全连接网络.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn.functional as F\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### loss\n",
    "Mean Squared Error:\n",
    "    \n",
    "$$loss=\\sum[y-(xw+b)]^2$$\n",
    "\n",
    "\n",
    "$$\\frac{\\partial loss}{\\partial \\theta} = 2 \\sum[f_\\theta(x)-y] \\frac{\\partial f_\\theta \\left(x \\right )}{\\partial \\theta} $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gradient API"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### torch.autograd.grad(loss,[w1,w2...])\n",
    "[w1 grad, w2 grad ...]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([2.]),)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# y_pred = xw\n",
    "# x=1 w=2 y=1\n",
    "x = torch.ones(1)\n",
    "w = torch.full([1],2) # tensor([2.])\n",
    "mse = F.mse_loss(x*w, torch.ones(1))  # tensor(1.)\n",
    "\n",
    "# torch.autograd.grad(mse,[w])\n",
    "\n",
    "w.requires_grad_() # tensor([2.], requires_grad=True)\n",
    "\n",
    "mse = F.mse_loss(x*w, torch.ones(1))\n",
    "\n",
    "# 2(1-2)\n",
    "torch.autograd.grad(mse, [w])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### loss.backward()\n",
    "w1.grad\n",
    "w2.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2.])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = torch.ones(1)\n",
    "w = torch.full([1],2,requires_grad=True) # tensor([2.])\n",
    "mse = F.mse_loss(x*w, torch.ones(1))  # tensor(1.)\n",
    "mse.backward()\n",
    "w.grad\n",
    "# w.grad.norm()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> softmax (soft version of max)\n",
    "\n",
    "> $$S(y_i)=\\frac{e^{y_i}}{\\sum{e^{y_j}}}$$\n",
    "\n",
    "> 适用于多分类问题，将输入转化为PROVABILITIES。\n",
    "\n",
    "> 输入[2,1,0.1] -> [0.7,0.2,0.1] 2=1*2 0.7=0.2*3.5 具有优势的类别的概率会被放大\n",
    "\n",
    "> ![derivativei=j](./photo/softmax1.png)\n",
    "\n",
    "> ![softmax2](./photo/softmax2.png)\n",
    "\n",
    "> ![softmax](./photo/softmax.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.3333, 0.1632, 0.3189], requires_grad=True)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=torch.rand(3,requires_grad=True)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([3])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(tensor([-0.1054,  0.2093, -0.1039]),)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# p1 对a求导。 相对应的为正(第二个)，第一个和第三个为负\n",
    "p=F.softmax(a,dim=0)\n",
    "print(p.shape)\n",
    "torch.autograd.grad(p[1],[a],retain_graph=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 单输出感知机 Perceptron"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![one-outputPerceptron](./photo/one_output.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-0.0013, -0.0308, -0.0485, -0.0194, -0.0345, -0.0135, -0.0143, -0.0058,\n",
       "         -0.0152, -0.0173]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = torch.rand(1,10)\n",
    "w = torch.rand(1,10,requires_grad=True)\n",
    "\n",
    "o = torch.sigmoid(x@w.t())\n",
    "\n",
    "loss = F.mse_loss(torch.ones(1,1),o)\n",
    "\n",
    "loss.backward()\n",
    "\n",
    "w.grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 多输出感知机梯度"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![multi-outputPerceptron](./photo/multi_output.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([[-0.0061, -0.0071, -0.0031, -0.0024, -0.0041, -0.0027, -0.0070, -0.0094,\n",
       "         -0.0059, -0.0096],\n",
       "        [-0.0003, -0.0004, -0.0002, -0.0001, -0.0002, -0.0001, -0.0004, -0.0005,\n",
       "         -0.0003, -0.0005]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = torch.rand(1,10)\n",
    "w = torch.rand(2,10,requires_grad=True)\n",
    "\n",
    "o = torch.sigmoid(x@w.t())\n",
    "\n",
    "loss = F.mse_loss(torch.ones(1,2),o)\n",
    "print(loss.shape)\n",
    "loss.backward()\n",
    "\n",
    "w.grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 链式法则"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(True)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = torch.tensor(1.)\n",
    "w1 = torch.tensor(2.,requires_grad=True)\n",
    "b1 = torch.tensor(1.)\n",
    "w2 = torch.tensor(2.,requires_grad=True)\n",
    "b2 = torch.tensor(1.)\n",
    "\n",
    "y1 = x*w1 + b1\n",
    "y2 = y1*w2 + b2\n",
    "\n",
    "dy2_dy1 = torch.autograd.grad(y2,[y1],retain_graph=True)[0]\n",
    "dy1_dw1 = torch.autograd.grad(y1,[w1],retain_graph=True)[0]\n",
    "\n",
    "dy2_dw1 = torch.autograd.grad(y2,[w1],retain_graph=True)[0]\n",
    "\n",
    "dy2_dw1 == dy1_dw1*dy2_dy1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 优化问题实战 梯度下降"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x,y range:  (120,) (120,)\n",
      "X,Y maps:  (120, 120) (120, 120)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step 0: x = [0.0009999999310821295, 0.0009999999310821295], f(x) = 170.0\n",
      "step 2000: x = [2.3331806659698486, 1.9540694952011108], f(x) = 13.730916023254395\n",
      "step 4000: x = [2.9820079803466797, 2.0270984172821045], f(x) = 0.014858869835734367\n",
      "step 6000: x = [2.999983549118042, 2.0000221729278564], f(x) = 1.1074007488787174e-08\n",
      "step 8000: x = [2.9999938011169434, 2.0000083446502686], f(x) = 1.5572823031106964e-09\n",
      "step 10000: x = [2.999997854232788, 2.000002861022949], f(x) = 1.8189894035458565e-10\n",
      "step 12000: x = [2.9999992847442627, 2.0000009536743164], f(x) = 1.6370904631912708e-11\n",
      "step 14000: x = [2.999999761581421, 2.000000238418579], f(x) = 1.8189894035458565e-12\n",
      "step 16000: x = [3.0, 2.0], f(x) = 0.0\n",
      "step 18000: x = [3.0, 2.0], f(x) = 0.0\n",
      "type of pred: <class 'torch.Tensor'>\n",
      "type of x:  <class 'torch.Tensor'>\n",
      "tensor([3., 2.], requires_grad=True)\n",
      "tensor(0., grad_fn=<AddBackward0>)\n"
     ]
    }
   ],
   "source": [
    "def himmelblau(x):\n",
    "    return (x[0] ** 2 + x[1] -11) ** 2 + (x[0] + x[1] ** 2 - 7) ** 2\n",
    "\n",
    "x = np.arange(-6,6,0.1)\n",
    "y = np.arange(-6,6,0.1)\n",
    "print('x,y range: ',x.shape,y.shape)\n",
    "X,Y = np.meshgrid(x,y)\n",
    "print('X,Y maps: ',X.shape,Y.shape)\n",
    "Z = himmelblau([X,Y])\n",
    "\n",
    "fig = plt.figure('himmelblau')\n",
    "ax = fig.gca(projection='3d')\n",
    "ax.plot_surface(X,Y,Z)\n",
    "ax.view_init(50,-30)\n",
    "# ax.view_init(elev=elev,azim=azim)#改变绘制图像的视角,即相机的位置,azim沿着z轴旋转，elev沿着y轴\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "plt.show()\n",
    "\n",
    "x = torch.tensor([0.,0.], requires_grad=True)\n",
    "optimizer = torch.optim.Adam([x],lr=1e-3)\n",
    "for step in range(20000):\n",
    "    \n",
    "    pred = himmelblau(x)\n",
    "    optimizer.zero_grad()\n",
    "    pred.backward()\n",
    "    optimizer.step()\n",
    "    \n",
    "    # item()只适用tensor包含一个元素值的时候，将tensor转化为python纯数值\n",
    "    # tolist() 多个元素的tensor转化为python list\n",
    "    if step % 2000 == 0:\n",
    "        print('step {}: x = {}, f(x) = {}'\n",
    "             .format(step,x.tolist(),pred.item()))\n",
    "    \n",
    "print('type of pred:',type(pred))\n",
    "print('type of x: ',type(x))\n",
    "print(x)\n",
    "print(pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 熵越大越稳定"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.0313)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 熵 ： -plog_2(p)\n",
    "a = torch.full([4],1/4.)\n",
    "\n",
    "-(a * torch.log2(a)).sum() # tensor(2.)\n",
    "\n",
    "a = torch.tensor([0.1,0.1,0.1,0.7]) # tensor(1.3568)\n",
    "-(a * torch.log2(a)).sum()\n",
    "\n",
    "a = torch.tensor([0.001,0.001,0.001,0.999]) # tensor(0.0313)\n",
    "-(a * torch.log2(a)).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![crossEntropy](./photo/crossEntropy.png)\n",
    "\n",
    "softmax和cross entropy层分开会出现数据不稳定情况。\n",
    "\n",
    "![softmax_crossEntropy](./photo/softmax_cross.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### numerical stability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of logits:  torch.Size([1, 10])\n",
      "shape of pred: torch.Size([1, 10]),\n",
      "pred_after softmax: tensor([[4.5430e-16, 1.3342e-33, 9.1295e-16, 4.4121e-20, 4.0080e-39, 2.9548e-02,\n",
      "         5.9255e-36, 1.5178e-10, 2.7544e-23, 9.7045e-01]])\n",
      "tensor(44.5673)\n",
      "tensor(44.5673)\n"
     ]
    }
   ],
   "source": [
    "x = torch.randn(1,784)\n",
    "w = torch.randn(10,784)\n",
    "\n",
    "logits=x@w.t()\n",
    "print('shape of logits: ',logits.shape)\n",
    "\n",
    "pred = F.softmax(logits, dim=1)\n",
    "print('shape of pred: {},\\npred_after softmax: {}'.format(pred.shape,pred))\n",
    "\n",
    "pred_log = torch.log(pred)\n",
    "\n",
    "print(F.cross_entropy(logits,torch.tensor([3]))) # tensor(0.0780)\n",
    "print(F.nll_loss(pred_log,torch.tensor([3]))) # tensor(65.0113)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Network Architecture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![networdArchitecture](./photo/network_arch.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#数据集下载\n",
    "# http://yann.lecun.com/exdb/mnist/\n",
    "from torchvision import datasets\n",
    "import torchvision.transforms as transforms\n",
    "batch_size=200\n",
    "learning_rate=0.01\n",
    "epochs=10\n",
    "\n",
    "train_loader = torch.utils.data.DataLoader(\n",
    "    datasets.MNIST('./data',train=True,\n",
    "                  transform=transforms.Compose([\n",
    "                  transforms.ToTensor(),\n",
    "                  transforms.Normalize((0.1307,),(0.3081,))\n",
    "                  ])),batch_size=batch_size,shuffle=True)\n",
    "\n",
    "test_loader = torch.utils.data.DataLoader(\n",
    "    datasets.MNIST('./data',train=False,transform=transforms.Compose([\n",
    "        transforms.ToTensor(),\n",
    "        transforms.Normalize((0.1307,),(0.3081,))\n",
    "    ])),batch_size=batch_size,shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
      "        [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
      "        [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
      "        ...,\n",
      "        [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
      "        [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
      "        [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242]])\n"
     ]
    }
   ],
   "source": [
    "for batch_idx,(data, target) in enumerate(train_loader):\n",
    "    data = data.view(-1,28*28)\n",
    "    if batch_idx>1:\n",
    "        print(data)\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train Epoch: 0 [0/60000 (0%)]\tLoss:3.666276\n",
      "Train Epoch: 0 [20000/60000 (33%)]\tLoss:0.732064\n",
      "Train Epoch: 0 [40000/60000 (67%)]\tLoss:0.660332\n",
      "Train Epoch: 1 [0/60000 (0%)]\tLoss:0.593860\n",
      "Train Epoch: 1 [20000/60000 (33%)]\tLoss:0.513246\n",
      "Train Epoch: 1 [40000/60000 (67%)]\tLoss:0.606892\n",
      "Train Epoch: 2 [0/60000 (0%)]\tLoss:0.467232\n",
      "Train Epoch: 2 [20000/60000 (33%)]\tLoss:0.593296\n",
      "Train Epoch: 2 [40000/60000 (67%)]\tLoss:0.448865\n",
      "Train Epoch: 3 [0/60000 (0%)]\tLoss:0.401008\n",
      "Train Epoch: 3 [20000/60000 (33%)]\tLoss:0.387399\n",
      "Train Epoch: 3 [40000/60000 (67%)]\tLoss:0.470612\n",
      "Train Epoch: 4 [0/60000 (0%)]\tLoss:0.421968\n",
      "Train Epoch: 4 [20000/60000 (33%)]\tLoss:0.432721\n",
      "Train Epoch: 4 [40000/60000 (67%)]\tLoss:0.406733\n",
      "Train Epoch: 5 [0/60000 (0%)]\tLoss:0.468163\n",
      "Train Epoch: 5 [20000/60000 (33%)]\tLoss:0.377463\n",
      "Train Epoch: 5 [40000/60000 (67%)]\tLoss:0.361798\n",
      "Train Epoch: 6 [0/60000 (0%)]\tLoss:0.450970\n",
      "Train Epoch: 6 [20000/60000 (33%)]\tLoss:0.277905\n",
      "Train Epoch: 6 [40000/60000 (67%)]\tLoss:0.451050\n",
      "Train Epoch: 7 [0/60000 (0%)]\tLoss:0.355615\n",
      "Train Epoch: 7 [20000/60000 (33%)]\tLoss:0.362469\n",
      "Train Epoch: 7 [40000/60000 (67%)]\tLoss:0.163363\n",
      "Train Epoch: 8 [0/60000 (0%)]\tLoss:0.221540\n",
      "Train Epoch: 8 [20000/60000 (33%)]\tLoss:0.124955\n",
      "Train Epoch: 8 [40000/60000 (67%)]\tLoss:0.160428\n",
      "Train Epoch: 9 [0/60000 (0%)]\tLoss:0.165878\n",
      "Train Epoch: 9 [20000/60000 (33%)]\tLoss:0.140942\n",
      "Train Epoch: 9 [40000/60000 (67%)]\tLoss:0.102176\n",
      "\n",
      "Test set: Average Loss : 0.0008, Accuracy: 9535/10000(95%\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "batch_size=200\n",
    "learning_rate=0.01\n",
    "epochs=10\n",
    "\n",
    "w1,b1 = torch.rand(200,784,requires_grad=True),\\\n",
    "        torch.rand(200,requires_grad=True)\n",
    "w2,b2 = torch.rand(200,200,requires_grad=True),\\\n",
    "        torch.rand(200,requires_grad=True)\n",
    "w3,b3 = torch.rand(10,200,requires_grad=True),\\\n",
    "        torch.rand(10,requires_grad=True)\n",
    "\n",
    "# 初始化\n",
    "torch.nn.init.kaiming_normal_(w1)\n",
    "torch.nn.init.kaiming_normal_(w2)\n",
    "torch.nn.init.kaiming_normal_(w3)\n",
    "\n",
    "def forward(x):\n",
    "    x = x@w1.t() + b1\n",
    "    x = F.relu(x)\n",
    "    x = x@w2.t() + b2\n",
    "    x = F.relu(x)\n",
    "    x = x@w3.t() + b3\n",
    "    x = F.relu(x)\n",
    "    return x\n",
    "\n",
    "optimizer = torch.optim.SGD([w1,b1,w2,b2,w3,b3],lr=learning_rate)\n",
    "criteon = torch.nn.CrossEntropyLoss()\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    \n",
    "    for batch_idx,(data, target) in enumerate(train_loader):\n",
    "        \n",
    "        data = data.view(-1,28*28)\n",
    "        \n",
    "        logits = forward(data)\n",
    "        loss = criteon(logits,target)\n",
    "        \n",
    "        optimizer.zero_grad()\n",
    "        loss.backward()\n",
    "        \n",
    "        optimizer.step()\n",
    "        \n",
    "        if batch_idx % 100 == 0:\n",
    "            print('Train Epoch: {} [{}/{} ({:.0f}%)]\\tLoss:{:.6f}'.format(\n",
    "                epoch,batch_idx*len(data),len(train_loader.dataset),\n",
    "                100. * batch_idx / len(train_loader),loss.item()))\n",
    "test_loss = 0\n",
    "correct = 0\n",
    "for data, target in test_loader:\n",
    "    data = data.view(-1,28*28)\n",
    "    logits = forward(data)\n",
    "    test_loss += criteon(logits,target).item()\n",
    "    #torch.max(a,0) 返回每一列中最大值的那个元素，且返回索引（返回最大元素在这一列的行索引）\n",
    "    #torch.max(a,1) 返回每一行中最大值的那个元素，且返回其索引（返回最大元素在这一行的列索引）\n",
    "    #torch.max()[0]， 只返回最大值的每个数\n",
    "    #troch.max()[1]， 只返回最大值的每个索引\n",
    "    \n",
    "    # argmax() 返回最大值的索引\n",
    "    # pred = logits.argmax(dim=1)\n",
    "    # correct += pred.eq(target).float().sum().item()\n",
    "    \n",
    "    # 返回每一行中最大值的索引\n",
    "    pred = logits.data.max(1)[1]\n",
    "    correct += pred.eq(target.data).sum()\n",
    "    \n",
    "test_loss /= len(test_loader.dataset)\n",
    "print('\\nTest set: Average Loss : {:.4f}, Accuracy: {}/{}({:.0f}%\\n)'.format(\n",
    "    test_loss, correct, len(test_loader.dataset),\n",
    "    100.*correct / len(test_loader.dataset)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 完整代码"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train: 60000 test: 10000\n",
      "db1: 50000 db2:"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Setting up a new session...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 10000\n",
      "Train Epoch: 0 [0/50000 (0%)]\tLoss:2.295877\n",
      "Train Epoch: 0 [20000/50000 (40%)]\tLoss:2.000010\n",
      "Train Epoch: 0 [40000/50000 (80%)]\tLoss:1.362778\n",
      "\n",
      "VAL set: Average Loss : 0.0050, Accuracy: 7611/10000(76%\n",
      ")\n",
      "Train Epoch: 1 [0/50000 (0%)]\tLoss:0.957616\n",
      "Train Epoch: 1 [20000/50000 (40%)]\tLoss:0.615890\n",
      "Train Epoch: 1 [40000/50000 (80%)]\tLoss:0.493029\n",
      "\n",
      "VAL set: Average Loss : 0.0024, Accuracy: 8734/10000(87%\n",
      ")\n",
      "Train Epoch: 2 [0/50000 (0%)]\tLoss:0.515746\n",
      "Train Epoch: 2 [20000/50000 (40%)]\tLoss:0.407794\n",
      "Train Epoch: 2 [40000/50000 (80%)]\tLoss:0.448579\n",
      "\n",
      "VAL set: Average Loss : 0.0020, Accuracy: 8899/10000(89%\n",
      ")\n",
      "Train Epoch: 3 [0/50000 (0%)]\tLoss:0.350236\n",
      "Train Epoch: 3 [20000/50000 (40%)]\tLoss:0.437432\n",
      "Train Epoch: 3 [40000/50000 (80%)]\tLoss:0.407213\n",
      "\n",
      "VAL set: Average Loss : 0.0017, Accuracy: 9004/10000(90%\n",
      ")\n",
      "Train Epoch: 4 [0/50000 (0%)]\tLoss:0.333286\n",
      "Train Epoch: 4 [20000/50000 (40%)]\tLoss:0.353578\n",
      "Train Epoch: 4 [40000/50000 (80%)]\tLoss:0.377329\n",
      "\n",
      "VAL set: Average Loss : 0.0016, Accuracy: 9059/10000(91%\n",
      ")\n",
      "Train Epoch: 5 [0/50000 (0%)]\tLoss:0.215794\n",
      "Train Epoch: 5 [20000/50000 (40%)]\tLoss:0.350708\n",
      "Train Epoch: 5 [40000/50000 (80%)]\tLoss:0.259393\n",
      "\n",
      "VAL set: Average Loss : 0.0015, Accuracy: 9107/10000(91%\n",
      ")\n",
      "Train Epoch: 6 [0/50000 (0%)]\tLoss:0.230178\n",
      "Train Epoch: 6 [20000/50000 (40%)]\tLoss:0.288761\n",
      "Train Epoch: 6 [40000/50000 (80%)]\tLoss:0.381483\n",
      "\n",
      "VAL set: Average Loss : 0.0015, Accuracy: 9157/10000(92%\n",
      ")\n",
      "Train Epoch: 7 [0/50000 (0%)]\tLoss:0.265693\n",
      "Train Epoch: 7 [20000/50000 (40%)]\tLoss:0.263791\n",
      "Train Epoch: 7 [40000/50000 (80%)]\tLoss:0.398609\n",
      "\n",
      "VAL set: Average Loss : 0.0014, Accuracy: 9206/10000(92%\n",
      ")\n",
      "Train Epoch: 8 [0/50000 (0%)]\tLoss:0.230513\n",
      "Train Epoch: 8 [20000/50000 (40%)]\tLoss:0.233550\n",
      "Train Epoch: 8 [40000/50000 (80%)]\tLoss:0.202184\n",
      "\n",
      "VAL set: Average Loss : 0.0013, Accuracy: 9231/10000(92%\n",
      ")\n",
      "Train Epoch: 9 [0/50000 (0%)]\tLoss:0.233977\n",
      "Train Epoch: 9 [20000/50000 (40%)]\tLoss:0.210254\n",
      "Train Epoch: 9 [40000/50000 (80%)]\tLoss:0.272901\n",
      "\n",
      "VAL set: Average Loss : 0.0013, Accuracy: 9242/10000(92%\n",
      ")\n",
      "\n",
      "Test set: Average Loss : 0.0012, Accuracy: 9335/10000(93%\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "from visdom import Visdom\n",
    "#数据集下载\n",
    "# http://yann.lecun.com/exdb/mnist/\n",
    "from torchvision import datasets\n",
    "import torchvision.transforms as transforms\n",
    "\n",
    "batch_size=200\n",
    "learning_rate=0.01\n",
    "epochs=10\n",
    "global_step=0\n",
    "\n",
    "\n",
    "# 加载数据集\n",
    "# train_loader,val_loader,test_loader\n",
    "train_db = datasets.MNIST('./data',train=True,\n",
    "                  transform=transforms.Compose([\n",
    "                  transforms.ToTensor(),\n",
    "                  transforms.Normalize((0.1307,),(0.3081,))\n",
    "                  ]))\n",
    "train_loader = torch.utils.data.DataLoader(train_db,batch_size=batch_size,shuffle=True)\n",
    "\n",
    "test_db = datasets.MNIST('./data',train=False,transform=transforms.Compose([\n",
    "        transforms.ToTensor(),\n",
    "        transforms.Normalize((0.1307,),(0.3081,))\n",
    "    ]))\n",
    "test_loader = torch.utils.data.DataLoader(test_db,batch_size=batch_size,shuffle=True)\n",
    "\n",
    "print('train:',len(train_db),'test:',len(test_db))\n",
    "train_db,val_db = torch.utils.data.random_split(train_db,[50000,10000])\n",
    "print('db1:',len(train_db),'db2:',len(val_db))\n",
    "train_loader = torch.utils.data.DataLoader(train_db,batch_size=batch_size,shuffle=True)\n",
    "val_loader = torch.utils.data.DataLoader(val_db,batch_size=batch_size,shuffle=True)\n",
    "\n",
    "\n",
    "mean = 0.1307\n",
    "std = 0.3081\n",
    "\n",
    "\n",
    "    \n",
    "    \n",
    "# 网络模型　model\n",
    "class MLP(nn.Module):\n",
    "    \n",
    "    def __init__(self):\n",
    "        super(MLP, self).__init__()\n",
    "        \n",
    "        self.model = nn.Sequential(\n",
    "            nn.Linear(784,200),\n",
    "            nn.LeakyReLU(inplace=True),\n",
    "            nn.Linear(200,200),\n",
    "            nn.LeakyReLU(inplace=True),\n",
    "            nn.Linear(200,10),\n",
    "            nn.LeakyReLU(inplace=True),\n",
    "        )\n",
    "        \n",
    "    def forward(self,x):\n",
    "        # 调用__call__ 中的forward()方法\n",
    "        x = self.model(x)\n",
    "            \n",
    "        return x\n",
    "        \n",
    "# device = torch.device('cuda:0')\n",
    "# net = MLP().to(device)\n",
    "net = MLP()\n",
    "optimizer = torch.optim.SGD(net.parameters(), lr=learning_rate)\n",
    "# criteon = nn.CrossEntropyLoss().to(device)\n",
    "criteon = nn.CrossEntropyLoss()\n",
    "\n",
    "# 可视化\n",
    "viz = Visdom()\n",
    "viz.line([0.], [0.], win='train_loss', opts=dict(title='train loss'))\n",
    "viz.line([[0.0, 0.0]], [0.], win='test', opts=dict(title='test loss&acc.',\n",
    "                                                legend=['loss', 'acc.']))\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    \n",
    "    for batch_idx, (data,target) in enumerate(train_loader):\n",
    "        data = data.view(-1,28*28)\n",
    "#         data, target = data.to(device),target.cudda()\n",
    "        logits = net(data)\n",
    "        loss = criteon(logits, target)\n",
    "        \n",
    "        optimizer.zero_grad()\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        \n",
    "        # loss可视化\n",
    "        global_step += 1\n",
    "        viz.line([loss.item()],[global_step],win='train_loss',update='append')\n",
    "        \n",
    "        # log输出\n",
    "        # 100次batch训练　batch_size=200\n",
    "        if batch_idx % 100 == 0:\n",
    "            print('Train Epoch: {} [{}/{} ({:.0f}%)]\\tLoss:{:.6f}'.format(\n",
    "                epoch,batch_idx*len(data),len(train_loader.dataset),\n",
    "                100. * batch_idx / len(train_loader),loss.item()))\n",
    "\n",
    "    test_loss = 0\n",
    "    correct = 0\n",
    "    for data, target in val_loader:\n",
    "        data = data.view(-1,28*28)\n",
    "        logits = net(data)\n",
    "        test_loss += criteon(logits,target).item()\n",
    "\n",
    "        pred = logits.data.max(1)[1]\n",
    "        correct += pred.eq(target.data).sum().item()\n",
    "    test_loss /= len(val_loader.dataset)\n",
    "    print('\\nVAL set: Average Loss : {:.4f}, Accuracy: {}/{}({:.0f}%\\n)'.format(\n",
    "        test_loss, correct, len(test_loader.dataset),\n",
    "        100.*correct / len(test_loader.dataset)))\n",
    "    \n",
    "    viz.line([[test_loss, correct / len(test_loader.dataset)]],\n",
    "            [global_step], win='test', update='append')\n",
    "    img_data = data * std + mean\n",
    "    viz.images(img_data.view(-1, 1, 28, 28),nrow=6, win='x',opts={'title':'imgs'})\n",
    "    viz.text(str(pred.detach().numpy()), win='pred',opts=dict(title='pred'))\n",
    "\n",
    "        \n",
    "test_loss = 0\n",
    "correct = 0\n",
    "for data, target in test_loader:\n",
    "    data = data.view(-1,28*28)\n",
    "    logits = net(data)\n",
    "    test_loss += criteon(logits,target).item()\n",
    "\n",
    "    pred = logits.data.max(1)[1]\n",
    "    correct += pred.eq(target.data).sum().item()\n",
    "\n",
    "    \n",
    "test_loss /= len(test_loader.dataset)\n",
    "print('\\nTest set: Average Loss : {:.4f}, Accuracy: {}/{}({:.0f}%\\n)'.format(\n",
    "    test_loss, correct, len(test_loader.dataset),\n",
    "    100.*correct / len(test_loader.dataset)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 激活函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "sigmoid 0-1 容易出现梯度离散。当x值很大或者很小。\n",
    "\n",
    "Tanh -1-1  RNN常用\n",
    "\n",
    "\n",
    "ReLU R(z)=max(0,z) 梯度为1\n",
    "\n",
    "\n",
    "Leaky ReLU x<0 为斜率很小的线\n",
    "\n",
    "softplus \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visdom可视化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "安装：\n",
    "\n",
    "        pip install -i https://pypi.tuna.tsinghua.edu.cn/simple visdom\n",
    "        pip uninstall visdom\n",
    "      \n",
    "github安装：\n",
    "        https://github.com/facebookresearch/visdom\n",
    "        >pip install -e .\n",
    "        \n",
    "启动：\n",
    "        \n",
    "        python -m visdom.server\n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Setting up a new session...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[0., 0., 0.,  ..., 0., 0., 0.],\n",
      "        [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "        [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "        ...,\n",
      "        [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "        [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "        [0., 0., 0.,  ..., 0., 0., 0.]])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'x'"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import visdom\n",
    "import torch\n",
    "# 新建一个连接客户端\n",
    "# 指定env = 'test2'，默认是'main',注意在浏览器界面做环境的切换\n",
    "vis = visdom.Visdom(env='test2')\n",
    "# 绘制正弦函数\n",
    "x = torch.arange(1, 100, 0.01)\n",
    "y = torch.sin(x)\n",
    "vis.line(X=x,Y=y, win='sinx',opts={'title':'y=sin(x)'})\n",
    "# # 绘制36张图片随机的彩色图片\n",
    "# vis.images(torch.randn(36,3,64,64).numpy(),nrow=6, win='imgs',opts={'title':'imgs'})\n",
    "test_loader = torch.utils.data.DataLoader(\n",
    "    datasets.MNIST('./data',train=False,transform=transforms.Compose([\n",
    "        transforms.ToTensor()\n",
    "    ])),batch_size=batch_size,shuffle=True)\n",
    "for batch_idx,(data, target) in enumerate(test_loader):\n",
    "    data = data.view(-1,28*28)\n",
    "    if batch_idx>1:\n",
    "        print(data)\n",
    "        break\n",
    "\n",
    "vis.images(data.view(-1, 1, 28, 28), win='x')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 过拟合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**交叉验证**\n",
    "\n",
    "**Regularization**\n",
    "        \n",
    "        L2-regularization:\n",
    "```python\n",
    "    net = MLP()\n",
    "    optimizer = optim.SGD(net.parameters(),lr=learning_rate,weight_decay=0.01)\n",
    "    criteon = nn.CrossEntropyLoss()\n",
    "```\n",
    "\n",
    "        L1-regularization: (pytorch中并没有实现　自己编写代码)\n",
    "     \n",
    "```python\n",
    "    regularization_loss = 0\n",
    "    for param in model.parameters():\n",
    "        regularization_loss += torch.sum(torch.abs(param))\n",
    "    \n",
    "    classify_loss = criteon(logits,target)\n",
    "    loss = classfy_loss + 0.01*regularization_loss\n",
    "    \n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "```\n",
    "\n",
    "**动量, Adam自带动量更新。**\n",
    "```python\n",
    "optimizer = torch.optim.SGD(model.parameters(),args.lr,\n",
    "                           momentum=args.momentum,\n",
    "                           weight_decay=args.weight_decay)\n",
    "scheduler = ReduceLROnPlateau(optimizer,'min',patience=10) # 学习率衰减 patience 耐心值\n",
    "\n",
    "for epoch in xrange(args.start_epoch,args.epochs):\n",
    "    tarin(train_loader,model,,criterion,optimizer,epoch)\n",
    "    result_avg, loss_val = validate(val_loader, model,criterion,epoch)\n",
    "    scheduler.step(loss_val)　# 监听loss 是否达到饱和\n",
    "    \n",
    "\n",
    "scheduler = StepLR(optimizer,step_size=30,gamma=0.1)\n",
    "for epoch in range(100):\n",
    "    scheduler.step()\n",
    "    tran()\n",
    "    validate()\n",
    "```\n",
    "\n",
    "**early stopping**\n",
    "\n",
    "**dropout**\n",
    "\n",
    "```python\n",
    "net = torch.nn.Squential(\n",
    "    torch.nn.Linear(784,200),\n",
    "    torch.nn.Dropout(0.5)\n",
    "    torch.nn.ReLU(),\n",
    "    torch.nn.Linear(200,200),\n",
    "    torch.nn.Dropout(0.5)\n",
    "    torch.nn.ReLU(),\n",
    "    torch.nn.Linear(200,10)\n",
    ")\n",
    "\n",
    "# when test:\n",
    "for epoch in range(epochs):\n",
    "   # train\n",
    "    net.train()\n",
    "    for batch_idx,(,) in enumerate(train_loader):\n",
    "        ...\n",
    "    net.eval() # behavior between train an test\n",
    "    test_loss = 0 \n",
    "    corrent = 0\n",
    "    for data,target in test_loader:\n",
    "        ...\n",
    "```\n",
    "\n",
    "**stochastic Gradient Descent**\n",
    "\n",
    "Not single usually\n",
    "\n",
    "batch = 16,32,64,128"
   ]
  },
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   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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