84_注意力机制.ipynb

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   "source": [
    "# 1. 注意力机制\n",
    "### 注意力汇聚：Nadaraya-Watson核回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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     "execution_count": 5,
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   "source": [
    "# 生成数据集\n",
    "\n",
    "n_train = 50\n",
    "\n",
    "\n",
    "# 给出的真实函数\n",
    "def f(x):\n",
    "    return 2 * torch.sin(x) + x**0.8\n",
    "\n",
    "# torch.sort解析：https://hxhen.com/archives/226\n",
    "# 默认按照dim=1按行排序，默认descending=False从小到大排序\n",
    "x_train, _ = torch.sort(torch.rand(n_train) * 5)  # 生成50个随机的[0, 5)之间的数字，并升序排序，作为train数据\n",
    "y_train = f(x_train) + torch.normal(0.0, 0.5, (n_train,))  # 训练数据上面加上噪音\n",
    "\n",
    "x_test = torch.arange(0, 5, 0.1)  # 生成连续数组作为test数据\n",
    "y_truth = f(x_test)\n",
    "\n",
    "n_test = len(x_test)\n",
    "n_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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    "def plot_kernel_reg(y_hat):\n",
    "    d2l.plot(x_test, [y_truth, y_hat], 'x', 'y', legend=['Truth','Pred'],\n",
    "             xlim=[0,5], ylim=[-1,5])\n",
    "    \n",
    "    d2l.plt.plot(x_train, y_train, 'o', alpha=0.5)\n",
    "\n",
    "# 最简单的预测：直接求平均y_train.mean()\n",
    "# 所以画出来是一条紫色的虚线\n",
    "# ps：repeat_interleave函数解析：https://blog.csdn.net/weixin_45261707/article/details/119187799\n",
    "# 所以这里就是将这份平均值复制了50遍，作为最后的输出，所以才是一条水平线\n",
    "y_hat = torch.repeat_interleave(y_train.mean(), n_test)\n",
    "plot_kernel_reg(y_hat)\n",
    "\n",
    "\n",
    "# 黄色的点是随机的那些x_train和y_train的点们\n",
    "# 蓝色的线是y_truth画出的线\n",
    "# 紫色的线上y_hat（预测值）画出的线"
   ]
  },
  {
   "cell_type": "code",
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     "name": "stdout",
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      "torch.Size([50])\n",
      "torch.Size([50])\n",
      "torch.Size([50, 50])\n",
      "torch.Size([50, 50])\n",
      "torch.Size([50])\n",
      "torch.Size([50])\n"
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   "source": [
    "# 非参数注意力汇聚（原翻译：非参数注意力池化，并不好理解）\n",
    "\n",
    "# 此时X_repeat的大小变成了n_test * n_train\n",
    "# 也就是把x_test重复了50遍的结果\n",
    "X_repeat = x_test.repeat_interleave(n_train).reshape((-1, n_train))\n",
    "print(x_train.shape)\n",
    "print(x_test.shape)\n",
    "print(X_repeat.shape)\n",
    "\n",
    "# 使用Nadaraya-Watson核回归方法 + 高斯核函数来获得注意力权重\n",
    "# nn.functional.softmax解析：https://www.cnblogs.com/wanghui-garcia/p/10675588.html\n",
    "# 另一个解析为：https://blog.csdn.net/Will_Ye/article/details/104994504\n",
    "# 相当于给更近的点以更大的权重\n",
    "attention_weights = nn.functional.softmax(-(X_repeat - x_train)**2 / 2, dim=1)\n",
    "print(attention_weights.shape)\n",
    "\n",
    "# 相当于预测x_test中的每个点时，都看到了x_train中所有的50个点；但是看到的每个点的权重不同，近的点会有更高的权重\n",
    "y_hat = torch.matmul(attention_weights, y_train)\n",
    "print(y_train.shape)\n",
    "print(y_hat.shape)\n",
    "\n",
    "plot_kernel_reg(y_hat)"
   ]
  },
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   "execution_count": 14,
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   "source": [
    "# 注意力权重\n",
    "\n",
    "# 这个图是逐行逐行看的\n",
    "# attention_weights是50*50，\n",
    "# 也即对于x_test中的每个点，画出他看到的x_train中所有的50个点的不同点的权重值\n",
    "d2l.show_heatmaps(attention_weights.unsqueeze(0).unsqueeze(0),\n",
    "                  xlabel='Sorted training inputs', ylabel='Sorted test inputs')   "
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  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 带参数注意力汇聚\n",
    "\n",
    "# 先介绍torch.bmm乘法（带batch的矩阵乘法）\n",
    "# 假定两个张量的形状分别是(n,a,b)和(n,b,c)，它们的批量矩阵乘法输出的形状为(n.a,c)  \n",
    "X = torch.ones((2,1,4))\n",
    "Y = torch.ones((2,4,6))\n",
    "torch.bmm(X, Y).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[ 4.5000]],\n",
       "\n",
       "        [[14.5000]]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 使用小批量矩阵乘法来计算小批量数据中的加权平均值\n",
    "\n",
    "weights = torch.ones((2,10)) * 0.1\n",
    "values = torch.arange(20.0).reshape((2,10))\n",
    "torch.bmm(weights.unsqueeze(1), values.unsqueeze(-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 带参数的注意力汇聚\n",
    "# 就是在非参数的基础上，再加一个w参数进来\n",
    "class NWKernelRegression(nn.Module):\n",
    "    def __init__(self, **kwargs):\n",
    "        super().__init__(**kwargs)\n",
    "        self.w = nn.Parameter(torch.rand((1,),requires_grad=True))  \n",
    "        \n",
    "    def forward(self, queries, keys, values):\n",
    "        queries = queries.repeat_interleave(keys.shape[1]).reshape(-1,keys.shape[1])   \n",
    "        self.attention_weights = nn.functional.softmax(-((queries - keys) * self.w)**2/2,dim=1)     \n",
    "        return torch.bmm(self.attention_weights.unsqueeze(1),values.unsqueeze(-1)).reshape(-1)   "
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  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 将训练数据集转换为键和值\n",
    "X_tile = x_train.repeat((n_train, 1))\n",
    "Y_tile = y_train.repeat((n_train, 1))\n",
    "keys = X_tile[(1 - torch.eye(n_train)).type(torch.bool)].reshape((n_train,-1))  \n",
    "values = Y_tile[(1 - torch.eye(n_train)).type(torch.bool)].reshape(n_train, -1) "
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   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
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   "source": [
    "# 训练带参数的注意力汇聚模型\n",
    "net = NWKernelRegression()\n",
    "loss = nn.MSELoss(reduction='none')\n",
    "trainer = torch.optim.SGD(net.parameters(), lr=0.5)\n",
    "animator = d2l.Animator(xlabel='epoch',ylabel='loss',xlim=[1,5])\n",
    "\n",
    "for epoch in range(5):\n",
    "    trainer.zero_grad()\n",
    "    l = loss(net(x_train, keys, values), y_train) / 2\n",
    "    l.sum().backward()\n",
    "    trainer.step()\n",
    "    print(f'epoch {epoch+1}, loss {float(l.sum()):.6f}')\n",
    "    animator.add(epoch+1, float(l.sum()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
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   "source": [
    "# 预测结果绘制\n",
    "keys = x_train.repeat((n_test, 1))\n",
    "values = y_train.repeat((n_test, 1))\n",
    "y_hat = net(x_test, keys, values).unsqueeze(1).detach()\n",
    "plot_kernel_reg(y_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 250x250 with 2 Axes>"
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     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "# 曲线在注意力权重较大的区域变得更不平滑\n",
    "d2l.show_heatmaps(net.attention_weights.unsqueeze(0).unsqueeze(0),\n",
    "                 xlabel='Sorted training inputs', ylabel='Sorted testing inputs')   "
   ]
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   "source": []
  }
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