86-池化层-卷积神经网络.ipynb

{
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   "cell_type": "markdown",
   "id": "df5cec76-1a44-4d1b-94a5-093c3ebee1d5",
   "metadata": {},
   "source": [
    "\n",
    "* 1. 二维最大池化层和平均池化层</br>\n",
    "![image.png](attachment:bbbefdf2-760d-45e0-948c-323410b6ad27.png)</br>\n",
    "$\\begin{split}\\max(0,1,3,4)=4,\\\\\n",
    "\\max(1,2,4,5)=5,\\\\\n",
    "\\max(3,4,6,7)=7,\\\\\n",
    "\\max(4,5,7,8)=8.\\\\\\end{split}$\n",
    "* 2. 填充和步幅\n",
    "* 3. 多通道\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5c7f75e0-4f53-4138-bca6-c726e465421b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "import dltools\n",
    "\n",
    "def pool2d(X, pool_size, mode='max'):\n",
    "    p_h, p_w = pool_size\n",
    "    Y = torch.zeros((X.shape[0] - p_h + 1, X.shape[1] - p_w + 1))\n",
    "    for i in range(Y.shape[0]):\n",
    "        for j in range(Y.shape[1]):\n",
    "            if mode == 'max':\n",
    "                Y[i, j] = X[i: i + p_h, j: j + p_w].max()\n",
    "            elif mode == 'avg':\n",
    "                Y[i, j] = X[i: i + p_h, j: j + p_w].mean()\n",
    "    return Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7934ab0f-7428-466d-81aa-1fd99807cb77",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[4., 5.],\n",
       "        [7., 8.]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = torch.tensor([[0.0, 1.0, 2.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]])\n",
    "pool2d(X, (2, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ee416947-c82c-4116-8e3c-d3384d480ad1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2., 3.],\n",
       "        [5., 6.]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pool2d(X, (2, 2), 'avg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fe01ae21-7791-44de-bc7d-13481b239b4f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[[ 0.,  1.,  2.,  3.],\n",
       "          [ 4.,  5.,  6.,  7.],\n",
       "          [ 8.,  9., 10., 11.],\n",
       "          [12., 13., 14., 15.]]]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# padding and stride\n",
    "X = torch.arange(16, dtype=torch.float32).reshape((1, 1, 4, 4))\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5f68e80c-bc5a-4074-9503-d082ca412dd0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[[10.]]]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pool2d = nn.MaxPool2d(3)\n",
    "pool2d(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "36923e6a-8de8-4d3b-b74c-9b2656352227",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[[ 5.,  7.],\n",
       "          [13., 15.]]]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pool2d = nn.MaxPool2d(3, padding=1, stride=2)\n",
    "pool2d(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "60dcddb2-e408-47fb-a3bb-bb0cde94224c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[[ 5.,  7.],\n",
       "          [13., 15.]]]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# stride=(2, 3)：窗口将每次向右滑动三个元素位置，或者向下滑动两个元素位置\n",
    "# padding=(0, 1)：表示在上下两个方向填充零行0，在左右两个方向各填充一列0\n",
    "pool2d = nn.MaxPool2d((2, 3), stride=(2, 3), padding=(0, 1)) \n",
    "pool2d(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "76010bee-9b4a-40e9-901d-68814d8e6d82",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[[ 0.,  1.,  2.,  3.],\n",
       "          [ 4.,  5.,  6.,  7.],\n",
       "          [ 8.,  9., 10., 11.],\n",
       "          [12., 13., 14., 15.]],\n",
       "\n",
       "         [[ 1.,  2.,  3.,  4.],\n",
       "          [ 5.,  6.,  7.,  8.],\n",
       "          [ 9., 10., 11., 12.],\n",
       "          [13., 14., 15., 16.]]]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 多个通道\n",
    "X = torch.cat((X, X + 1), 1)\n",
    "X\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7f27d44e-7792-43ed-bc46-c32f2c35088e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[[ 5.,  7.],\n",
       "          [13., 15.]],\n",
       "\n",
       "         [[ 6.,  8.],\n",
       "          [14., 16.]]]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pool2d = nn.MaxPool2d(3, padding=1, stride=2)\n",
    "pool2d(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "87245102-02cb-43bb-ae49-663d3791526c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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