语言模型

1.预测文本序列出现的概率

2.应用在做预训练模型

3.生成文本，给定前面几个词，不断生成后续文本

4.判断多个序列中哪个更常见

真实数据集的统计

《时光机器》数据集构建词表， 并打印前10个最常用的（频率最高的）单词。

!pip install --upgrade d2l==0.17.5  #d2l需要更新

Collecting d2l==0.17.5
  Downloading d2l-0.17.5-py3-none-any.whl (82 kB)
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[?25hRequirement already satisfied: jupyter==1.0.0 in /usr/local/lib/python3.10/dist-packages (from d2l==0.17.5) (1.0.0)
Collecting numpy==1.21.5 (from d2l==0.17.5)
  Downloading numpy-1.21.5-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (15.9 MB)
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[?25hCollecting matplotlib==3.5.1 (from d2l==0.17.5)
  Downloading matplotlib-3.5.1-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (11.9 MB)
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[?25hCollecting requests==2.25.1 (from d2l==0.17.5)
  Downloading requests-2.25.1-py2.py3-none-any.whl (61 kB)
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[?25hCollecting pandas==1.2.4 (from d2l==0.17.5)
  Downloading pandas-1.2.4.tar.gz (5.5 MB)
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[?25h  Installing build dependencies ... [?25l[?25hdone
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Requirement already satisfied: pytz>=2017.3 in /usr/local/lib/python3.10/dist-packages (from pandas==1.2.4->d2l==0.17.5) (2023.4)
Collecting chardet<5,>=3.0.2 (from requests==2.25.1->d2l==0.17.5)
  Downloading chardet-4.0.0-py2.py3-none-any.whl (178 kB)
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[?25hCollecting idna<3,>=2.5 (from requests==2.25.1->d2l==0.17.5)
  Downloading idna-2.10-py2.py3-none-any.whl (58 kB)
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[?25hCollecting urllib3<1.27,>=1.21.1 (from requests==2.25.1->d2l==0.17.5)
  Downloading urllib3-1.26.18-py2.py3-none-any.whl (143 kB)
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Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.7->matplotlib==3.5.1->d2l==0.17.5) (1.16.0)
Requirement already satisfied: ipython-genutils in /usr/local/lib/python3.10/dist-packages (from ipykernel->jupyter==1.0.0->d2l==0.17.5) (0.2.0)
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Requirement already satisfied: traitlets>=4.1.0 in /usr/local/lib/python3.10/dist-packages (from ipykernel->jupyter==1.0.0->d2l==0.17.5) (5.7.1)
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Requirement already satisfied: jupyterlab-widgets>=1.0.0 in /usr/local/lib/python3.10/dist-packages (from ipywidgets->jupyter==1.0.0->d2l==0.17.5) (3.0.10)
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Requirement already satisfied: pygments in /usr/local/lib/python3.10/dist-packages (from jupyter-console->jupyter==1.0.0->d2l==0.17.5) (2.16.1)
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Requirement already satisfied: nbclient>=0.5.0 in /usr/local/lib/python3.10/dist-packages (from nbconvert->jupyter==1.0.0->d2l==0.17.5) (0.10.0)
Requirement already satisfied: nbformat>=5.1 in /usr/local/lib/python3.10/dist-packages (from nbconvert->jupyter==1.0.0->d2l==0.17.5) (5.10.4)
Requirement already satisfied: pandocfilters>=1.4.1 in /usr/local/lib/python3.10/dist-packages (from nbconvert->jupyter==1.0.0->d2l==0.17.5) (1.5.1)
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Requirement already satisfied: pyzmq<25,>=17 in /usr/local/lib/python3.10/dist-packages (from notebook->jupyter==1.0.0->d2l==0.17.5) (23.2.1)
Requirement already satisfied: argon2-cffi in /usr/local/lib/python3.10/dist-packages (from notebook->jupyter==1.0.0->d2l==0.17.5) (23.1.0)
Requirement already satisfied: nest-asyncio>=1.5 in /usr/local/lib/python3.10/dist-packages (from notebook->jupyter==1.0.0->d2l==0.17.5) (1.6.0)
Requirement already satisfied: Send2Trash>=1.8.0 in /usr/local/lib/python3.10/dist-packages (from notebook->jupyter==1.0.0->d2l==0.17.5) (1.8.3)
Requirement already satisfied: terminado>=0.8.3 in /usr/local/lib/python3.10/dist-packages (from notebook->jupyter==1.0.0->d2l==0.17.5) (0.18.1)
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Requirement already satisfied: qtpy>=2.4.0 in /usr/local/lib/python3.10/dist-packages (from qtconsole->jupyter==1.0.0->d2l==0.17.5) (2.4.1)
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Requirement already satisfied: jedi>=0.16 in /usr/local/lib/python3.10/dist-packages (from ipython>=5.0.0->ipykernel->jupyter==1.0.0->d2l==0.17.5) (0.19.1)
Requirement already satisfied: decorator in /usr/local/lib/python3.10/dist-packages (from ipython>=5.0.0->ipykernel->jupyter==1.0.0->d2l==0.17.5) (4.4.2)
Requirement already satisfied: pickleshare in /usr/local/lib/python3.10/dist-packages (from ipython>=5.0.0->ipykernel->jupyter==1.0.0->d2l==0.17.5) (0.7.5)
Requirement already satisfied: backcall in /usr/local/lib/python3.10/dist-packages (from ipython>=5.0.0->ipykernel->jupyter==1.0.0->d2l==0.17.5) (0.2.0)
Requirement already satisfied: matplotlib-inline in /usr/local/lib/python3.10/dist-packages (from ipython>=5.0.0->ipykernel->jupyter==1.0.0->d2l==0.17.5) (0.1.7)
Requirement already satisfied: pexpect>4.3 in /usr/local/lib/python3.10/dist-packages (from ipython>=5.0.0->ipykernel->jupyter==1.0.0->d2l==0.17.5) (4.9.0)
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Requirement already satisfied: sniffio>=1.1 in /usr/local/lib/python3.10/dist-packages (from anyio<4,>=3.1.0->jupyter-server>=1.8->nbclassic>=0.4.7->notebook->jupyter==1.0.0->d2l==0.17.5) (1.3.1)
Requirement already satisfied: exceptiongroup in /usr/local/lib/python3.10/dist-packages (from anyio<4,>=3.1.0->jupyter-server>=1.8->nbclassic>=0.4.7->notebook->jupyter==1.0.0->d2l==0.17.5) (1.2.0)
Requirement already satisfied: pycparser in /usr/local/lib/python3.10/dist-packages (from cffi>=1.0.1->argon2-cffi-bindings->argon2-cffi->notebook->jupyter==1.0.0->d2l==0.17.5) (2.22)
Building wheels for collected packages: pandas
  Building wheel for pandas (pyproject.toml) ... [?25l[?25hdone
  Created wheel for pandas: filename=pandas-1.2.4-cp310-cp310-linux_x86_64.whl size=34333057 sha256=9fc84123762ca7690bf9255b36611a3a874d4ad9f175184ec1debcbe80364d4c
  Stored in directory: /root/.cache/pip/wheels/1b/10/28/2a37b26cf3e4dc59d82430e3812f8571518d2c1d81c288af98
Successfully built pandas
Installing collected packages: urllib3, numpy, idna, chardet, requests, pandas, matplotlib, d2l
  Attempting uninstall: urllib3
    Found existing installation: urllib3 2.0.7
    Uninstalling urllib3-2.0.7:
      Successfully uninstalled urllib3-2.0.7
  Attempting uninstall: numpy
    Found existing installation: numpy 1.25.2
    Uninstalling numpy-1.25.2:
      Successfully uninstalled numpy-1.25.2
  Attempting uninstall: idna
    Found existing installation: idna 3.7
    Uninstalling idna-3.7:
      Successfully uninstalled idna-3.7
  Attempting uninstall: chardet
    Found existing installation: chardet 5.2.0
    Uninstalling chardet-5.2.0:
      Successfully uninstalled chardet-5.2.0
  Attempting uninstall: requests
    Found existing installation: requests 2.31.0
    Uninstalling requests-2.31.0:
      Successfully uninstalled requests-2.31.0
  Attempting uninstall: pandas
    Found existing installation: pandas 2.0.3
    Uninstalling pandas-2.0.3:
      Successfully uninstalled pandas-2.0.3
  Attempting uninstall: matplotlib
    Found existing installation: matplotlib 3.7.1
    Uninstalling matplotlib-3.7.1:
      Successfully uninstalled matplotlib-3.7.1
  Attempting uninstall: d2l
    Found existing installation: d2l 1.0.0a0
    Uninstalling d2l-1.0.0a0:
      Successfully uninstalled d2l-1.0.0a0
[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.
arviz 0.15.1 requires pandas>=1.3.0, but you have pandas 1.2.4 which is incompatible.
bigframes 1.2.0 requires matplotlib>=3.7.1, but you have matplotlib 3.5.1 which is incompatible.
bigframes 1.2.0 requires pandas>=1.5.0, but you have pandas 1.2.4 which is incompatible.
bigframes 1.2.0 requires requests>=2.27.1, but you have requests 2.25.1 which is incompatible.
chex 0.1.86 requires numpy>=1.24.1, but you have numpy 1.21.5 which is incompatible.
flax 0.8.2 requires numpy>=1.22, but you have numpy 1.21.5 which is incompatible.
google-colab 1.0.0 requires pandas==2.0.3, but you have pandas 1.2.4 which is incompatible.
google-colab 1.0.0 requires requests==2.31.0, but you have requests 2.25.1 which is incompatible.
ibis-framework 8.0.0 requires pandas<3,>=1.2.5, but you have pandas 1.2.4 which is incompatible.
jax 0.4.26 requires numpy>=1.22, but you have numpy 1.21.5 which is incompatible.
jaxlib 0.4.26+cuda12.cudnn89 requires numpy>=1.22, but you have numpy 1.21.5 which is incompatible.
mizani 0.9.3 requires pandas>=1.3.5, but you have pandas 1.2.4 which is incompatible.
numba 0.58.1 requires numpy<1.27,>=1.22, but you have numpy 1.21.5 which is incompatible.
pandas-stubs 2.0.3.230814 requires numpy>=1.25.0; python_version >= "3.9", but you have numpy 1.21.5 which is incompatible.
plotnine 0.12.4 requires matplotlib>=3.6.0, but you have matplotlib 3.5.1 which is incompatible.
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[0mSuccessfully installed chardet-4.0.0 d2l-0.17.5 idna-2.10 matplotlib-3.5.1 numpy-1.21.5 pandas-1.2.4 requests-2.25.1 urllib3-1.26.18

import random
import torch
from d2l import torch as d2l

tokens = d2l.tokenize(d2l.read_time_machine())
# 因为每个文本行不一定是一个句子或一个段落，因此我们把所有文本行拼接到一起
corpus = [token for line in tokens for token in line]
vocab = d2l.Vocab(corpus)
vocab.token_freqs[:10]

[('the', 2261),
 ('i', 1267),
 ('and', 1245),
 ('of', 1155),
 ('a', 816),
 ('to', 695),
 ('was', 552),
 ('in', 541),
 ('that', 443),
 ('my', 440)]

这些词很无聊，通常被称为停用词（stop words），因此可以被过滤掉。

词频衰减的速度相当地快。 例如，最常用单词的词频对比，第10个还不到第1个的
1/5。 为了更好地理解，我们可以画出的词频图：

词频图

freqs = [freq for token, freq in vocab.token_freqs]
d2l.plot(freqs, xlabel='token: x', ylabel='frequency: n(x)',
         xscale='log', yscale='log')

二元语法的频率是否与一元语法的频率表现出相同的行为方式？

bigram_tokens = [pair for pair in zip(corpus[:-1], corpus[1:])]
bigram_vocab = d2l.Vocab(bigram_tokens)
bigram_vocab.token_freqs[:10]

[(('of', 'the'), 309),
 (('in', 'the'), 169),
 (('i', 'had'), 130),
 (('i', 'was'), 112),
 (('and', 'the'), 109),
 (('the', 'time'), 102),
 (('it', 'was'), 99),
 (('to', 'the'), 85),
 (('as', 'i'), 78),
 (('of', 'a'), 73)]

在十个最频繁的词对中，有九个是由两个停用词组成的， 只有一个与“the time”有关。 我们再进一步看看三元语法的频率是否表现出相同的行为方式？

trigram_tokens = [triple for triple in zip(
    corpus[:-2], corpus[1:-1], corpus[2:])]
trigram_vocab = d2l.Vocab(trigram_tokens)
trigram_vocab.token_freqs[:10]

[(('the', 'time', 'traveller'), 59),
 (('the', 'time', 'machine'), 30),
 (('the', 'medical', 'man'), 24),
 (('it', 'seemed', 'to'), 16),
 (('it', 'was', 'a'), 15),
 (('here', 'and', 'there'), 15),
 (('seemed', 'to', 'me'), 14),
 (('i', 'did', 'not'), 14),
 (('i', 'saw', 'the'), 13),
 (('i', 'began', 'to'), 13)]

直观地对比三种模型中的词元频率：一元语法、二元语法和三元语法。

bigram_freqs = [freq for token, freq in bigram_vocab.token_freqs]
trigram_freqs = [freq for token, freq in trigram_vocab.token_freqs]
d2l.plot([freqs, bigram_freqs, trigram_freqs], xlabel='token: x',
         ylabel='frequency: n(x)', xscale='log', yscale='log',
         legend=['unigram', 'bigram', 'trigram'])

随机采样

每次可以从数据中随机生成一个小批量。 在这里，参数batch_size指定了每个小批量中子序列样本的数目， 参数num_steps是每个子序列中预定义的时间步数。

def seq_data_iter_random(corpus, batch_size, num_steps):
    """使用随机抽样生成一个小批量子序列"""
    # 从随机偏移量开始对序列进行分区，随机范围包括num_steps-1
    corpus = corpus[random.randint(0, num_steps - 1):]
    # 减去1，是因为我们需要考虑标签
    num_subseqs = (len(corpus) - 1) // num_steps
    # 长度为num_steps的子序列的起始索引
    initial_indices = list(range(0, num_subseqs * num_steps, num_steps))
    # 在随机抽样的迭代过程中，
    # 来自两个相邻的、随机的、小批量中的子序列不一定在原始序列上相邻
    random.shuffle(initial_indices)

    def data(pos):
        # 返回从pos位置开始的长度为num_steps的序列
        return corpus[pos: pos + num_steps]

    num_batches = num_subseqs // batch_size
    for i in range(0, batch_size * num_batches, batch_size):
        # 在这里，initial_indices包含子序列的随机起始索引
        initial_indices_per_batch = initial_indices[i: i + batch_size]
        X = [data(j) for j in initial_indices_per_batch]
        Y = [data(j + 1) for j in initial_indices_per_batch]
        yield torch.tensor(X), torch.tensor(Y)

生成一个从0到34的序列。 假设批量大小为2，时间步数为5，这意味着可以生成6个“特征标签”子序列对。 如果设置小批量大小为2，我们只能得到3个小批量。

my_seq = list(range(35))
for X, Y in seq_data_iter_random(my_seq, batch_size=2, num_steps=5):
    print('X: ', X, '\nY:', Y)

X:  tensor([[23, 24, 25, 26, 27],
        [ 8,  9, 10, 11, 12]]) 
Y: tensor([[24, 25, 26, 27, 28],
        [ 9, 10, 11, 12, 13]])
X:  tensor([[13, 14, 15, 16, 17],
        [ 3,  4,  5,  6,  7]]) 
Y: tensor([[14, 15, 16, 17, 18],
        [ 4,  5,  6,  7,  8]])
X:  tensor([[18, 19, 20, 21, 22],
        [28, 29, 30, 31, 32]]) 
Y: tensor([[19, 20, 21, 22, 23],
        [29, 30, 31, 32, 33]])

顺序分区

在迭代过程中，除了对原始序列可以随机抽样外， 我们还可以保证两个相邻的小批量中的子序列在原始序列上也是相邻的。 这种策略在基于小批量的迭代过程中保留了拆分的子序列的顺序，因此称为顺序分区。

def seq_data_iter_sequential(corpus, batch_size, num_steps):
    """使用顺序分区生成一个小批量子序列"""
    # 从随机偏移量开始划分序列
    offset = random.randint(0, num_steps)
    num_tokens = ((len(corpus) - offset - 1) // batch_size) * batch_size
    Xs = torch.tensor(corpus[offset: offset + num_tokens])
    Ys = torch.tensor(corpus[offset + 1: offset + 1 + num_tokens])
    Xs, Ys = Xs.reshape(batch_size, -1), Ys.reshape(batch_size, -1)
    num_batches = Xs.shape[1] // num_steps
    for i in range(0, num_steps * num_batches, num_steps):
        X = Xs[:, i: i + num_steps]
        Y = Ys[:, i: i + num_steps]
        yield X, Y

基于相同的设置，通过顺序分区读取每个小批量的子序列的特征X和标签Y。 通过将它们打印出来可以发现： 迭代期间来自两个相邻的小批量中的子序列在原始序列中确实是相邻的。

for X, Y in seq_data_iter_sequential(my_seq, batch_size=2, num_steps=5):
    print('X: ', X, '\nY:', Y)

X:  tensor([[ 1,  2,  3,  4,  5],
        [17, 18, 19, 20, 21]]) 
Y: tensor([[ 2,  3,  4,  5,  6],
        [18, 19, 20, 21, 22]])
X:  tensor([[ 6,  7,  8,  9, 10],
        [22, 23, 24, 25, 26]]) 
Y: tensor([[ 7,  8,  9, 10, 11],
        [23, 24, 25, 26, 27]])
X:  tensor([[11, 12, 13, 14, 15],
        [27, 28, 29, 30, 31]]) 
Y: tensor([[12, 13, 14, 15, 16],
        [28, 29, 30, 31, 32]])

将上面的两个采样函数包装到一个类中， 以便稍后可以将其用作数据迭代器.

class SeqDataLoader:
    """加载序列数据的迭代器"""
    def __init__(self, batch_size, num_steps, use_random_iter, max_tokens):
        if use_random_iter:
            self.data_iter_fn = d2l.seq_data_iter_random
        else:
            self.data_iter_fn = d2l.seq_data_iter_sequential
        self.corpus, self.vocab = d2l.load_corpus_time_machine(max_tokens)
        self.batch_size, self.num_steps = batch_size, num_steps

    def __iter__(self):
        return self.data_iter_fn(self.corpus, self.batch_size, self.num_steps)

定义了一个函数load_data_time_machine， 它同时返回数据迭代器和词表， 因此可以与其他带有load_data前缀的函数类似使用

def load_data_time_machine(batch_size, num_steps,
                           use_random_iter=False, max_tokens=10000):
    """返回时光机器数据集的迭代器和词表"""
    data_iter = SeqDataLoader(
        batch_size, num_steps, use_random_iter, max_tokens)
    return data_iter, data_iter.vocab