6290 lines
233 KiB
Plaintext
6290 lines
233 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "8d462bf4",
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"metadata": {
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"origin_pos": 1
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},
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"source": [
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"# Sequence-to-Sequence Learning for Machine Translation\n",
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":label:`sec_seq2seq`\n",
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"\n",
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"In so-called sequence-to-sequence problems such as machine translation\n",
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"(as discussed in :numref:`sec_machine_translation`),\n",
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"where inputs and outputs each consist \n",
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"of variable-length unaligned sequences,\n",
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"we generally rely on encoder--decoder architectures\n",
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"(:numref:`sec_encoder-decoder`).\n",
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"In this section,\n",
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"we will demonstrate the application \n",
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"of an encoder--decoder architecture,\n",
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"where both the encoder and decoder \n",
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"are implemented as RNNs,\n",
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"to the task of machine translation\n",
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":cite:`Sutskever.Vinyals.Le.2014,Cho.Van-Merrienboer.Gulcehre.ea.2014`.\n",
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"\n",
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"Here, the encoder RNN will take a variable-length sequence as input \n",
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"and transform it into a fixed-shape hidden state.\n",
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"Later, in :numref:`chap_attention-and-transformers`,\n",
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"we will introduce attention mechanisms, \n",
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"which allow us to access encoded inputs\n",
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"without having to compress the entire input\n",
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"into a single fixed-length representation.\n",
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"\n",
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"Then to generate the output sequence, \n",
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"one token at a time,\n",
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"the decoder model, \n",
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"consisting of a separate RNN,\n",
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"will predict each successive target token\n",
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"given both the input sequence\n",
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"and the preceding tokens in the output.\n",
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"During training, the decoder will typically\n",
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"be conditioned upon the preceding tokens\n",
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"in the official \"ground truth\" label. \n",
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"However, at test time, we will want to condition\n",
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"each output of the decoder on the tokens already predicted. \n",
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"Note that if we ignore the encoder,\n",
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"the decoder in a sequence-to-sequence architecture \n",
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"behaves just like a normal language model.\n",
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":numref:`fig_seq2seq` illustrates\n",
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"how to use two RNNs\n",
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"for sequence-to-sequence learning\n",
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"in machine translation.\n",
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"\n",
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"\n",
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"\n",
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":label:`fig_seq2seq`\n",
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"\n",
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"In :numref:`fig_seq2seq`,\n",
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"the special \"<eos>\" token\n",
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"marks the end of the sequence.\n",
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"Our model can stop making predictions\n",
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"once this token is generated.\n",
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"At the initial time step of the RNN decoder,\n",
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"there are two special design decisions to be aware of:\n",
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"First, we begin every input with a special \n",
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"beginning-of-sequence \"<bos>\" token.\n",
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"Second, we may feed\n",
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"the final hidden state of the encoder\n",
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"into the decoder\n",
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"at every single decoding time step :cite:`Cho.Van-Merrienboer.Gulcehre.ea.2014`.\n",
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"In some other designs,\n",
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"such as that of :citet:`Sutskever.Vinyals.Le.2014`,\n",
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"the final hidden state of the RNN encoder\n",
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"is used\n",
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"to initiate the hidden state of the decoder\n",
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"only at the first decoding step.\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": "d30d0899",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T19:55:28.840265Z",
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"iopub.status.busy": "2023-08-18T19:55:28.839686Z",
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"iopub.status.idle": "2023-08-18T19:55:32.081579Z",
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"shell.execute_reply": "2023-08-18T19:55:32.080287Z"
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},
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"origin_pos": 3,
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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 collections\n",
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"import math\n",
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"import torch\n",
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"from torch import nn\n",
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"from torch.nn import functional as F\n",
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"from d2l import torch as d2l"
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]
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},
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{
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"cell_type": "markdown",
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"id": "50066a7a",
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"metadata": {
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"origin_pos": 6
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},
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"source": [
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"## Teacher Forcing\n",
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"\n",
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"While running the encoder on the input sequence\n",
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"is relatively straightforward,\n",
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"handling the input and output \n",
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"of the decoder requires more care. \n",
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"The most common approach is sometimes called *teacher forcing*.\n",
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"Here, the original target sequence (token labels)\n",
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"is fed into the decoder as input.\n",
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"More concretely,\n",
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"the special beginning-of-sequence token\n",
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"and the original target sequence,\n",
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"excluding the final token,\n",
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"are concatenated as input to the decoder,\n",
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"while the decoder output (labels for training) is\n",
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"the original target sequence,\n",
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"shifted by one token:\n",
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"\"<bos>\", \"Ils\", \"regardent\", \".\" $\\rightarrow$\n",
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"\"Ils\", \"regardent\", \".\", \"<eos>\" (:numref:`fig_seq2seq`).\n",
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"\n",
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"Our implementation in\n",
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":numref:`subsec_loading-seq-fixed-len`\n",
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"prepared training data for teacher forcing,\n",
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"where shifting tokens for self-supervised learning\n",
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"is similar to the training of language models in\n",
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":numref:`sec_language-model`.\n",
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"An alternative approach is\n",
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"to feed the *predicted* token\n",
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"from the previous time step\n",
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"as the current input to the decoder.\n",
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"\n",
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"\n",
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"In the following, we explain the design \n",
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"depicted in :numref:`fig_seq2seq`\n",
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"in greater detail.\n",
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"We will train this model for machine translation\n",
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"on the English--French dataset as introduced in\n",
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":numref:`sec_machine_translation`.\n",
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"\n",
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"## Encoder\n",
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"\n",
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"Recall that the encoder transforms an input sequence of variable length\n",
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"into a fixed-shape *context variable* $\\mathbf{c}$ (see :numref:`fig_seq2seq`).\n",
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"\n",
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"\n",
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"Consider a single sequence example (batch size 1).\n",
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"Suppose the input sequence is $x_1, \\ldots, x_T$, \n",
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"such that $x_t$ is the $t^{\\textrm{th}}$ token.\n",
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"At time step $t$, the RNN transforms\n",
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"the input feature vector $\\mathbf{x}_t$ for $x_t$\n",
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"and the hidden state $\\mathbf{h} _{t-1}$ \n",
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"from the previous time step \n",
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"into the current hidden state $\\mathbf{h}_t$.\n",
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"We can use a function $f$ to express \n",
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"the transformation of the RNN's recurrent layer:\n",
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"\n",
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"$$\\mathbf{h}_t = f(\\mathbf{x}_t, \\mathbf{h}_{t-1}). $$\n",
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"\n",
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"In general, the encoder transforms \n",
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"the hidden states at all time steps\n",
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"into a context variable through a customized function $q$:\n",
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"\n",
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"$$\\mathbf{c} = q(\\mathbf{h}_1, \\ldots, \\mathbf{h}_T).$$\n",
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"\n",
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"For example, in :numref:`fig_seq2seq`,\n",
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"the context variable is just the hidden state $\\mathbf{h}_T$\n",
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"corresponding to the encoder RNN's representation\n",
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"after processing the final token of the input sequence.\n",
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"\n",
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"In this example, we have used a unidirectional RNN\n",
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"to design the encoder,\n",
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"where the hidden state only depends on the input subsequence \n",
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"at and before the time step of the hidden state.\n",
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"We can also construct encoders using bidirectional RNNs.\n",
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"In this case, a hidden state depends on the subsequence before and after the time step \n",
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"(including the input at the current time step), \n",
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"which encodes the information of the entire sequence.\n",
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"\n",
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"\n",
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"Now let's [**implement the RNN encoder**].\n",
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"Note that we use an *embedding layer*\n",
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"to obtain the feature vector for each token in the input sequence.\n",
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"The weight of an embedding layer is a matrix,\n",
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"where the number of rows corresponds to \n",
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"the size of the input vocabulary (`vocab_size`)\n",
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"and number of columns corresponds to \n",
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"the feature vector's dimension (`embed_size`).\n",
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"For any input token index $i$,\n",
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"the embedding layer fetches the $i^{\\textrm{th}}$ row \n",
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"(starting from 0) of the weight matrix\n",
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"to return its feature vector.\n",
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"Here we implement the encoder with a multilayer GRU.\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": "cd36a65e",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T19:55:32.087883Z",
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"iopub.status.busy": "2023-08-18T19:55:32.086755Z",
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"iopub.status.idle": "2023-08-18T19:55:32.094916Z",
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"shell.execute_reply": "2023-08-18T19:55:32.093791Z"
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},
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"origin_pos": 8,
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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_seq2seq(module): #@save\n",
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" \"\"\"Initialize weights for sequence-to-sequence learning.\"\"\"\n",
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" if type(module) == nn.Linear:\n",
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" nn.init.xavier_uniform_(module.weight)\n",
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" if type(module) == nn.GRU:\n",
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" for param in module._flat_weights_names:\n",
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" if \"weight\" in param:\n",
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" nn.init.xavier_uniform_(module._parameters[param])"
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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": "7b8df492",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T19:55:32.100040Z",
|
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"iopub.status.busy": "2023-08-18T19:55:32.099233Z",
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"iopub.status.idle": "2023-08-18T19:55:32.107817Z",
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"shell.execute_reply": "2023-08-18T19:55:32.106716Z"
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},
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"origin_pos": 9,
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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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"class Seq2SeqEncoder(d2l.Encoder): #@save\n",
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" \"\"\"The RNN encoder for sequence-to-sequence learning.\"\"\"\n",
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" def __init__(self, vocab_size, embed_size, num_hiddens, num_layers,\n",
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" dropout=0):\n",
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" super().__init__()\n",
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" self.embedding = nn.Embedding(vocab_size, embed_size)\n",
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" self.rnn = d2l.GRU(embed_size, num_hiddens, num_layers, dropout)\n",
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" self.apply(init_seq2seq)\n",
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"\n",
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" def forward(self, X, *args):\n",
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" # X shape: (batch_size, num_steps)\n",
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" embs = self.embedding(X.t().type(torch.int64))\n",
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" # embs shape: (num_steps, batch_size, embed_size)\n",
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" outputs, state = self.rnn(embs)\n",
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" # outputs shape: (num_steps, batch_size, num_hiddens)\n",
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" # state shape: (num_layers, batch_size, num_hiddens)\n",
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" return outputs, state"
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]
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},
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{
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"cell_type": "markdown",
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"id": "24c21c8e",
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"metadata": {
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"origin_pos": 12
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},
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"source": [
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"Let's use a concrete example\n",
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"to [**illustrate the above encoder implementation.**]\n",
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"Below, we instantiate a two-layer GRU encoder\n",
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"whose number of hidden units is 16.\n",
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"Given a minibatch of sequence inputs `X`\n",
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"(batch size $=4$; number of time steps $=9$),\n",
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"the hidden states of the final layer\n",
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"at all the time steps\n",
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"(`enc_outputs` returned by the encoder's recurrent layers)\n",
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"are a tensor of shape\n",
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"(number of time steps, batch size, number of hidden units).\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": "89d5cb2e",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T19:55:32.112983Z",
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"iopub.status.busy": "2023-08-18T19:55:32.112158Z",
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"iopub.status.idle": "2023-08-18T19:55:32.150498Z",
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"shell.execute_reply": "2023-08-18T19:55:32.149041Z"
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},
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"origin_pos": 13,
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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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"vocab_size, embed_size, num_hiddens, num_layers = 10, 8, 16, 2\n",
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"batch_size, num_steps = 4, 9\n",
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"encoder = Seq2SeqEncoder(vocab_size, embed_size, num_hiddens, num_layers)\n",
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"X = torch.zeros((batch_size, num_steps))\n",
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"enc_outputs, enc_state = encoder(X)\n",
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"d2l.check_shape(enc_outputs, (num_steps, batch_size, num_hiddens))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "f827b6d3",
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"metadata": {
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"origin_pos": 14
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},
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"source": [
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"Since we are using a GRU here,\n",
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"the shape of the multilayer hidden states\n",
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"at the final time step is\n",
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"(number of hidden layers, batch size, number of hidden units).\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": "0e8eab95",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T19:55:32.155159Z",
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"iopub.status.busy": "2023-08-18T19:55:32.154233Z",
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"iopub.status.idle": "2023-08-18T19:55:32.160686Z",
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"shell.execute_reply": "2023-08-18T19:55:32.159216Z"
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},
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"origin_pos": 15,
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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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"d2l.check_shape(enc_state, (num_layers, batch_size, num_hiddens))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "8a35aecf",
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"metadata": {
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"origin_pos": 16
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},
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"source": [
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"## [**Decoder**]\n",
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":label:`sec_seq2seq_decoder`\n",
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"\n",
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"Given a target output sequence $y_1, y_2, \\ldots, y_{T'}$\n",
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"for each time step $t'$\n",
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"(we use $t^\\prime$ to differentiate from the input sequence time steps),\n",
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"the decoder assigns a predicted probability\n",
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"to each possible token occurring at step $y_{t'+1}$\n",
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"conditioned upon the previous tokens in the target\n",
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"$y_1, \\ldots, y_{t'}$ \n",
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"and the context variable \n",
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"$\\mathbf{c}$, i.e., $P(y_{t'+1} \\mid y_1, \\ldots, y_{t'}, \\mathbf{c})$.\n",
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"\n",
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"To predict the subsequent token $t^\\prime+1$ in the target sequence,\n",
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"the RNN decoder takes the previous step's target token $y_{t^\\prime}$,\n",
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"the hidden RNN state from the previous time step $\\mathbf{s}_{t^\\prime-1}$,\n",
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"and the context variable $\\mathbf{c}$ as its input,\n",
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"and transforms them into the hidden state \n",
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"$\\mathbf{s}_{t^\\prime}$ at the current time step.\n",
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"We can use a function $g$ to express \n",
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"the transformation of the decoder's hidden layer:\n",
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"\n",
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"$$\\mathbf{s}_{t^\\prime} = g(y_{t^\\prime-1}, \\mathbf{c}, \\mathbf{s}_{t^\\prime-1}).$$\n",
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":eqlabel:`eq_seq2seq_s_t`\n",
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"\n",
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"After obtaining the hidden state of the decoder,\n",
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"we can use an output layer and the softmax operation \n",
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"to compute the predictive distribution\n",
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"$p(y_{t^{\\prime}+1} \\mid y_1, \\ldots, y_{t^\\prime}, \\mathbf{c})$ \n",
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"over the subsequent output token ${t^\\prime+1}$.\n",
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"\n",
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"Following :numref:`fig_seq2seq`,\n",
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"when implementing the decoder as follows,\n",
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"we directly use the hidden state at the final time step\n",
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"of the encoder\n",
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"to initialize the hidden state of the decoder.\n",
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"This requires that the RNN encoder and the RNN decoder \n",
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"have the same number of layers and hidden units.\n",
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"To further incorporate the encoded input sequence information,\n",
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"the context variable is concatenated\n",
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"with the decoder input at all the time steps.\n",
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"To predict the probability distribution of the output token,\n",
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"we use a fully connected layer\n",
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"to transform the hidden state \n",
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"at the final layer of the RNN decoder.\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": 6,
|
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"id": "1c318811",
|
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T19:55:32.165108Z",
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"iopub.status.busy": "2023-08-18T19:55:32.164049Z",
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"iopub.status.idle": "2023-08-18T19:55:32.176473Z",
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"shell.execute_reply": "2023-08-18T19:55:32.175009Z"
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},
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"origin_pos": 18,
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"tab": [
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"pytorch"
|
|
]
|
|
},
|
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"outputs": [],
|
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"source": [
|
|
"class Seq2SeqDecoder(d2l.Decoder):\n",
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" \"\"\"The RNN decoder for sequence to sequence learning.\"\"\"\n",
|
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" def __init__(self, vocab_size, embed_size, num_hiddens, num_layers,\n",
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" dropout=0):\n",
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" super().__init__()\n",
|
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" self.embedding = nn.Embedding(vocab_size, embed_size)\n",
|
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" self.rnn = d2l.GRU(embed_size+num_hiddens, num_hiddens,\n",
|
|
" num_layers, dropout)\n",
|
|
" self.dense = nn.LazyLinear(vocab_size)\n",
|
|
" self.apply(init_seq2seq)\n",
|
|
"\n",
|
|
" def init_state(self, enc_all_outputs, *args):\n",
|
|
" return enc_all_outputs\n",
|
|
"\n",
|
|
" def forward(self, X, state):\n",
|
|
" # X shape: (batch_size, num_steps)\n",
|
|
" # embs shape: (num_steps, batch_size, embed_size)\n",
|
|
" embs = self.embedding(X.t().type(torch.int32))\n",
|
|
" enc_output, hidden_state = state\n",
|
|
" # context shape: (batch_size, num_hiddens)\n",
|
|
" context = enc_output[-1]\n",
|
|
" # Broadcast context to (num_steps, batch_size, num_hiddens)\n",
|
|
" context = context.repeat(embs.shape[0], 1, 1)\n",
|
|
" # Concat at the feature dimension\n",
|
|
" embs_and_context = torch.cat((embs, context), -1)\n",
|
|
" outputs, hidden_state = self.rnn(embs_and_context, hidden_state)\n",
|
|
" outputs = self.dense(outputs).swapaxes(0, 1)\n",
|
|
" # outputs shape: (batch_size, num_steps, vocab_size)\n",
|
|
" # hidden_state shape: (num_layers, batch_size, num_hiddens)\n",
|
|
" return outputs, [enc_output, hidden_state]"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "195041fa",
|
|
"metadata": {
|
|
"origin_pos": 21
|
|
},
|
|
"source": [
|
|
"To [**illustrate the implemented decoder**],\n",
|
|
"below we instantiate it with the same hyperparameters from the aforementioned encoder.\n",
|
|
"As we can see, the output shape of the decoder becomes (batch size, number of time steps, vocabulary size),\n",
|
|
"where the final dimension of the tensor stores the predicted token distribution.\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"id": "a51f8b17",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2023-08-18T19:55:32.180880Z",
|
|
"iopub.status.busy": "2023-08-18T19:55:32.179836Z",
|
|
"iopub.status.idle": "2023-08-18T19:55:32.197802Z",
|
|
"shell.execute_reply": "2023-08-18T19:55:32.196352Z"
|
|
},
|
|
"origin_pos": 22,
|
|
"tab": [
|
|
"pytorch"
|
|
]
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"decoder = Seq2SeqDecoder(vocab_size, embed_size, num_hiddens, num_layers)\n",
|
|
"state = decoder.init_state(encoder(X))\n",
|
|
"dec_outputs, state = decoder(X, state)\n",
|
|
"d2l.check_shape(dec_outputs, (batch_size, num_steps, vocab_size))\n",
|
|
"d2l.check_shape(state[1], (num_layers, batch_size, num_hiddens))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "f87599b6",
|
|
"metadata": {
|
|
"origin_pos": 23
|
|
},
|
|
"source": [
|
|
"The layers in the above RNN encoder--decoder model \n",
|
|
"are summarized in :numref:`fig_seq2seq_details`.\n",
|
|
"\n",
|
|
"\n",
|
|
":label:`fig_seq2seq_details`\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"## Encoder--Decoder for Sequence-to-Sequence Learning\n",
|
|
"\n",
|
|
"\n",
|
|
"Putting it all together in code yields the following:\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"id": "4e30d226",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2023-08-18T19:55:32.207516Z",
|
|
"iopub.status.busy": "2023-08-18T19:55:32.206334Z",
|
|
"iopub.status.idle": "2023-08-18T19:55:32.219468Z",
|
|
"shell.execute_reply": "2023-08-18T19:55:32.218248Z"
|
|
},
|
|
"origin_pos": 24,
|
|
"tab": [
|
|
"pytorch"
|
|
]
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"class Seq2Seq(d2l.EncoderDecoder): #@save\n",
|
|
" \"\"\"The RNN encoder--decoder for sequence to sequence learning.\"\"\"\n",
|
|
" def __init__(self, encoder, decoder, tgt_pad, lr):\n",
|
|
" super().__init__(encoder, decoder)\n",
|
|
" self.save_hyperparameters()\n",
|
|
"\n",
|
|
" def validation_step(self, batch):\n",
|
|
" Y_hat = self(*batch[:-1])\n",
|
|
" self.plot('loss', self.loss(Y_hat, batch[-1]), train=False)\n",
|
|
"\n",
|
|
" def configure_optimizers(self):\n",
|
|
" # Adam optimizer is used here\n",
|
|
" return torch.optim.Adam(self.parameters(), lr=self.lr)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "81fe6c0d",
|
|
"metadata": {
|
|
"origin_pos": 26
|
|
},
|
|
"source": [
|
|
"## Loss Function with Masking\n",
|
|
"\n",
|
|
"At each time step, the decoder predicts \n",
|
|
"a probability distribution for the output tokens.\n",
|
|
"As with language modeling, \n",
|
|
"we can apply softmax \n",
|
|
"to obtain the distribution\n",
|
|
"and calculate the cross-entropy loss for optimization.\n",
|
|
"Recall from :numref:`sec_machine_translation`\n",
|
|
"that the special padding tokens\n",
|
|
"are appended to the end of sequences\n",
|
|
"and so sequences of varying lengths\n",
|
|
"can be efficiently loaded\n",
|
|
"in minibatches of the same shape.\n",
|
|
"However, prediction of padding tokens\n",
|
|
"should be excluded from loss calculations.\n",
|
|
"To this end, we can \n",
|
|
"[**mask irrelevant entries with zero values**]\n",
|
|
"so that multiplication \n",
|
|
"of any irrelevant prediction\n",
|
|
"with zero equates to zero.\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 9,
|
|
"id": "9baec321",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2023-08-18T19:55:32.224892Z",
|
|
"iopub.status.busy": "2023-08-18T19:55:32.224198Z",
|
|
"iopub.status.idle": "2023-08-18T19:55:32.232039Z",
|
|
"shell.execute_reply": "2023-08-18T19:55:32.230833Z"
|
|
},
|
|
"origin_pos": 27,
|
|
"tab": [
|
|
"pytorch"
|
|
]
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"@d2l.add_to_class(Seq2Seq)\n",
|
|
"def loss(self, Y_hat, Y):\n",
|
|
" l = super(Seq2Seq, self).loss(Y_hat, Y, averaged=False)\n",
|
|
" mask = (Y.reshape(-1) != self.tgt_pad).type(torch.float32)\n",
|
|
" return (l * mask).sum() / mask.sum()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "876a6584",
|
|
"metadata": {
|
|
"origin_pos": 29
|
|
},
|
|
"source": [
|
|
"## [**Training**]\n",
|
|
":label:`sec_seq2seq_training`\n",
|
|
"\n",
|
|
"Now we can [**create and train an RNN encoder--decoder model**]\n",
|
|
"for sequence-to-sequence learning on the machine translation dataset.\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"id": "2e0ee6e7",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2023-08-18T19:55:32.246700Z",
|
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"iopub.status.busy": "2023-08-18T19:55:32.246014Z",
|
|
"iopub.status.idle": "2023-08-18T19:56:06.984975Z",
|
|
"shell.execute_reply": "2023-08-18T19:56:06.983766Z"
|
|
},
|
|
"origin_pos": 30,
|
|
"tab": [
|
|
"pytorch"
|
|
]
|
|
},
|
|
"outputs": [
|
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"metadata": {},
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}
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],
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"source": [
|
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"data = d2l.MTFraEng(batch_size=128)\n",
|
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"embed_size, num_hiddens, num_layers, dropout = 256, 256, 2, 0.2\n",
|
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"encoder = Seq2SeqEncoder(\n",
|
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" len(data.src_vocab), embed_size, num_hiddens, num_layers, dropout)\n",
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"decoder = Seq2SeqDecoder(\n",
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|
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|
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{
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"id": "3914d070",
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"metadata": {
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"source": [
|
|
"## [**Prediction**]\n",
|
|
"\n",
|
|
"To predict the output sequence\n",
|
|
"at each step, \n",
|
|
"the predicted token from the previous\n",
|
|
"time step is fed into the decoder as an input.\n",
|
|
"One simple strategy is to sample whichever token\n",
|
|
"that has been assigned by the decoder the highest probability\n",
|
|
"when predicting at each step.\n",
|
|
"As in training, at the initial time step\n",
|
|
"the beginning-of-sequence (\"<bos>\") token\n",
|
|
"is fed into the decoder.\n",
|
|
"This prediction process\n",
|
|
"is illustrated in :numref:`fig_seq2seq_predict`.\n",
|
|
"When the end-of-sequence (\"<eos>\") token is predicted,\n",
|
|
"the prediction of the output sequence is complete.\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
":label:`fig_seq2seq_predict`\n",
|
|
"\n",
|
|
"In the next section, we will introduce \n",
|
|
"more sophisticated strategies \n",
|
|
"based on beam search (:numref:`sec_beam-search`).\n"
|
|
]
|
|
},
|
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"id": "1c19a4a9",
|
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"origin_pos": 32,
|
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"tab": [
|
|
"pytorch"
|
|
]
|
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|
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"outputs": [],
|
|
"source": [
|
|
"@d2l.add_to_class(d2l.EncoderDecoder) #@save\n",
|
|
"def predict_step(self, batch, device, num_steps,\n",
|
|
" save_attention_weights=False):\n",
|
|
" batch = [a.to(device) for a in batch]\n",
|
|
" src, tgt, src_valid_len, _ = batch\n",
|
|
" enc_all_outputs = self.encoder(src, src_valid_len)\n",
|
|
" dec_state = self.decoder.init_state(enc_all_outputs, src_valid_len)\n",
|
|
" outputs, attention_weights = [tgt[:, (0)].unsqueeze(1), ], []\n",
|
|
" for _ in range(num_steps):\n",
|
|
" Y, dec_state = self.decoder(outputs[-1], dec_state)\n",
|
|
" outputs.append(Y.argmax(2))\n",
|
|
" # Save attention weights (to be covered later)\n",
|
|
" if save_attention_weights:\n",
|
|
" attention_weights.append(self.decoder.attention_weights)\n",
|
|
" return torch.cat(outputs[1:], 1), attention_weights"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "cb8f0164",
|
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"metadata": {
|
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"origin_pos": 34
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},
|
|
"source": [
|
|
"## Evaluation of Predicted Sequences\n",
|
|
"\n",
|
|
"We can evaluate a predicted sequence\n",
|
|
"by comparing it with the\n",
|
|
"target sequence (the ground truth).\n",
|
|
"But what precisely is the appropriate measure \n",
|
|
"for comparing similarity between two sequences?\n",
|
|
"\n",
|
|
"\n",
|
|
"Bilingual Evaluation Understudy (BLEU),\n",
|
|
"though originally proposed for evaluating\n",
|
|
"machine translation results :cite:`Papineni.Roukos.Ward.ea.2002`,\n",
|
|
"has been extensively used in measuring\n",
|
|
"the quality of output sequences for different applications.\n",
|
|
"In principle, for any $n$-gram (:numref:`subsec_markov-models-and-n-grams`) in the predicted sequence,\n",
|
|
"BLEU evaluates whether this $n$-gram appears\n",
|
|
"in the target sequence.\n",
|
|
"\n",
|
|
"Denote by $p_n$ the precision of an $n$-gram,\n",
|
|
"defined as the ratio \n",
|
|
"of the number of matched $n$-grams in\n",
|
|
"the predicted and target sequences\n",
|
|
"to the number of $n$-grams in the predicted sequence.\n",
|
|
"To explain, given a target sequence $A$, $B$, $C$, $D$, $E$, $F$,\n",
|
|
"and a predicted sequence $A$, $B$, $B$, $C$, $D$,\n",
|
|
"we have $p_1 = 4/5$, $p_2 = 3/4$, $p_3 = 1/3$, and $p_4 = 0$.\n",
|
|
"Now let $\\textrm{len}_{\\textrm{label}}$ and $\\textrm{len}_{\\textrm{pred}}$\n",
|
|
"be the numbers of tokens in the target sequence \n",
|
|
"and the predicted sequence, respectively.\n",
|
|
"Then, BLEU is defined as\n",
|
|
"\n",
|
|
"$$ \\exp\\left(\\min\\left(0, 1 - \\frac{\\textrm{len}_{\\textrm{label}}}{\\textrm{len}_{\\textrm{pred}}}\\right)\\right) \\prod_{n=1}^k p_n^{1/2^n},$$\n",
|
|
":eqlabel:`eq_bleu`\n",
|
|
"\n",
|
|
"where $k$ is the longest $n$-gram for matching.\n",
|
|
"\n",
|
|
"Based on the definition of BLEU in :eqref:`eq_bleu`,\n",
|
|
"whenever the predicted sequence is the same as the target sequence, BLEU is 1.\n",
|
|
"Moreover,\n",
|
|
"since matching longer $n$-grams is more difficult,\n",
|
|
"BLEU assigns a greater weight\n",
|
|
"when a longer $n$-gram has high precision.\n",
|
|
"Specifically, when $p_n$ is fixed,\n",
|
|
"$p_n^{1/2^n}$ increases as $n$ grows (the original paper uses $p_n^{1/n}$).\n",
|
|
"Furthermore,\n",
|
|
"since\n",
|
|
"predicting shorter sequences\n",
|
|
"tends to yield a higher $p_n$ value,\n",
|
|
"the coefficient before the multiplication term in :eqref:`eq_bleu`\n",
|
|
"penalizes shorter predicted sequences.\n",
|
|
"For example, when $k=2$,\n",
|
|
"given the target sequence $A$, $B$, $C$, $D$, $E$, $F$ and the predicted sequence $A$, $B$,\n",
|
|
"although $p_1 = p_2 = 1$, the penalty factor $\\exp(1-6/2) \\approx 0.14$ lowers the BLEU.\n",
|
|
"\n",
|
|
"We [**implement the BLEU measure**] as follows.\n"
|
|
]
|
|
},
|
|
{
|
|
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|
|
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|
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"id": "904e4635",
|
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|
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"origin_pos": 35,
|
|
"tab": [
|
|
"pytorch"
|
|
]
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def bleu(pred_seq, label_seq, k): #@save\n",
|
|
" \"\"\"Compute the BLEU.\"\"\"\n",
|
|
" pred_tokens, label_tokens = pred_seq.split(' '), label_seq.split(' ')\n",
|
|
" len_pred, len_label = len(pred_tokens), len(label_tokens)\n",
|
|
" score = math.exp(min(0, 1 - len_label / len_pred))\n",
|
|
" for n in range(1, min(k, len_pred) + 1):\n",
|
|
" num_matches, label_subs = 0, collections.defaultdict(int)\n",
|
|
" for i in range(len_label - n + 1):\n",
|
|
" label_subs[' '.join(label_tokens[i: i + n])] += 1\n",
|
|
" for i in range(len_pred - n + 1):\n",
|
|
" if label_subs[' '.join(pred_tokens[i: i + n])] > 0:\n",
|
|
" num_matches += 1\n",
|
|
" label_subs[' '.join(pred_tokens[i: i + n])] -= 1\n",
|
|
" score *= math.pow(num_matches / (len_pred - n + 1), math.pow(0.5, n))\n",
|
|
" return score"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "99544f4a",
|
|
"metadata": {
|
|
"origin_pos": 36
|
|
},
|
|
"source": [
|
|
"In the end,\n",
|
|
"we use the trained RNN encoder--decoder\n",
|
|
"to [**translate a few English sentences into French**]\n",
|
|
"and compute the BLEU of the results.\n"
|
|
]
|
|
},
|
|
{
|
|
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|
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"iopub.status.idle": "2023-08-18T19:56:07.028981Z",
|
|
"shell.execute_reply": "2023-08-18T19:56:07.028094Z"
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},
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"origin_pos": 37,
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"tab": [
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"pytorch"
|
|
]
|
|
},
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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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"go . => ['va', '!'], bleu,1.000\n",
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"i lost . => [\"j'ai\", 'perdu', '.'], bleu,1.000\n",
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"he's calm . => ['elle', 'court', '.'], bleu,0.000\n",
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"i'm home . => ['je', 'suis', 'chez', 'moi', '.'], bleu,1.000\n"
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]
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}
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],
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"source": [
|
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"engs = ['go .', 'i lost .', 'he\\'s calm .', 'i\\'m home .']\n",
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"fras = ['va !', 'j\\'ai perdu .', 'il est calme .', 'je suis chez moi .']\n",
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"preds, _ = model.predict_step(\n",
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" data.build(engs, fras), d2l.try_gpu(), data.num_steps)\n",
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"for en, fr, p in zip(engs, fras, preds):\n",
|
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" translation = []\n",
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" for token in data.tgt_vocab.to_tokens(p):\n",
|
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" if token == '<eos>':\n",
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" break\n",
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" translation.append(token)\n",
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" print(f'{en} => {translation}, bleu,'\n",
|
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" f'{bleu(\" \".join(translation), fr, k=2):.3f}')"
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]
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},
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{
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|
"cell_type": "markdown",
|
|
"id": "dd49dd46",
|
|
"metadata": {
|
|
"origin_pos": 38
|
|
},
|
|
"source": [
|
|
"## Summary\n",
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"\n",
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"Following the design of the encoder--decoder architecture, we can use two RNNs to design a model for sequence-to-sequence learning.\n",
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"In encoder--decoder training, the teacher forcing approach feeds original output sequences (in contrast to predictions) into the decoder.\n",
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"When implementing the encoder and the decoder, we can use multilayer RNNs.\n",
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"We can use masks to filter out irrelevant computations, such as when calculating the loss.\n",
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"For evaluating output sequences,\n",
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"BLEU is a popular measure that matches $n$-grams between the predicted sequence and the target sequence.\n",
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"\n",
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"\n",
|
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"## Exercises\n",
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"\n",
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"1. Can you adjust the hyperparameters to improve the translation results?\n",
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"1. Rerun the experiment without using masks in the loss calculation. What results do you observe? Why?\n",
|
|
"1. If the encoder and the decoder differ in the number of layers or the number of hidden units, how can we initialize the hidden state of the decoder?\n",
|
|
"1. In training, replace teacher forcing with feeding the prediction at the previous time step into the decoder. How does this influence the performance?\n",
|
|
"1. Rerun the experiment by replacing GRU with LSTM.\n",
|
|
"1. Are there any other ways to design the output layer of the decoder?\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "994069ec",
|
|
"metadata": {
|
|
"origin_pos": 40,
|
|
"tab": [
|
|
"pytorch"
|
|
]
|
|
},
|
|
"source": [
|
|
"[Discussions](https://discuss.d2l.ai/t/1062)\n"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"language_info": {
|
|
"name": "python"
|
|
},
|
|
"required_libs": []
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
} |