1992 lines
73 KiB
Plaintext
1992 lines
73 KiB
Plaintext
{
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"metadata": {
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"origin_pos": 0
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},
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"source": [
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"# 长短期记忆网络（LSTM）\n",
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":label:`sec_lstm`\n",
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"\n",
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"长期以来，隐变量模型存在着长期信息保存和短期输入缺失的问题。\n",
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"解决这一问题的最早方法之一是长短期存储器（long short-term memory，LSTM）\n",
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" :cite:`Hochreiter.Schmidhuber.1997`。\n",
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"它有许多与门控循环单元（ :numref:`sec_gru`）一样的属性。\n",
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"有趣的是，长短期记忆网络的设计比门控循环单元稍微复杂一些，\n",
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"却比门控循环单元早诞生了近20年。\n",
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"\n",
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"## 门控记忆元\n",
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"\n",
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"可以说，长短期记忆网络的设计灵感来自于计算机的逻辑门。\n",
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"长短期记忆网络引入了*记忆元*（memory cell），或简称为*单元*（cell）。\n",
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"有些文献认为记忆元是隐状态的一种特殊类型，\n",
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"它们与隐状态具有相同的形状，其设计目的是用于记录附加的信息。\n",
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"为了控制记忆元，我们需要许多门。\n",
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"其中一个门用来从单元中输出条目，我们将其称为*输出门*（output gate）。\n",
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"另外一个门用来决定何时将数据读入单元，我们将其称为*输入门*（input gate）。\n",
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"我们还需要一种机制来重置单元的内容，由*遗忘门*（forget gate）来管理，\n",
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"这种设计的动机与门控循环单元相同，\n",
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"能够通过专用机制决定什么时候记忆或忽略隐状态中的输入。\n",
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"让我们看看这在实践中是如何运作的。\n",
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"\n",
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"### 输入门、忘记门和输出门\n",
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"\n",
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"就如在门控循环单元中一样，\n",
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"当前时间步的输入和前一个时间步的隐状态\n",
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"作为数据送入长短期记忆网络的门中，\n",
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"如 :numref:`lstm_0`所示。\n",
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"它们由三个具有sigmoid激活函数的全连接层处理，\n",
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"以计算输入门、遗忘门和输出门的值。\n",
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"因此，这三个门的值都在$(0, 1)$的范围内。\n",
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"\n",
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"\n",
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":label:`lstm_0`\n",
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"\n",
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"我们来细化一下长短期记忆网络的数学表达。\n",
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"假设有$h$个隐藏单元，批量大小为$n$，输入数为$d$。\n",
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"因此，输入为$\\mathbf{X}_t \\in \\mathbb{R}^{n \\times d}$，\n",
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"前一时间步的隐状态为$\\mathbf{H}_{t-1} \\in \\mathbb{R}^{n \\times h}$。\n",
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"相应地，时间步$t$的门被定义如下：\n",
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"输入门是$\\mathbf{I}_t \\in \\mathbb{R}^{n \\times h}$，\n",
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"遗忘门是$\\mathbf{F}_t \\in \\mathbb{R}^{n \\times h}$，\n",
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"输出门是$\\mathbf{O}_t \\in \\mathbb{R}^{n \\times h}$。\n",
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"它们的计算方法如下：\n",
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"\n",
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"$$\n",
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"\\begin{aligned}\n",
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"\\mathbf{I}_t &= \\sigma(\\mathbf{X}_t \\mathbf{W}_{xi} + \\mathbf{H}_{t-1} \\mathbf{W}_{hi} + \\mathbf{b}_i),\\\\\n",
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"\\mathbf{F}_t &= \\sigma(\\mathbf{X}_t \\mathbf{W}_{xf} + \\mathbf{H}_{t-1} \\mathbf{W}_{hf} + \\mathbf{b}_f),\\\\\n",
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"\\mathbf{O}_t &= \\sigma(\\mathbf{X}_t \\mathbf{W}_{xo} + \\mathbf{H}_{t-1} \\mathbf{W}_{ho} + \\mathbf{b}_o),\n",
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"\\end{aligned}\n",
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"$$\n",
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"\n",
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"其中$\\mathbf{W}_{xi}, \\mathbf{W}_{xf}, \\mathbf{W}_{xo} \\in \\mathbb{R}^{d \\times h}$\n",
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"和$\\mathbf{W}_{hi}, \\mathbf{W}_{hf}, \\mathbf{W}_{ho} \\in \\mathbb{R}^{h \\times h}$是权重参数，\n",
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"$\\mathbf{b}_i, \\mathbf{b}_f, \\mathbf{b}_o \\in \\mathbb{R}^{1 \\times h}$是偏置参数。\n",
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"\n",
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"### 候选记忆元\n",
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"\n",
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"由于还没有指定各种门的操作，所以先介绍*候选记忆元*（candidate memory cell）\n",
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"$\\tilde{\\mathbf{C}}_t \\in \\mathbb{R}^{n \\times h}$。\n",
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"它的计算与上面描述的三个门的计算类似，\n",
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"但是使用$\\tanh$函数作为激活函数，函数的值范围为$(-1, 1)$。\n",
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"下面导出在时间步$t$处的方程：\n",
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"\n",
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"$$\\tilde{\\mathbf{C}}_t = \\text{tanh}(\\mathbf{X}_t \\mathbf{W}_{xc} + \\mathbf{H}_{t-1} \\mathbf{W}_{hc} + \\mathbf{b}_c),$$\n",
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"\n",
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"其中$\\mathbf{W}_{xc} \\in \\mathbb{R}^{d \\times h}$和\n",
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"$\\mathbf{W}_{hc} \\in \\mathbb{R}^{h \\times h}$是权重参数，\n",
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"$\\mathbf{b}_c \\in \\mathbb{R}^{1 \\times h}$是偏置参数。\n",
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"\n",
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"候选记忆元的如 :numref:`lstm_1`所示。\n",
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"\n",
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"\n",
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":label:`lstm_1`\n",
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"\n",
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"### 记忆元\n",
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"\n",
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"在门控循环单元中，有一种机制来控制输入和遗忘（或跳过）。\n",
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"类似地，在长短期记忆网络中，也有两个门用于这样的目的：\n",
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"输入门$\\mathbf{I}_t$控制采用多少来自$\\tilde{\\mathbf{C}}_t$的新数据，\n",
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"而遗忘门$\\mathbf{F}_t$控制保留多少过去的\n",
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"记忆元$\\mathbf{C}_{t-1} \\in \\mathbb{R}^{n \\times h}$的内容。\n",
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"使用按元素乘法，得出：\n",
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"\n",
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"$$\\mathbf{C}_t = \\mathbf{F}_t \\odot \\mathbf{C}_{t-1} + \\mathbf{I}_t \\odot \\tilde{\\mathbf{C}}_t.$$\n",
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"\n",
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"如果遗忘门始终为$1$且输入门始终为$0$，\n",
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"则过去的记忆元$\\mathbf{C}_{t-1}$\n",
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"将随时间被保存并传递到当前时间步。\n",
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"引入这种设计是为了缓解梯度消失问题，\n",
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"并更好地捕获序列中的长距离依赖关系。\n",
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"\n",
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"这样我们就得到了计算记忆元的流程图，如 :numref:`lstm_2`。\n",
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"\n",
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"\n",
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"\n",
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":label:`lstm_2`\n",
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"\n",
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"### 隐状态\n",
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"\n",
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"最后，我们需要定义如何计算隐状态\n",
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"$\\mathbf{H}_t \\in \\mathbb{R}^{n \\times h}$，\n",
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"这就是输出门发挥作用的地方。\n",
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"在长短期记忆网络中，它仅仅是记忆元的$\\tanh$的门控版本。\n",
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"这就确保了$\\mathbf{H}_t$的值始终在区间$(-1, 1)$内：\n",
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"\n",
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"$$\\mathbf{H}_t = \\mathbf{O}_t \\odot \\tanh(\\mathbf{C}_t).$$\n",
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"\n",
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"只要输出门接近$1$，我们就能够有效地将所有记忆信息传递给预测部分，\n",
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"而对于输出门接近$0$，我们只保留记忆元内的所有信息，而不需要更新隐状态。\n",
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"\n",
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" :numref:`lstm_3`提供了数据流的图形化演示。\n",
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"\n",
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"\n",
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":label:`lstm_3`\n",
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"\n",
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"## 从零开始实现\n",
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"\n",
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"现在，我们从零开始实现长短期记忆网络。\n",
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"与 :numref:`sec_rnn_scratch`中的实验相同，\n",
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"我们首先加载时光机器数据集。\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "96a7231c",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T07:24:18.324326Z",
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"iopub.status.busy": "2023-08-18T07:24:18.323673Z",
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"iopub.status.idle": "2023-08-18T07:24:21.607373Z",
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"shell.execute_reply": "2023-08-18T07:24:21.606483Z"
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},
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"origin_pos": 2,
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"tab": [
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"pytorch"
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]
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},
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"outputs": [],
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"source": [
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"import torch\n",
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"from torch import nn\n",
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"from d2l import torch as d2l\n",
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"\n",
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"batch_size, num_steps = 32, 35\n",
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"train_iter, vocab = d2l.load_data_time_machine(batch_size, num_steps)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "3ef97237",
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"metadata": {
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"origin_pos": 5
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},
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"source": [
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"### [**初始化模型参数**]\n",
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"\n",
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"接下来，我们需要定义和初始化模型参数。\n",
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"如前所述，超参数`num_hiddens`定义隐藏单元的数量。\n",
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"我们按照标准差$0.01$的高斯分布初始化权重，并将偏置项设为$0$。\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "2d90745d",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T07:24:21.612618Z",
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"shell.execute_reply": "2023-08-18T07:24:21.618267Z"
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},
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"origin_pos": 7,
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"tab": [
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"pytorch"
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]
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},
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"outputs": [],
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"source": [
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"def get_lstm_params(vocab_size, num_hiddens, device):\n",
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" num_inputs = num_outputs = vocab_size\n",
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"\n",
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" def normal(shape):\n",
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" return torch.randn(size=shape, device=device)*0.01\n",
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"\n",
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" def three():\n",
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" return (normal((num_inputs, num_hiddens)),\n",
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" normal((num_hiddens, num_hiddens)),\n",
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" torch.zeros(num_hiddens, device=device))\n",
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"\n",
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" W_xi, W_hi, b_i = three() # 输入门参数\n",
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" W_xf, W_hf, b_f = three() # 遗忘门参数\n",
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" W_xo, W_ho, b_o = three() # 输出门参数\n",
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" W_xc, W_hc, b_c = three() # 候选记忆元参数\n",
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" # 输出层参数\n",
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" W_hq = normal((num_hiddens, num_outputs))\n",
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" b_q = torch.zeros(num_outputs, device=device)\n",
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" # 附加梯度\n",
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" params = [W_xi, W_hi, b_i, W_xf, W_hf, b_f, W_xo, W_ho, b_o, W_xc, W_hc,\n",
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" b_c, W_hq, b_q]\n",
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" for param in params:\n",
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" param.requires_grad_(True)\n",
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" return params"
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]
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},
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{
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"cell_type": "markdown",
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"id": "57aecd87",
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"metadata": {
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"origin_pos": 10
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},
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"source": [
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"### 定义模型\n",
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"\n",
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"在[**初始化函数**]中，\n",
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"长短期记忆网络的隐状态需要返回一个*额外*的记忆元，\n",
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"单元的值为0，形状为（批量大小，隐藏单元数）。\n",
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"因此，我们得到以下的状态初始化。\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "beeae3b9",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T07:24:21.623788Z",
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"iopub.status.busy": "2023-08-18T07:24:21.623183Z",
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"iopub.status.idle": "2023-08-18T07:24:21.628423Z",
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"shell.execute_reply": "2023-08-18T07:24:21.627603Z"
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},
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"origin_pos": 12,
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"tab": [
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"pytorch"
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]
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},
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"outputs": [],
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"source": [
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"def init_lstm_state(batch_size, num_hiddens, device):\n",
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" return (torch.zeros((batch_size, num_hiddens), device=device),\n",
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" torch.zeros((batch_size, num_hiddens), device=device))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "9c45563d",
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"metadata": {
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"origin_pos": 15
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},
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"source": [
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"[**实际模型**]的定义与我们前面讨论的一样：\n",
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"提供三个门和一个额外的记忆元。\n",
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"请注意，只有隐状态才会传递到输出层，\n",
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"而记忆元$\\mathbf{C}_t$不直接参与输出计算。\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"id": "50de4e9c",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T07:24:21.632468Z",
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"iopub.status.busy": "2023-08-18T07:24:21.631955Z",
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"iopub.status.idle": "2023-08-18T07:24:21.638292Z",
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"shell.execute_reply": "2023-08-18T07:24:21.637498Z"
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},
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"origin_pos": 17,
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"tab": [
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"pytorch"
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]
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},
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"outputs": [],
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"source": [
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"def lstm(inputs, state, params):\n",
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" [W_xi, W_hi, b_i, W_xf, W_hf, b_f, W_xo, W_ho, b_o, W_xc, W_hc, b_c,\n",
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" W_hq, b_q] = params\n",
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" (H, C) = state\n",
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" outputs = []\n",
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" for X in inputs:\n",
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" I = torch.sigmoid((X @ W_xi) + (H @ W_hi) + b_i)\n",
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" F = torch.sigmoid((X @ W_xf) + (H @ W_hf) + b_f)\n",
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" O = torch.sigmoid((X @ W_xo) + (H @ W_ho) + b_o)\n",
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" C_tilda = torch.tanh((X @ W_xc) + (H @ W_hc) + b_c)\n",
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" C = F * C + I * C_tilda\n",
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" H = O * torch.tanh(C)\n",
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" Y = (H @ W_hq) + b_q\n",
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" outputs.append(Y)\n",
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" return torch.cat(outputs, dim=0), (H, C)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "c36361aa",
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"metadata": {
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"origin_pos": 20
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},
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"source": [
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"### [**训练**]和预测\n",
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"\n",
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"让我们通过实例化 :numref:`sec_rnn_scratch`中\n",
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"引入的`RNNModelScratch`类来训练一个长短期记忆网络，\n",
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"就如我们在 :numref:`sec_gru`中所做的一样。\n"
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]
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},
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{
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"cell_type": "code",
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||
"execution_count": 5,
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||
"id": "e2025d7a",
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"metadata": {
|
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"execution": {
|
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"iopub.execute_input": "2023-08-18T07:24:21.642387Z",
|
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"iopub.status.busy": "2023-08-18T07:24:21.641860Z",
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||
"iopub.status.idle": "2023-08-18T07:28:54.778673Z",
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||
"shell.execute_reply": "2023-08-18T07:28:54.777826Z"
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||
},
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||
"origin_pos": 21,
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"tab": [
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"pytorch"
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]
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"perplexity 1.3, 17736.0 tokens/sec on cuda:0\n",
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"time traveller for so it will leong go it we melenot ir cove i s\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"traveller care be can so i ngrecpely as along the time dime\n"
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]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/svg+xml": [
|
||
"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
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"vocab_size, num_hiddens, device = len(vocab), 256, d2l.try_gpu()\n",
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"num_epochs, lr = 500, 1\n",
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"model = d2l.RNNModelScratch(len(vocab), num_hiddens, device, get_lstm_params,\n",
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||
" init_lstm_state, lstm)\n",
|
||
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"## [**简洁实现**]\n",
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"\n",
|
||
"使用高级API，我们可以直接实例化`LSTM`模型。\n",
|
||
"高级API封装了前文介绍的所有配置细节。\n",
|
||
"这段代码的运行速度要快得多，\n",
|
||
"因为它使用的是编译好的运算符而不是Python来处理之前阐述的许多细节。\n"
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"perplexity 1.1, 234815.0 tokens/sec on cuda:0\n",
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"num_inputs = vocab_size\n",
|
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"lstm_layer = nn.LSTM(num_inputs, num_hiddens)\n",
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"model = d2l.RNNModel(lstm_layer, len(vocab))\n",
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"source": [
|
||
"长短期记忆网络是典型的具有重要状态控制的隐变量自回归模型。\n",
|
||
"多年来已经提出了其许多变体，例如，多层、残差连接、不同类型的正则化。\n",
|
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"然而，由于序列的长距离依赖性，训练长短期记忆网络\n",
|
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"和其他序列模型（例如门控循环单元）的成本是相当高的。\n",
|
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"在后面的内容中，我们将讲述更高级的替代模型，如Transformer。\n",
|
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"\n",
|
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"## 小结\n",
|
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"\n",
|
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"* 长短期记忆网络有三种类型的门：输入门、遗忘门和输出门。\n",
|
||
"* 长短期记忆网络的隐藏层输出包括“隐状态”和“记忆元”。只有隐状态会传递到输出层，而记忆元完全属于内部信息。\n",
|
||
"* 长短期记忆网络可以缓解梯度消失和梯度爆炸。\n",
|
||
"\n",
|
||
"\n",
|
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"## 练习\n",
|
||
"\n",
|
||
"1. 调整和分析超参数对运行时间、困惑度和输出顺序的影响。\n",
|
||
"1. 如何更改模型以生成适当的单词，而不是字符序列？\n",
|
||
"1. 在给定隐藏层维度的情况下，比较门控循环单元、长短期记忆网络和常规循环神经网络的计算成本。要特别注意训练和推断成本。\n",
|
||
"1. 既然候选记忆元通过使用$\\tanh$函数来确保值范围在$(-1,1)$之间，那么为什么隐状态需要再次使用$\\tanh$函数来确保输出值范围在$(-1,1)$之间呢？\n",
|
||
"1. 实现一个能够基于时间序列进行预测而不是基于字符序列进行预测的长短期记忆网络模型。\n"
|
||
]
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"id": "416f6654",
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"origin_pos": 31,
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"tab": [
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"pytorch"
|
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]
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},
|
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"source": [
|
||
"[Discussions](https://discuss.d2l.ai/t/2768)\n"
|
||
]
|
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}
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],
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