03-back-propagation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 反向传播\n",
    "\n",
    "### 一个两层神经网络\n",
    "\n",
    "$$ \\hat{y} = W_2 ( W_1 \\cdot x + b_1 ) + b_2 $$\n",
    "\n",
    "[Matrix Cookbook](https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted value(Before Training): 0.0\n",
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      "Progress: 100/100 Loss: 0.0\n",
      "Predicted value(After Training): 8.0\n"
     ]
    }
   ],
   "source": [
    "x_data = [float(i) for i in range(1, 6)]\n",
    "y_data = [2 * i for i in x_data]\n",
    "\n",
    "w1 = torch.Tensor([0.0])\n",
    "w1.requires_grad = True\n",
    "\n",
    "def forward(x):\n",
    "    return x * w1\n",
    "\n",
    "def loss(x, y):\n",
    "    y_pred = forward(x)\n",
    "    return (y_pred - y) ** 2\n",
    "\n",
    "print(f\"Predicted value(Before Training): {forward(4).item()}\")\n",
    "\n",
    "for epoch in range(100):\n",
    "    for x, y in zip(x_data, y_data):\n",
    "        l = loss(x, y)\n",
    "        l.backward()\n",
    "        print(f\"\\t gradient: {w1.grad.item()} x:{x} y:{y}\")\n",
    "        w1.data -= .01 * w1.grad.data\n",
    "        w1.grad.zero_()\n",
    "    print(f\"Progress: {epoch+1}/{100} Loss: {l.item()}\")\n",
    "\n",
    "print(f\"Predicted value(After Training): {forward(4).item()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 作业\n",
    "\n",
    "预测模型使用二次模型: \n",
    "\n",
    "$$ \\hat y = \\omega_1x^2 + \\omega_2x + b $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted value(Before Training): 0.0\n",
      "\t gradient: -4.0 x:1.0 y:2.0\n",
      "\t gradient: -29.760000228881836 x:2.0 y:4.0\n",
      "\t gradient: -41.05440139770508 x:3.0 y:6.0\n",
      "\t gradient: 173.85321044921875 x:4.0 y:8.0\n",
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      "Progress: 1/100 Loss: 1242.79296875\n",
      "\t gradient: 37.61802291870117 x:1.0 y:2.0\n",
      "\t gradient: 540.006591796875 x:2.0 y:4.0\n",
      "\t gradient: 1652.2308349609375 x:3.0 y:6.0\n",
      "\t gradient: -3906.296875 x:4.0 y:8.0\n",
      "\t gradient: 42382.22265625 x:5.0 y:10.0\n",
      "Progress: 2/100 Loss: 718501.125\n",
      "\t gradient: -979.8092041015625 x:1.0 y:2.0\n",
      "\t gradient: -13397.98828125 x:2.0 y:4.0\n",
      "\t gradient: -39779.1015625 x:3.0 y:6.0\n",
      "\t gradient: 95917.1328125 x:4.0 y:8.0\n",
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      "\t gradient: 973873.875 x:3.0 y:6.0\n",
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      "Progress: 6/100 Loss: 9.236723166032691e+16\n",
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      "\t gradient: nan x:1.0 y:2.0\n",
      "\t gradient: nan x:2.0 y:4.0\n",
      "\t gradient: nan x:3.0 y:6.0\n",
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      "Progress: 70/100 Loss: nan\n",
      "\t gradient: nan x:1.0 y:2.0\n",
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      "Progress: 71/100 Loss: nan\n",
      "\t gradient: nan x:1.0 y:2.0\n",
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      "Progress: 72/100 Loss: nan\n",
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      "Progress: 82/100 Loss: nan\n",
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      "Progress: 83/100 Loss: nan\n",
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      "Progress: 84/100 Loss: nan\n",
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      "Progress: 85/100 Loss: nan\n",
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      "Progress: 86/100 Loss: nan\n",
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      "Progress: 87/100 Loss: nan\n",
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      "Progress: 88/100 Loss: nan\n",
      "\t gradient: nan x:1.0 y:2.0\n",
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      "\t gradient: nan x:4.0 y:8.0\n",
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      "Progress: 89/100 Loss: nan\n",
      "\t gradient: nan x:1.0 y:2.0\n",
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      "Progress: 90/100 Loss: nan\n",
      "\t gradient: nan x:1.0 y:2.0\n",
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      "Progress: 91/100 Loss: nan\n",
      "\t gradient: nan x:1.0 y:2.0\n",
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      "Progress: 92/100 Loss: nan\n",
      "\t gradient: nan x:1.0 y:2.0\n",
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      "Progress: 95/100 Loss: nan\n",
      "\t gradient: nan x:1.0 y:2.0\n",
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      "\t gradient: nan x:3.0 y:6.0\n",
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      "Progress: 96/100 Loss: nan\n",
      "\t gradient: nan x:1.0 y:2.0\n",
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      "\t gradient: nan x:3.0 y:6.0\n",
      "\t gradient: nan x:4.0 y:8.0\n",
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      "Progress: 97/100 Loss: nan\n",
      "\t gradient: nan x:1.0 y:2.0\n",
      "\t gradient: nan x:2.0 y:4.0\n",
      "\t gradient: nan x:3.0 y:6.0\n",
      "\t gradient: nan x:4.0 y:8.0\n",
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      "Progress: 98/100 Loss: nan\n",
      "\t gradient: nan x:1.0 y:2.0\n",
      "\t gradient: nan x:2.0 y:4.0\n",
      "\t gradient: nan x:3.0 y:6.0\n",
      "\t gradient: nan x:4.0 y:8.0\n",
      "\t gradient: nan x:5.0 y:10.0\n",
      "Progress: 99/100 Loss: nan\n",
      "\t gradient: nan x:1.0 y:2.0\n",
      "\t gradient: nan x:2.0 y:4.0\n",
      "\t gradient: nan x:3.0 y:6.0\n",
      "\t gradient: nan x:4.0 y:8.0\n",
      "\t gradient: nan x:5.0 y:10.0\n",
      "Progress: 100/100 Loss: nan\n",
      "Predicted value(After Training): nan\n"
     ]
    }
   ],
   "source": [
    "# 这个写错了\n",
    "\n",
    "x_data = [float(i) for i in range(1, 6)]\n",
    "y_data = [2 * i for i in x_data]\n",
    "\n",
    "w1 = torch.Tensor([0.0])\n",
    "w1.requires_grad = True\n",
    "w2 = torch.Tensor([0.0])\n",
    "w2.requires_grad = True\n",
    "b = torch.Tensor([0.0])\n",
    "b.requires_grad = True\n",
    "\n",
    "def forward(x):\n",
    "    return x ** 2 * w1 + x * w2 + b\n",
    "\n",
    "def loss(x, y):\n",
    "    y_pred = forward(x)\n",
    "    return (y_pred - y) ** 2\n",
    "\n",
    "print(f\"Predicted value(Before Training): {forward(4).item()}\")\n",
    "\n",
    "for epoch in range(100):\n",
    "    for x, y in zip(x_data, y_data):\n",
    "        l = loss(x, y)\n",
    "        l.backward()\n",
    "        print(f\"\\t gradient: {w1.grad.item()} x:{x} y:{y}\")\n",
    "        w1.data -= .01 * w1.grad.data\n",
    "        w1.grad.zero_()\n",
    "        w2.data -= .01 * w2.grad.data\n",
    "        w2.grad.zero_()\n",
    "        b.data -= .01 * b.grad.data\n",
    "        b.grad.zero_()\n",
    "    print(f\"Progress: {epoch+1}/{100} Loss: {l.item()}\")\n",
    "\n",
    "print(f\"Predicted value(After Training): {forward(4).item()}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted value(Before Training): 0.7660875916481018\n",
      "Progress: 1/100 Loss: 34.55890545845032\n",
      "Progress: 2/100 Loss: 32.43955912590027\n",
      "Progress: 3/100 Loss: 29.33141803741455\n",
      "Progress: 4/100 Loss: 26.848632526397704\n",
      "Progress: 5/100 Loss: 23.129837942123412\n",
      "Progress: 6/100 Loss: 20.25961079597473\n",
      "Progress: 7/100 Loss: 17.214896512031554\n",
      "Progress: 8/100 Loss: 14.091981887817383\n",
      "Progress: 9/100 Loss: 10.496461084485054\n",
      "Progress: 10/100 Loss: 7.55832233466208\n",
      "Progress: 11/100 Loss: 4.927307554380969\n",
      "Progress: 12/100 Loss: 3.0796390742063524\n",
      "Progress: 13/100 Loss: 1.8786957561969757\n",
      "Progress: 14/100 Loss: 0.7441763982176781\n",
      "Progress: 15/100 Loss: 0.3114735117182136\n",
      "Progress: 16/100 Loss: 0.33080676645040513\n",
      "Progress: 17/100 Loss: 0.3056004121084698\n",
      "Progress: 18/100 Loss: 0.3372853070497513\n",
      "Progress: 19/100 Loss: 0.33312640599906446\n",
      "Progress: 20/100 Loss: 0.30767078828066585\n",
      "Progress: 21/100 Loss: 0.27925955690407134\n",
      "Progress: 22/100 Loss: 0.26400391552597285\n",
      "Progress: 23/100 Loss: 0.2607827642932534\n",
      "Progress: 24/100 Loss: 0.24816805496811867\n",
      "Progress: 25/100 Loss: 0.24723607897758484\n",
      "Progress: 26/100 Loss: 0.24469761177897453\n",
      "Progress: 27/100 Loss: 0.23933434598147868\n",
      "Progress: 28/100 Loss: 0.23375325761735438\n",
      "Progress: 29/100 Loss: 0.22793229073286056\n",
      "Progress: 30/100 Loss: 0.22249009720981122\n",
      "Progress: 31/100 Loss: 0.22013663835823535\n",
      "Progress: 32/100 Loss: 0.21571661457419394\n",
      "Progress: 33/100 Loss: 0.21181350573897362\n",
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      "Progress: 41/100 Loss: 0.17405287735164165\n",
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      "Progress: 51/100 Loss: 0.13383123092353344\n",
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      "Progress: 58/100 Loss: 0.11119975112378597\n",
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      "Progress: 62/100 Loss: 0.09572899267077446\n",
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      "Progress: 83/100 Loss: 0.04474944719113409\n",
      "Progress: 84/100 Loss: 0.04436974385753274\n",
      "Progress: 85/100 Loss: 0.04065261939540506\n",
      "Progress: 86/100 Loss: 0.03970192642882466\n",
      "Progress: 87/100 Loss: 0.036741390079259875\n",
      "Progress: 88/100 Loss: 0.03572582388296723\n",
      "Progress: 89/100 Loss: 0.03497616739477962\n",
      "Progress: 90/100 Loss: 0.03260294198989868\n",
      "Progress: 91/100 Loss: 0.031341712549328805\n",
      "Progress: 92/100 Loss: 0.03016330488026142\n",
      "Progress: 93/100 Loss: 0.029197119968011977\n",
      "Progress: 94/100 Loss: 0.027495256857946515\n",
      "Progress: 95/100 Loss: 0.02610145010985434\n",
      "Progress: 96/100 Loss: 0.025417900690808893\n",
      "Progress: 97/100 Loss: 0.024171789712272584\n",
      "Progress: 98/100 Loss: 0.022638658888172358\n",
      "Progress: 99/100 Loss: 0.021181999100372197\n",
      "Progress: 100/100 Loss: 0.02065137675963342\n",
      "Predicted value(After Training): 7.965635299682617\n"
     ]
    }
   ],
   "source": [
    "# 导入必要的模块\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import torch.utils.data as data\n",
    "\n",
    "# 定义数据\n",
    "x_data = torch.Tensor([float(i) for i in range(1, 6)])\n",
    "y_data = torch.Tensor([2 * i for i in x_data])\n",
    "\n",
    "# 定义数据集和数据加载器\n",
    "dataset = data.TensorDataset(x_data, y_data)\n",
    "dataloader = data.DataLoader(dataset, batch_size=1, shuffle=True)\n",
    "\n",
    "# 定义模型\n",
    "model = nn.Sequential(\n",
    "    nn.Linear(1, 1), # 线性层，输入和输出都是一维的\n",
    "    nn.PReLU(), # 激活函数，可以增加模型的非线性\n",
    "    nn.Linear(1, 1) # 线性层，输入和输出都是一维的\n",
    ")\n",
    "\n",
    "# 定义损失函数\n",
    "criterion = nn.MSELoss()\n",
    "\n",
    "# 定义优化器\n",
    "optimizer = optim.Adam(model.parameters(), lr=0.01)\n",
    "\n",
    "# 定义训练轮数\n",
    "epochs = 100\n",
    "\n",
    "# 训练模型\n",
    "print(f\"Predicted value(Before Training): {model(torch.Tensor([4])).item()}\")\n",
    "for epoch in range(epochs):\n",
    "    running_loss = 0.0\n",
    "    for x, y in dataloader:\n",
    "        # 清零梯度\n",
    "        optimizer.zero_grad()\n",
    "        # 前向传播\n",
    "        y_pred = model(x)\n",
    "        # 计算损失\n",
    "        loss = criterion(y_pred, y)\n",
    "        # 反向传播\n",
    "        loss.backward()\n",
    "        # 更新参数\n",
    "        optimizer.step()\n",
    "        # 累计损失\n",
    "        running_loss += loss.item()\n",
    "    # 打印每轮的平均损失\n",
    "    print(f\"Progress: {epoch+1}/{epochs} Loss: {running_loss/len(dataloader)}\")\n",
    "print(f\"Predicted value(After Training): {model(torch.Tensor([4])).item()}\")\n"
   ]
  }
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