sigmoid_and_softmax.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 载入必要的库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-05-19T18:00:23.694137Z",
     "start_time": "2018-05-19T18:00:21.258953Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import h5py\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "from keras.layers import *\n",
    "from keras.models import *\n",
    "from keras.optimizers import *\n",
    "from keras.utils import to_categorical\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 读取数据集并且分割为训练集和测试集\n",
    "\n",
    "此处数据集为猫狗大战的数据集，通过在 ImageNet 上预训练过的 Xception 模型导出的特征。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-05-19T18:00:24.553140Z",
     "start_time": "2018-05-19T18:00:23.695481Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(20180520)\n",
    "\n",
    "filename = \"gap_Xception.h5\"\n",
    "with h5py.File(filename, 'r') as h:\n",
    "    X = np.array(h['train'])\n",
    "    y = np.array(h['label'])\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
    "\n",
    "y_train_softmax = to_categorical(y_train)\n",
    "y_test_softmax = to_categorical(y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 首先搭建一个 softmax 的分类器\n",
    "\n",
    "此处学习率设置为了 1e-3。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-05-19T18:00:26.527011Z",
     "start_time": "2018-05-19T18:00:24.557101Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 20000 samples, validate on 5000 samples\n",
      "Epoch 1/5\n",
      "20000/20000 [==============================] - 0s 23us/step - loss: 0.5584 - acc: 0.7508 - val_loss: 0.4302 - val_acc: 0.9476\n",
      "Epoch 2/5\n",
      "20000/20000 [==============================] - 0s 16us/step - loss: 0.3745 - acc: 0.9306 - val_loss: 0.3103 - val_acc: 0.9800\n",
      "Epoch 3/5\n",
      "20000/20000 [==============================] - 0s 16us/step - loss: 0.2843 - acc: 0.9647 - val_loss: 0.2440 - val_acc: 0.9852\n",
      "Epoch 4/5\n",
      "20000/20000 [==============================] - 0s 17us/step - loss: 0.2296 - acc: 0.9775 - val_loss: 0.2029 - val_acc: 0.9858\n",
      "Epoch 5/5\n",
      "20000/20000 [==============================] - 0s 15us/step - loss: 0.1952 - acc: 0.9825 - val_loss: 0.1751 - val_acc: 0.9862\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(20180520)\n",
    "\n",
    "input_tensor = Input(X.shape[1:])\n",
    "x = input_tensor\n",
    "x = Dropout(0.5)(x)\n",
    "softmax = Dense(2, activation='softmax')\n",
    "x = softmax(x)\n",
    "model = Model(input_tensor, x)\n",
    "model.compile(optimizer=SGD(1e-3),\n",
    "              loss='categorical_crossentropy',\n",
    "              metrics=['accuracy'])\n",
    "\n",
    "softmax_weights, softmax_bias = softmax.get_weights()\n",
    "\n",
    "history_softmax = model.fit(X_train, y_train_softmax, batch_size=128, epochs=5, \n",
    "                            validation_data=(X_test, y_test_softmax))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在二分类的情况下，对于 Sigmod，有：\n",
    "$$\\begin{equation} \n",
    "p(y = 1 | x) = \\frac{1}{1 + e^{-\\theta^Tx}} \n",
    "\\end{equation}$$\n",
    "\n",
    "$$\\begin{equation} \n",
    "p(y = 0 | x) = 1 – p(y = 1 | x) = \\frac{e^{-\\theta^Tx}}{1 + e^{-\\theta^Tx}} \n",
    "\\end{equation}$$\n",
    "\n",
    "而对 $K=2$ 的 Softmax ，有：\n",
    "\n",
    "$$\\begin{equation} \n",
    "p(y = 1|x) = \\frac{e^{\\theta_1^Tx}}{e^{\\theta_0^Tx} + e^{\\theta_1^Tx}} = \\frac{1}{1 + e^{(\\theta_0^T – \\theta_1^T)x}} = \\frac{1}{1 + e^{-\\beta x}} \n",
    "\\end{equation}$$\n",
    "\n",
    "$$\\begin{equation} \n",
    "p(y = 0|x) = \\frac{e^{\\theta_0^Tx}}{e^{\\theta_0^Tx} + e^{\\theta_1^Tx}} = \\frac{e^{(\\theta_0^T-\\theta_1^T)x}}{1 + e^{(\\theta_0^T-\\theta_1^T)x}} = \\frac{e^{-\\beta x}}{1 + e^{-\\beta x}} \n",
    "\\end{equation}$$\n",
    "\n",
    "其中\n",
    "\n",
    "$$\\begin{equation} \n",
    "\\beta = -(\\theta_0^T – \\theta_1^T) \n",
    "\\end{equation}$$\n",
    "\n",
    "可见在二元分类的情况下，Softmax 退化为了 Sigmoid。\n",
    "\n",
    "下面让我们计算出 $\\beta$，并且设置为 sigmoid 层的权值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-05-19T18:00:26.532071Z",
     "start_time": "2018-05-19T18:00:26.528529Z"
    }
   },
   "outputs": [],
   "source": [
    "beta = -(softmax_weights[:,0] - softmax_weights[:,1]).reshape((-1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 搭建 sigmoid 模型，并且设置权值为 beta\n",
    "\n",
    "注意此处学习率为 2e-3。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-05-19T18:00:28.647023Z",
     "start_time": "2018-05-19T18:00:26.533810Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 20000 samples, validate on 5000 samples\n",
      "Epoch 1/5\n",
      "20000/20000 [==============================] - 0s 23us/step - loss: 0.5584 - acc: 0.7508 - val_loss: 0.4302 - val_acc: 0.9476\n",
      "Epoch 2/5\n",
      "20000/20000 [==============================] - 0s 18us/step - loss: 0.3745 - acc: 0.9306 - val_loss: 0.3103 - val_acc: 0.9800\n",
      "Epoch 3/5\n",
      "20000/20000 [==============================] - 0s 18us/step - loss: 0.2843 - acc: 0.9647 - val_loss: 0.2440 - val_acc: 0.9852\n",
      "Epoch 4/5\n",
      "20000/20000 [==============================] - 0s 19us/step - loss: 0.2296 - acc: 0.9775 - val_loss: 0.2029 - val_acc: 0.9858\n",
      "Epoch 5/5\n",
      "20000/20000 [==============================] - 0s 16us/step - loss: 0.1952 - acc: 0.9825 - val_loss: 0.1751 - val_acc: 0.9862\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(20180520)\n",
    "input_tensor = Input(X.shape[1:])\n",
    "x = input_tensor\n",
    "x = Dropout(0.5)(x)\n",
    "sigmoid = Dense(1, activation='sigmoid')\n",
    "x = sigmoid(x)\n",
    "model = Model(input_tensor, x)\n",
    "model.compile(optimizer=SGD(2e-3),\n",
    "              loss='binary_crossentropy',\n",
    "              metrics=['accuracy'])\n",
    "\n",
    "sigmoid.set_weights([beta, np.zeros(1)]) # set beta to sigmoid weights\n",
    "\n",
    "history_sigmoid = model.fit(X_train, y_train, batch_size=128, epochs=5, validation_data=(X_test, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 随机初始化一个 sigmoid 模型进行训练"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-05-19T18:00:30.706065Z",
     "start_time": "2018-05-19T18:00:28.648460Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 20000 samples, validate on 5000 samples\n",
      "Epoch 1/5\n",
      "20000/20000 [==============================] - 0s 25us/step - loss: 0.5265 - acc: 0.8169 - val_loss: 0.4163 - val_acc: 0.9730\n",
      "Epoch 2/5\n",
      "20000/20000 [==============================] - 0s 16us/step - loss: 0.3589 - acc: 0.9604 - val_loss: 0.3025 - val_acc: 0.9876\n",
      "Epoch 3/5\n",
      "20000/20000 [==============================] - 0s 17us/step - loss: 0.2728 - acc: 0.9809 - val_loss: 0.2392 - val_acc: 0.9890\n",
      "Epoch 4/5\n",
      "20000/20000 [==============================] - 0s 20us/step - loss: 0.2220 - acc: 0.9859 - val_loss: 0.1997 - val_acc: 0.9890\n",
      "Epoch 5/5\n",
      "20000/20000 [==============================] - 0s 17us/step - loss: 0.1897 - acc: 0.9867 - val_loss: 0.1728 - val_acc: 0.9896\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(20180520)\n",
    "input_tensor = Input(X.shape[1:])\n",
    "x = input_tensor\n",
    "x = Dropout(0.5)(x)\n",
    "sigmoid = Dense(1, activation='sigmoid')\n",
    "x = sigmoid(x)\n",
    "model = Model(input_tensor, x)\n",
    "model.compile(optimizer=SGD(2e-3),\n",
    "              loss='binary_crossentropy',\n",
    "              metrics=['accuracy'])\n",
    "\n",
    "history_sigmoid_2 = model.fit(X_train, y_train, batch_size=128, epochs=5, validation_data=(X_test, y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-05-19T18:00:30.712980Z",
     "start_time": "2018-05-19T18:00:30.707373Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((2048, 2), (2048, 1))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_weights.shape, beta.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-05-19T17:53:16.916903Z",
     "start_time": "2018-05-19T17:53:16.910687Z"
    }
   },
   "source": [
    "# 可视化\n",
    "\n",
    "下面让我们看看 sigmoid 模型和 softmax 模型的训练曲线，可以看到几乎完全重合。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-05-19T18:00:31.008207Z",
     "start_time": "2018-05-19T18:00:30.714654Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11589b438>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 263,
       "width": 393
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(history_sigmoid.history['loss'])\n",
    "plt.plot(history_softmax.history['loss'])\n",
    "\n",
    "plt.plot(history_sigmoid.history['val_loss'])\n",
    "plt.plot(history_softmax.history['val_loss'])\n",
    "\n",
    "plt.ylabel('loss')\n",
    "plt.xlabel('epoch')\n",
    "\n",
    "plt.legend(['sigmoid_loss', 'softmax_loss', \n",
    "            'sigmoid_val_loss', 'softmax_val_loss'], loc='upper right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 差值可视化\n",
    "\n",
    "* 蓝线：sigmoid 模型和 softmax 模型的 loss 差\n",
    "* 黄线：不同 random_state 训练出来的 sigmoid 模型的 loss 差\n",
    "\n",
    "#### 可以看到黄线的差值很大，这代表不设置 beta 权值，也就是不同的 random_state，会影响模型训练过程的 loss 曲线。\n",
    "#### 可以看到蓝线几乎在0左右，我们可以认为设置了正确的 beta 值的 sigmoid 模型与 softmax 模型等价。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-05-19T18:01:28.768820Z",
     "start_time": "2018-05-19T18:01:28.478288Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x115f2e748>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 263,
       "width": 400
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.array(history_sigmoid.history['val_loss']) - np.array(history_softmax.history['val_loss']))\n",
    "plt.plot(np.array(history_sigmoid.history['val_loss']) - np.array(history_sigmoid_2.history['val_loss']))\n",
    "\n",
    "plt.ylabel('loss')\n",
    "plt.xlabel('epoch')\n",
    "\n",
    "plt.legend(['sigmoid_softmax_beta_gap', 'sigmoid_random_weight_gap'], loc='upper right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 结论\n",
    "\n",
    "* 在二分类问题下，sigmoid 与 softmax 完全等价。\n",
    "* 在二分类问题下，sigmoid 和 softmax 分类器的权值可以互转。\n",
    "* 在二分类问题下，softmax 的学习率是 sigmoid 学习率的2倍。\n",
    "* 在二分类问题下，使用 softmax 会浪费2倍的权值空间。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-05-19T18:01:43.672871Z",
     "start_time": "2018-05-19T18:01:43.666663Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.24520871e-09,  4.52995302e-09, -2.33650208e-09,  5.38825987e-09,\n",
       "        1.37567520e-08])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(history_sigmoid.history['val_loss']) - np.array(history_softmax.history['val_loss'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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