259_注意力机制.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. 注意力机制"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "# 生成数据集\n",
    "# 训练集样本数量\n",
    "n_train = 50\n",
    "# 生成训练集特征x_train，范围为[0, 5)，并进行排序\n",
    "x_train, _ = torch.sort(torch.rand(n_train) * 5)\n",
    "# 定义函数f，用于生成标签y\n",
    "def f(x):\n",
    "    return 2 * torch.sin(x) + x**0.8\n",
    "# 生成训练集标签y_train，并加上服从正态分布的噪声\n",
    "y_train = f(x_train) + torch.normal(0.0, 0.5, (n_train,))\n",
    "# 生成测试集特征x_test，范围为[0, 5)，步长为0.1\n",
    "x_test = torch.arange(0, 5, 0.1)\n",
    "# 生成测试集的真实标签y_truth\n",
    "y_truth = f(x_test)\n",
    "# 计算测试集样本数量\n",
    "n_test = len(x_test)\n",
    "n_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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   "source": [
    "# 绘制核回归结果的图像\n",
    "def plot_kernel_reg(y_hat):\n",
    "    # 绘制x_test和对应的真实标签y_truth以及预测标签y_hat的图像\n",
    "    d2l.plot(x_test, [y_truth, y_hat], 'x', 'y', legend=['Truth','Pred'],\n",
    "            xlim=[0,5], ylim=[-1,5])\n",
    "    # 绘制训练集的散点图，用圆圈表示\n",
    "    d2l.plt.plot(x_train, y_train, 'o', alpha=0.5)\n",
    "# 将y_train的均值重复n_test次作为预测标签y_hat  \n",
    "y_hat = torch.repeat_interleave(y_train.mean(), n_test)\n",
    "# 调用plot_kernel_reg函数，绘制核回归结果的图像\n",
    "plot_kernel_reg(y_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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   "source": [
    "# 非参数注意力汇聚\n",
    "# 将测试集特征x_test重复n_train次并重新reshape为二维矩阵\n",
    "X_repeat = x_test.repeat_interleave(n_train).reshape((-1, n_train))\n",
    "# 计算注意力权重，通过对特征差值的平方取负并除以2，再进行softmax归一化\n",
    "attention_weights = nn.functional.softmax(-(X_repeat - x_train)**2 / 2, dim=1)  \n",
    "# 注意力权重与训练集标签y_train进行矩阵乘法得到预测标签y_hat\n",
    "y_hat = torch.matmul(attention_weights, y_train)\n",
    "# 调用plot_kernel_reg函数，绘制非参数注意力汇聚的核回归结果图像\n",
    "plot_kernel_reg(y_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
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     },
     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
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   ],
   "source": [
    "# 注意力权重\n",
    "# 可视化注意力权重\n",
    "d2l.show_heatmaps(attention_weights.unsqueeze(0).unsqueeze(0),\n",
    "                xlabel='Sorted training inputs', ylabel='Sorted test inputs')   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 1, 6])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 带参数注意力汇聚\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",
    "# 创建形状为(2,1,4)的张量X，元素全为1\n",
    "X = torch.ones((2,1,4))\n",
    "# 创建形状为(2,4,6)的张量Y，元素全为1\n",
    "Y = torch.ones((2,4,6))\n",
    "# 执行批量矩阵乘法，并输出结果的形状\n",
    "torch.bmm(X, Y).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[ 4.5000]],\n",
       "\n",
       "        [[14.5000]]])"
      ]
     },
     "execution_count": 7,
     "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",
    "# 创建形状为(2,10)的权重张量，每个权重为0.1\n",
    "weights = torch.ones((2,10)) * 0.1\n",
    "# 创建形状为(2,10)的值张量，从0到19的连续数值\n",
    "values = torch.arange(20.0).reshape((2,10))\n",
    "# 执行小批量矩阵乘法，计算加权平均值\n",
    "torch.bmm(weights.unsqueeze(1), values.unsqueeze(-1))"
   ]
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  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 带参数的注意力汇聚\n",
    "class NWKernelRegression(nn.Module):\n",
    "    def __init__(self, **kwargs):\n",
    "        super().__init__(**kwargs)\n",
    "        # 创建形状为(1,)的参数张量w，用于调整注意力权重\n",
    "        self.w = nn.Parameter(torch.rand((1,),requires_grad=True))  \n",
    "        \n",
    "    def forward(self, queries, keys, values):\n",
    "        # 重复queries并调整形状，使其与keys具有相同的列数\n",
    "        queries = queries.repeat_interleave(keys.shape[1]).reshape(-1,keys.shape[1])   \n",
    "        # 计算注意力权重，通过调整参数w对注意力进行调节\n",
    "        self.attention_weights = nn.functional.softmax(-((queries - keys) * self.w)**2/2,dim=1)     \n",
    "        # 执行带参数的注意力汇聚，并返回最终结果的形状调整\n",
    "        return torch.bmm(self.attention_weights.unsqueeze(1),values.unsqueeze(-1)).reshape(-1)   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 将训练数据集转换为键和值\n",
    "# 将x_train在行维度上重复n_train次，形成一个矩阵X_tile\n",
    "X_tile = x_train.repeat((n_train, 1))\n",
    "# 将y_train在行维度上重复n_train次，形成一个矩阵Y_tile\n",
    "Y_tile = y_train.repeat((n_train, 1))\n",
    "# 通过掩码操作，从X_tile中排除对角线元素，得到键矩阵keys\n",
    "keys = X_tile[(1 - torch.eye(n_train)).type(torch.bool)].reshape((n_train,-1))  \n",
    "# 通过掩码操作，从Y_tile中排除对角线元素，得到值矩阵values\n",
    "values = Y_tile[(1 - torch.eye(n_train)).type(torch.bool)].reshape(n_train, -1) "
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   "source": [
    "# 训练带参数的注意力汇聚模型\n",
    "# 创建带参数的注意力汇聚模型\n",
    "net = NWKernelRegression()\n",
    "# 创建均方误差损失函数，用于计算损失\n",
    "loss = nn.MSELoss(reduction='none')\n",
    "# 创建随机梯度下降优化器，用于参数更新\n",
    "trainer = torch.optim.SGD(net.parameters(), lr=0.5)\n",
    "# 创建动画绘制器，用于绘制损失曲线\n",
    "animator = d2l.Animator(xlabel='epoch',ylabel='loss',xlim=[1,5])\n",
    "\n",
    "# 遍历5次\n",
    "for epoch in range(5):\n",
    "    # 清零梯度\n",
    "    trainer.zero_grad()\n",
    "    # 计算损失\n",
    "    l = loss(net(x_train, keys, values), y_train) / 2\n",
    "    # 反向传播，计算梯度\n",
    "    l.sum().backward()\n",
    "    # 更新参数\n",
    "    trainer.step()\n",
    "    # 打印当前的损失\n",
    "    print(f'epoch {epoch+1}, loss {float(l.sum()):.6f}')\n",
    "    # 绘制损失曲线\n",
    "    animator.add(epoch+1, float(l.sum()))"
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  },
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   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
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      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
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     "metadata": {
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     "output_type": "display_data"
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   ],
   "source": [
    "# 预测结果绘制\n",
    "# 将训练数据集的输入在行维度上重复n_test次，形成键矩阵keys\n",
    "keys = x_train.repeat((n_test, 1))\n",
    "# 将训练数据集的输出在行维度上重复n_test次，形成值矩阵values\n",
    "values = y_train.repeat((n_test, 1))\n",
    "# 使用训练好的模型进行预测，得到预测结果y_hat\n",
    "y_hat = net(x_test, keys, values).unsqueeze(1).detach()\n",
    "# 绘制预测结果\n",
    "plot_kernel_reg(y_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 180x180 with 2 Axes>"
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     },
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     "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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