447 lines
16 KiB
Plaintext
447 lines
16 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "2eef48dc",
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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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"# 子词嵌入\n",
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":label:`sec_fasttext`\n",
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"\n",
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"在英语中，“helps”“helped”和“helping”等单词都是同一个词“help”的变形形式。“dog”和“dogs”之间的关系与“cat”和“cats”之间的关系相同，“boy”和“boyfriend”之间的关系与“girl”和“girlfriend”之间的关系相同。在法语和西班牙语等其他语言中，许多动词有40多种变形形式，而在芬兰语中，名词最多可能有15种变形。在语言学中，形态学研究单词形成和词汇关系。但是，word2vec和GloVe都没有对词的内部结构进行探讨。\n",
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"\n",
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"## fastText模型\n",
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"\n",
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"回想一下词在word2vec中是如何表示的。在跳元模型和连续词袋模型中，同一词的不同变形形式直接由不同的向量表示，不需要共享参数。为了使用形态信息，*fastText模型*提出了一种*子词嵌入*方法，其中子词是一个字符$n$-gram :cite:`Bojanowski.Grave.Joulin.ea.2017`。fastText可以被认为是子词级跳元模型，而非学习词级向量表示，其中每个*中心词*由其子词级向量之和表示。\n",
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"\n",
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"让我们来说明如何以单词“where”为例获得fastText中每个中心词的子词。首先，在词的开头和末尾添加特殊字符“<”和“>”，以将前缀和后缀与其他子词区分开来。\n",
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"然后，从词中提取字符$n$-gram。\n",
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"例如，值$n=3$时，我们将获得长度为3的所有子词：\n",
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"“<wh”“whe”“her”“ere”“re>”和特殊子词“<where>”。\n",
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"\n",
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"在fastText中，对于任意词$w$，用$\\mathcal{G}_w$表示其长度在3和6之间的所有子词与其特殊子词的并集。词表是所有词的子词的集合。假设$\\mathbf{z}_g$是词典中的子词$g$的向量，则跳元模型中作为中心词的词$w$的向量$\\mathbf{v}_w$是其子词向量的和：\n",
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"\n",
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"$$\\mathbf{v}_w = \\sum_{g\\in\\mathcal{G}_w} \\mathbf{z}_g.$$\n",
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"\n",
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"fastText的其余部分与跳元模型相同。与跳元模型相比，fastText的词量更大，模型参数也更多。此外，为了计算一个词的表示，它的所有子词向量都必须求和，这导致了更高的计算复杂度。然而，由于具有相似结构的词之间共享来自子词的参数，罕见词甚至词表外的词在fastText中可能获得更好的向量表示。\n",
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"\n",
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"## 字节对编码（Byte Pair Encoding）\n",
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":label:`subsec_Byte_Pair_Encoding`\n",
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"\n",
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"在fastText中，所有提取的子词都必须是指定的长度，例如$3$到$6$，因此词表大小不能预定义。为了在固定大小的词表中允许可变长度的子词，我们可以应用一种称为*字节对编码*（Byte Pair Encoding，BPE）的压缩算法来提取子词 :cite:`Sennrich.Haddow.Birch.2015`。\n",
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"\n",
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"字节对编码执行训练数据集的统计分析，以发现单词内的公共符号，诸如任意长度的连续字符。从长度为1的符号开始，字节对编码迭代地合并最频繁的连续符号对以产生新的更长的符号。请注意，为提高效率，不考虑跨越单词边界的对。最后，我们可以使用像子词这样的符号来切分单词。字节对编码及其变体已经用于诸如GPT-2 :cite:`Radford.Wu.Child.ea.2019`和RoBERTa :cite:`Liu.Ott.Goyal.ea.2019`等自然语言处理预训练模型中的输入表示。在下面，我们将说明字节对编码是如何工作的。\n",
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"\n",
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"首先，我们将符号词表初始化为所有英文小写字符、特殊的词尾符号`'_'`和特殊的未知符号`'[UNK]'`。\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": "70df59d8",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T06:56:35.604170Z",
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"iopub.status.busy": "2023-08-18T06:56:35.603510Z",
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"iopub.status.idle": "2023-08-18T06:56:35.611979Z",
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"shell.execute_reply": "2023-08-18T06:56:35.611231Z"
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},
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"origin_pos": 1,
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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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"\n",
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"symbols = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm',\n",
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" 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z',\n",
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" '_', '[UNK]']"
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]
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},
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{
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"cell_type": "markdown",
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"id": "f94dab27",
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"metadata": {
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"origin_pos": 3
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},
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"source": [
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"因为我们不考虑跨越词边界的符号对，所以我们只需要一个字典`raw_token_freqs`将词映射到数据集中的频率（出现次数）。注意，特殊符号`'_'`被附加到每个词的尾部，以便我们可以容易地从输出符号序列（例如，“a_all er_man”）恢复单词序列（例如，“a_all er_man”）。由于我们仅从单个字符和特殊符号的词开始合并处理，所以在每个词（词典`token_freqs`的键）内的每对连续字符之间插入空格。换句话说，空格是词中符号之间的分隔符。\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": "6a26ec96",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T06:56:35.615843Z",
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"iopub.status.busy": "2023-08-18T06:56:35.615201Z",
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"iopub.status.idle": "2023-08-18T06:56:35.623942Z",
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"shell.execute_reply": "2023-08-18T06:56:35.623209Z"
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},
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"origin_pos": 4,
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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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"data": {
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"text/plain": [
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"{'f a s t _': 4, 'f a s t e r _': 3, 't a l l _': 5, 't a l l e r _': 4}"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"raw_token_freqs = {'fast_': 4, 'faster_': 3, 'tall_': 5, 'taller_': 4}\n",
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"token_freqs = {}\n",
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"for token, freq in raw_token_freqs.items():\n",
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" token_freqs[' '.join(list(token))] = raw_token_freqs[token]\n",
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"token_freqs"
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]
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},
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{
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"cell_type": "markdown",
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"id": "8ee2d216",
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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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"我们定义以下`get_max_freq_pair`函数，其返回词内最频繁的连续符号对，其中词来自输入词典`token_freqs`的键。\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": "874de73a",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T06:56:35.627616Z",
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"iopub.status.busy": "2023-08-18T06:56:35.627025Z",
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"iopub.status.idle": "2023-08-18T06:56:35.631950Z",
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"shell.execute_reply": "2023-08-18T06:56:35.631221Z"
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},
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"origin_pos": 6,
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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_max_freq_pair(token_freqs):\n",
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" pairs = collections.defaultdict(int)\n",
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" for token, freq in token_freqs.items():\n",
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" symbols = token.split()\n",
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" for i in range(len(symbols) - 1):\n",
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" # “pairs”的键是两个连续符号的元组\n",
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" pairs[symbols[i], symbols[i + 1]] += freq\n",
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" return max(pairs, key=pairs.get) # 具有最大值的“pairs”键"
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]
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},
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{
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"cell_type": "markdown",
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"id": "701a4399",
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"metadata": {
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"origin_pos": 7
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},
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"source": [
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"作为基于连续符号频率的贪心方法，字节对编码将使用以下`merge_symbols`函数来合并最频繁的连续符号对以产生新符号。\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": "877dce88",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T06:56:35.635554Z",
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"iopub.status.busy": "2023-08-18T06:56:35.634913Z",
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"iopub.status.idle": "2023-08-18T06:56:35.639631Z",
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"shell.execute_reply": "2023-08-18T06:56:35.638892Z"
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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 merge_symbols(max_freq_pair, token_freqs, symbols):\n",
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" symbols.append(''.join(max_freq_pair))\n",
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" new_token_freqs = dict()\n",
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" for token, freq in token_freqs.items():\n",
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" new_token = token.replace(' '.join(max_freq_pair),\n",
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" ''.join(max_freq_pair))\n",
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" new_token_freqs[new_token] = token_freqs[token]\n",
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" return new_token_freqs"
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]
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},
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{
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"cell_type": "markdown",
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"id": "63e888f9",
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"metadata": {
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"origin_pos": 9
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},
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"source": [
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"现在，我们对词典`token_freqs`的键迭代地执行字节对编码算法。在第一次迭代中，最频繁的连续符号对是`'t'`和`'a'`，因此字节对编码将它们合并以产生新符号`'ta'`。在第二次迭代中，字节对编码继续合并`'ta'`和`'l'`以产生另一个新符号`'tal'`。\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": "ea95bc7c",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T06:56:35.643247Z",
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"iopub.status.busy": "2023-08-18T06:56:35.642643Z",
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"iopub.status.idle": "2023-08-18T06:56:35.647847Z",
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"shell.execute_reply": "2023-08-18T06:56:35.647061Z"
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},
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"origin_pos": 10,
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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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"合并# 1: ('t', 'a')\n",
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"合并# 2: ('ta', 'l')\n",
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"合并# 3: ('tal', 'l')\n",
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"合并# 4: ('f', 'a')\n",
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"合并# 5: ('fa', 's')\n",
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"合并# 6: ('fas', 't')\n",
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"合并# 7: ('e', 'r')\n",
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"合并# 8: ('er', '_')\n",
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"合并# 9: ('tall', '_')\n",
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"合并# 10: ('fast', '_')\n"
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]
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}
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],
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"source": [
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"num_merges = 10\n",
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"for i in range(num_merges):\n",
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" max_freq_pair = get_max_freq_pair(token_freqs)\n",
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" token_freqs = merge_symbols(max_freq_pair, token_freqs, symbols)\n",
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" print(f'合并# {i+1}:',max_freq_pair)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4fe6d30f",
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"metadata": {
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"origin_pos": 11
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},
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"source": [
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"在字节对编码的10次迭代之后，我们可以看到列表`symbols`现在又包含10个从其他符号迭代合并而来的符号。\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": "14d6459f",
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"metadata": {
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"execution": {
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||
"iopub.execute_input": "2023-08-18T06:56:35.651408Z",
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||
"iopub.status.busy": "2023-08-18T06:56:35.650818Z",
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||
"iopub.status.idle": "2023-08-18T06:56:35.654893Z",
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||
"shell.execute_reply": "2023-08-18T06:56:35.654143Z"
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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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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z', '_', '[UNK]', 'ta', 'tal', 'tall', 'fa', 'fas', 'fast', 'er', 'er_', 'tall_', 'fast_']\n"
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]
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}
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],
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"source": [
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"print(symbols)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "70283228",
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||
"metadata": {
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||
"origin_pos": 13
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},
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||
"source": [
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"对于在词典`raw_token_freqs`的键中指定的同一数据集，作为字节对编码算法的结果，数据集中的每个词现在被子词“fast_”“fast”“er_”“tall_”和“tall”分割。例如，单词“fast er_”和“tall er_”分别被分割为“fast er_”和“tall er_”。\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": 7,
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"id": "93120bf0",
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"metadata": {
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||
"execution": {
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||
"iopub.execute_input": "2023-08-18T06:56:35.658487Z",
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||
"iopub.status.busy": "2023-08-18T06:56:35.657897Z",
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||
"iopub.status.idle": "2023-08-18T06:56:35.662020Z",
|
||
"shell.execute_reply": "2023-08-18T06:56:35.661268Z"
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||
},
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||
"origin_pos": 14,
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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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"['fast_', 'fast er_', 'tall_', 'tall er_']\n"
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]
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}
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],
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"source": [
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"print(list(token_freqs.keys()))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "83456139",
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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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"请注意，字节对编码的结果取决于正在使用的数据集。我们还可以使用从一个数据集学习的子词来切分另一个数据集的单词。作为一种贪心方法，下面的`segment_BPE`函数尝试将单词从输入参数`symbols`分成可能最长的子词。\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": 8,
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"id": "04e84fc1",
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"metadata": {
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||
"execution": {
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||
"iopub.execute_input": "2023-08-18T06:56:35.665538Z",
|
||
"iopub.status.busy": "2023-08-18T06:56:35.664918Z",
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||
"iopub.status.idle": "2023-08-18T06:56:35.670601Z",
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||
"shell.execute_reply": "2023-08-18T06:56:35.669830Z"
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||
},
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||
"origin_pos": 16,
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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 segment_BPE(tokens, symbols):\n",
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" outputs = []\n",
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" for token in tokens:\n",
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" start, end = 0, len(token)\n",
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" cur_output = []\n",
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" # 具有符号中可能最长子字的词元段\n",
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" while start < len(token) and start < end:\n",
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" if token[start: end] in symbols:\n",
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" cur_output.append(token[start: end])\n",
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" start = end\n",
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" end = len(token)\n",
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" else:\n",
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" end -= 1\n",
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" if start < len(token):\n",
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" cur_output.append('[UNK]')\n",
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" outputs.append(' '.join(cur_output))\n",
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" return outputs"
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]
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},
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{
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"cell_type": "markdown",
|
||
"id": "ce7118c8",
|
||
"metadata": {
|
||
"origin_pos": 17
|
||
},
|
||
"source": [
|
||
"我们使用列表`symbols`中的子词（从前面提到的数据集学习）来表示另一个数据集的`tokens`。\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "00e7e03a",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2023-08-18T06:56:35.674172Z",
|
||
"iopub.status.busy": "2023-08-18T06:56:35.673554Z",
|
||
"iopub.status.idle": "2023-08-18T06:56:35.677812Z",
|
||
"shell.execute_reply": "2023-08-18T06:56:35.677058Z"
|
||
},
|
||
"origin_pos": 18,
|
||
"tab": [
|
||
"pytorch"
|
||
]
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"['tall e s t _', 'fa t t er_']\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"tokens = ['tallest_', 'fatter_']\n",
|
||
"print(segment_BPE(tokens, symbols))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b4a5e47c",
|
||
"metadata": {
|
||
"origin_pos": 19
|
||
},
|
||
"source": [
|
||
"## 小结\n",
|
||
"\n",
|
||
"* fastText模型提出了一种子词嵌入方法：基于word2vec中的跳元模型，它将中心词表示为其子词向量之和。\n",
|
||
"* 字节对编码执行训练数据集的统计分析，以发现词内的公共符号。作为一种贪心方法，字节对编码迭代地合并最频繁的连续符号对。\n",
|
||
"* 子词嵌入可以提高稀有词和词典外词的表示质量。\n",
|
||
"\n",
|
||
"## 练习\n",
|
||
"\n",
|
||
"1. 例如，英语中大约有$3\\times 10^8$种可能的$6$-元组。子词太多会有什么问题呢？如何解决这个问题？提示:请参阅fastText论文第3.2节末尾 :cite:`Bojanowski.Grave.Joulin.ea.2017`。\n",
|
||
"1. 如何在连续词袋模型的基础上设计一个子词嵌入模型？\n",
|
||
"1. 要获得大小为$m$的词表，当初始符号词表大小为$n$时，需要多少合并操作？\n",
|
||
"1. 如何扩展字节对编码的思想来提取短语？\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "09bfff94",
|
||
"metadata": {
|
||
"origin_pos": 21,
|
||
"tab": [
|
||
"pytorch"
|
||
]
|
||
},
|
||
"source": [
|
||
"[Discussions](https://discuss.d2l.ai/t/5748)\n"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"language_info": {
|
||
"name": "python"
|
||
},
|
||
"required_libs": []
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
} |