \"class_name\": \"ELU\", \"config\": {\"name\": \"elu\", \"trainable\": true, \"dtype\": \"float32\", \"alpha\": 1.0}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 30]}}, \"use_bias\": true, \"kernel_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"GlorotUniform\", \"config\": {\"seed\": null}, \"registered_name\": null}, \"bias_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Zeros\", \"config\": {}, \"registered_name\": null}, \"kernel_regularizer\": null, \"bias_regularizer\": null, \"activity_regularizer\": null, \"kernel_constraint\": null, \"bias_constraint\": null}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 50]}}, {\"module\": \"keras.layers\", \"class_name\": \"Dense\", \"config\": {\"name\": \"dense_3\", \"trainable\": true, \"dtype\": \"float32\", \"units\": 3, \"activation\": \"softmax\", \"use_bias\": true, \"kernel_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"GlorotUniform\", \"config\": {\"seed\": null}, \"registered_name\": null}, \"bias_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Zeros\", \"config\": {}, \"registered_name\": null}, \"kernel_regularizer\": null, \"bias_regularizer\": null, \"activity_regularizer\": null, \"kernel_constraint\": null, \"bias_constraint\": null}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 30]}}]}, \"keras_version\": \"2.13.1\", \"backend\": \"tensorflow\"}\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.keras.activations import softmax\n",
    "from tensorflow.keras.layers import ELU, PReLU, InputLayer, Dense\n",
    "from tensorflow.keras.models import Sequential\n",
    "\n",
    "model = Sequential()\n",
    "elu = ELU(alpha=1)\n",
    "model.add(InputLayer(4))\n",
    "model.add(Dense(50, activation=\"sigmoid\")) # 문자열 이용 \n",
    "model.add(Dense(50, activation=PReLU()))   # 객체 이용 \n",
    "model.add(Dense(30, activation=elu))       # 객체 이용 \n",
    "model.add(Dense(3, activation=softmax))    # 함수이름 이용\n",
    "print(model.to_json())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential\"\n",
      "_________________________________________________________________\n",
      " Layer (type)                Output Shape              Param #   \n",
      "=================================================================\n",
      " dense (Dense)               (None, 50)                250       \n",
      "                                                                 \n",
      " dense_1 (Dense)             (None, 50)                2600      \n",
      "                                                                 \n",
      " dense_2 (Dense)             (None, 30)                1530      \n",
      "                                                                 \n",
      " dense_3 (Dense)             (None, 3)                 93        \n",
      "                                                                 \n",
      "=================================================================\n",
      "Total params: 4473 (17.47 KB)\n",
      "Trainable params: 4473 (17.47 KB)\n",
      "Non-trainable params: 0 (0.00 Byte)\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{\"class_name\": \"Sequential\", \"config\": {\"name\": \"sequential_1\", \"layers\": [{\"module\": \"keras.layers\", \"class_name\": \"InputLayer\", \"config\": {\"batch_input_shape\": [null, 4], \"dtype\": \"float32\", \"sparse\": false, \"ragged\": false, \"name\": \"input_2\"}, \"registered_name\": null}, {\"module\": \"keras.layers\", \"class_name\": \"Dense\", \"config\": {\"name\": \"dense_4\", \"trainable\": true, \"dtype\": \"float32\", \"units\": 50, \"activation\": \"sigmoid\", \"use_bias\": true, \"kernel_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"HeNormal\", \"config\": {\"seed\": null}, \"registered_name\": null}, \"bias_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Zeros\", \"config\": {}, \"registered_name\": null}, \"kernel_regularizer\": null, \"bias_regularizer\": null, \"activity_regularizer\": null, \"kernel_constraint\": null, \"bias_constraint\": null}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 4]}}, {\"module\": \"keras.layers\", \"class_name\": \"Dense\", \"config\": {\"name\": \"dense_5\", \"trainable\": true, \"dtype\": \"float32\", \"units\": 50, \"activation\": \"sigmoid\", \"use_bias\": true, \"kernel_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"GlorotUniform\", \"config\": {\"seed\": null}, \"registered_name\": null}, \"bias_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Zeros\", \"config\": {}, \"registered_name\": null}, \"kernel_regularizer\": null, \"bias_regularizer\": null, \"activity_regularizer\": null, \"kernel_constraint\": null, \"bias_constraint\": null}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 50]}}, {\"module\": \"keras.layers\", \"class_name\": \"Dense\", \"config\": {\"name\": \"dense_6\", \"trainable\": true, \"dtype\": \"float32\", \"units\": 30, \"activation\": \"sigmoid\", \"use_bias\": true, \"kernel_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"RandomNormal\", \"config\": {\"mean\": 0, \"stddev\": 0.1, \"seed\": null}, \"registered_name\": null}, \"bias_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Zeros\", \"config\": {}, \"registered_name\": null}, \"kernel_regularizer\": null, \"bias_regularizer\": null, \"activity_regularizer\": null, \"kernel_constraint\": null, \"bias_constraint\": null}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 50]}}, {\"module\": \"keras.layers\", \"class_name\": \"Dense\", \"config\": {\"name\": \"dense_7\", \"trainable\": true, \"dtype\": \"float32\", \"units\": 3, \"activation\": \"softmax\", \"use_bias\": true, \"kernel_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"GlorotUniform\", \"config\": {\"seed\": null}, \"registered_name\": null}, \"bias_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Zeros\", \"config\": {}, \"registered_name\": null}, \"kernel_regularizer\": null, \"bias_regularizer\": null, \"activity_regularizer\": null, \"kernel_constraint\": null, \"bias_constraint\": null}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 30]}}]}, \"keras_version\": \"2.13.1\", \"backend\": \"tensorflow\"}\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.keras.models import Sequential\n",
    "from tensorflow.keras.layers import InputLayer, Dense\n",
    "from tensorflow.keras.initializers import RandomNormal\n",
    "\n",
    "model = Sequential()\n",
    "\n",
    "model.add(InputLayer(4))\n",
    "model.add(Dense(50, activation=\"sigmoid\", kernel_initializer=\"he_normal\"))\n",
    "model.add(Dense(50, activation=\"sigmoid\", kernel_initializer=\"glorot_uniform\"))\n",
    "model.add(Dense(30, activation=\"sigmoid\", kernel_initializer=RandomNormal(0, 0.1)))\n",
    "model.add(Dense(3, activation=\"softmax\"))\n",
    "print(model.to_json())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{\"class_name\": \"Sequential\", \"config\": {\"name\": \"sequential_2\", \"layers\": [{\"module\": \"keras.layers\", \"class_name\": \"InputLayer\", \"config\": {\"batch_input_shape\": [null, 28, 28], \"dtype\": \"float32\", \"sparse\": false, \"ragged\": false, \"name\": \"flatten_input\"}, \"registered_name\": null}, {\"module\": \"keras.layers\", \"class_name\": \"Flatten\", \"config\": {\"name\": \"flatten\", \"trainable\": true, \"dtype\": \"float32\", \"batch_input_shape\": [null, 28, 28], \"data_format\": \"channels_last\"}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 28, 28]}}, {\"module\": \"keras.layers\", \"class_name\": \"Dense\", \"config\": {\"name\": \"dense_8\", \"trainable\": true, \"dtype\": \"float32\", \"units\": 360, \"activation\": \"relu\", \"use_bias\": true, \"kernel_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"GlorotUniform\", \"config\": {\"seed\": null}, \"registered_name\": null}, \"bias_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Zeros\", \"config\": {}, \"registered_name\": null}, \"kernel_regularizer\": null, \"bias_regularizer\": null, \"activity_regularizer\": null, \"kernel_constraint\": null, \"bias_constraint\": null}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 784]}}, {\"module\": \"keras.layers\", \"class_name\": \"Dropout\", \"config\": {\"name\": \"dropout\", \"trainable\": true, \"dtype\": \"float32\", \"rate\": 0.1, \"noise_shape\": null, \"seed\": null}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 360]}}, {\"module\": \"keras.layers\", \"class_name\": \"BatchNormalization\", \"config\": {\"name\": \"batch_normalization\", \"trainable\": true, \"dtype\": \"float32\", \"axis\": [1], \"momentum\": 0.99, \"epsilon\": 0.001, \"center\": true, \"scale\": true, \"beta_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Zeros\", \"config\": {}, \"registered_name\": null}, \"gamma_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Ones\", \"config\": {}, \"registered_name\": null}, \"moving_mean_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Zeros\", \"config\": {}, \"registered_name\": null}, \"moving_variance_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Ones\", \"config\": {}, \"registered_name\": null}, \"beta_regularizer\": null, \"gamma_regularizer\": null, \"beta_constraint\": null, \"gamma_constraint\": null}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 360]}}, {\"module\": \"keras.layers\", \"class_name\": \"Dense\", \"config\": {\"name\": \"dense_9\", \"trainable\": true, \"dtype\": \"float32\", \"units\": 128, \"activation\": \"relu\", \"use_bias\": true, \"kernel_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"GlorotUniform\", \"config\": {\"seed\": null}, \"registered_name\": null}, \"bias_initializer\": {\"module\": \"keras.initializers\", \"class_name\": \"Zeros\", \"config\": {}, \"registered_name\": null}, \"kernel_regularizer\": null, \"bias_regularizer\": null, \"activity_regularizer\": null, \"kernel_constraint\": null, \"bias_constraint\": null}, \"registered_name\": null, \"build_config\": {\"input_shape\": [null, 360]}}]}, \"keras_version\": \"2.13.1\", \"backend\": \"tensorflow\"}\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.keras.models import Sequential\n",
    "from tensorflow.keras.layers import Flatten, Dense, Dropout\n",
    "from tensorflow.keras.layers import BatchNormalization\n",
    "\n",
    "model = Sequential()\n",
    "\n",
    "model.add(Flatten(input_shape=(28, 28)))\n",
    "\n",
    "model.add(Dense(360, activation=\"relu\"))\n",
    "model.add(Dropout(0.1))\n",
    "model.add(BatchNormalization())\n",
    "model.add(Dense(128, activation=\"relu\"))\n",
    "print(model.to_json())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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