7_language_models_and_dataset.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import torch\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('the', 2261),\n",
       " ('i', 1267),\n",
       " ('and', 1245),\n",
       " ('of', 1155),\n",
       " ('a', 816),\n",
       " ('to', 695),\n",
       " ('was', 552),\n",
       " ('in', 541),\n",
       " ('that', 443),\n",
       " ('my', 440),\n",
       " ('it', 437),\n",
       " ('had', 354),\n",
       " ('me', 281),\n",
       " ('as', 270),\n",
       " ('at', 243),\n",
       " ('for', 221),\n",
       " ('with', 216),\n",
       " ('but', 204),\n",
       " ('time', 200),\n",
       " ('were', 158)]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 默认按照words来tokenize\n",
    "tokens = d2l.tokenize(d2l.read_time_machine())\n",
    "corpus = [token for line in tokens for token in line]\n",
    "vocab = d2l.Vocab(corpus)\n",
    "# vocab.token_freqs[:5],vocab.idx_to_token[:5],vocab.token_to_idx['time'],vocab[tokens[0]]\n",
    "vocab.token_freqs[:20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
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   "source": [
    "freqs = [freq for _, freq in vocab.token_freqs]\n",
    "# 为什么要用对数坐标?\n",
    "# 自然语言遵守Zipf定律，\n",
    "# 即在自然语言中，第n频繁的单词的频率大约为最频繁单词频率的a*1/n。\n",
    "# 在对数坐标图中，这种关系表现为一条直线\n",
    "d2l.plot(freqs,xlabel='token: x',ylabel='frequency:n(x)',\n",
    "         xscale='log', yscale='log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 为什么说技术统计和平滑来建模单词是不行的 ###\n",
    "1. 通过平滑增加低频词的频率，会大大高估低频词的频率，导致模型的预测不准确  \n",
    "1. 忽略了语法和语义结构，无法捕捉到语言的复杂性  \n",
    "1. 数据稀疏性问题导致的统计不准确，尤其是在处理新词和未见词时  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(('of', 'the'), 309),\n",
       " (('in', 'the'), 169),\n",
       " (('i', 'had'), 130),\n",
       " (('i', 'was'), 112),\n",
       " (('and', 'the'), 109),\n",
       " (('the', 'time'), 102),\n",
       " (('it', 'was'), 99),\n",
       " (('to', 'the'), 85),\n",
       " (('as', 'i'), 78),\n",
       " (('of', 'a'), 73)]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 尝试二元语法(计算相邻的两个词的概率)\n",
    "# corpus[:-1]除最后一个元素外的所有元素\n",
    "# corpus[1:]除第一个元素外的所有元素\n",
    "bigram_token = [pair for pair in zip(corpus[:-1],corpus[1:])]\n",
    "bigram_vocab = d2l.Vocab(bigram_token)\n",
    "bigram_vocab.token_freqs[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(('the', 'time', 'traveller'), 59),\n",
       " (('the', 'time', 'machine'), 30),\n",
       " (('the', 'medical', 'man'), 24),\n",
       " (('it', 'seemed', 'to'), 16),\n",
       " (('it', 'was', 'a'), 15),\n",
       " (('here', 'and', 'there'), 15),\n",
       " (('seemed', 'to', 'me'), 14),\n",
       " (('i', 'did', 'not'), 14),\n",
       " (('i', 'saw', 'the'), 13),\n",
       " (('i', 'began', 'to'), 13)]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trigram_token = [trip for trip in zip(\n",
    "    corpus[:-2],corpus[1:-1],corpus[2:]\n",
    ")]\n",
    "trigram_vocab = d2l.Vocab(trigram_token)\n",
    "trigram_vocab.token_freqs[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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   "source": [
    "bigram_freqs = [freq for _,freq in bigram_vocab.token_freqs]\n",
    "trigram_freqs = [freq for _,freq in trigram_vocab.token_freqs]\n",
    "d2l.plot([freqs,bigram_freqs,trigram_freqs], xlabel='token:x',\n",
    "         ylabel='frequency:n(x)',xscale='log',yscale='log',\n",
    "         legend=['unigram','bigram','trigram'])"
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   "metadata": {},
   "source": [
    "这张图非常令人振奋！原因有很多：\n",
    "\n",
    "1. 除了一元语法词，单词序列似乎也遵循齐普夫定律，\n",
    "尽管公式 :eqref:`eq_zipf_law`中的指数$\\alpha$更小\n",
    "（指数的大小受序列长度的影响）；\n",
    "2. 词表中$n$元组的数量并没有那么大，这说明语言中存在相当多的结构，\n",
    "这些结构给了我们应用模型的希望；\n",
    "3. 很多$n$元组很少出现，这使得拉普拉斯平滑非常不适合语言建模。\n",
    "作为代替，我们将使用基于深度学习的模型。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 随机采样\n",
    "def seq_data_iter_random(corpus, batch_size, num_steps):\n",
    "    # 从0~num_steps-1的返回内选一个随机偏移量开始对序列分区\n",
    "    #   假设corpus长度为30000，num_steps为5，那么初始索引可能是0~4，假设是0\n",
    "    corpus = corpus[random.randint(0,num_steps-1):]\n",
    "    #   29999//5=5999，所以有5999个子序列，每个子序列长度为5\n",
    "    num_subseqs = (len(corpus)-1) // num_steps\n",
    "    # 计算子序列的起始位置列表\n",
    "    #   intial_indices为[0,5,10,...,29990]\n",
    "    initial_indices = list(range(0,num_subseqs*num_steps,num_steps))\n",
    "    # 打乱起始位置实现随机采样\n",
    "    random.shuffle(initial_indices)\n",
    "\n",
    "    def data(pos):\n",
    "        # 返回pos开始的子序列\n",
    "        return corpus[pos:pos+num_steps]\n",
    "    \n",
    "    # 计算批量的长度\n",
    "    #   假设batch_size=3, num_batches=5999//3=1999\n",
    "    num_batches = num_subseqs // batch_size\n",
    "    # 计算每个批量的起始位置\n",
    "    #   [0, 3,..., 1994]\n",
    "    for i in range(0,batch_size*num_batches,batch_size):\n",
    "        # 从initial_indices中取出batch_size个起始位置\n",
    "        #   假设initial_indices_per_batch=[5,200,65]\n",
    "        initial_indices_per_batch = initial_indices[i:i+batch_size]\n",
    "        # 批量中的相邻子序列在原始数据中不一定相邻\n",
    "        # Y中的每个元素都是X在原序列中对应的下一个元素\n",
    "        #   X=[[5,6,7,8,9],[200,201,202,203,204],[65,66,67,68,69]]\n",
    "        #   Y=[[6,7,8,9,10],[201,202,203,204,205],[66,67,68,69,70]]\n",
    "        X = [data(j) for j in initial_indices_per_batch]\n",
    "        Y = [data(j+1) for j in initial_indices_per_batch]\n",
    "        yield torch.tensor(X),torch.tensor(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: tensor([[21, 22, 23, 24, 25],\n",
      "        [26, 27, 28, 29, 30]]) \n",
      "Y: tensor([[22, 23, 24, 25, 26],\n",
      "        [27, 28, 29, 30, 31]])\n",
      "X: tensor([[16, 17, 18, 19, 20],\n",
      "        [11, 12, 13, 14, 15]]) \n",
      "Y: tensor([[17, 18, 19, 20, 21],\n",
      "        [12, 13, 14, 15, 16]])\n",
      "X: tensor([[ 6,  7,  8,  9, 10],\n",
      "        [ 1,  2,  3,  4,  5]]) \n",
      "Y: tensor([[ 7,  8,  9, 10, 11],\n",
      "        [ 2,  3,  4,  5,  6]])\n"
     ]
    }
   ],
   "source": [
    "# 假设有长度为35的序列\n",
    "my_seq = list(range(35))\n",
    "# (35-1)//5=6, 有6个\"特征-标签\"子序列对\n",
    "for X,Y in seq_data_iter_random(my_seq, 2, 5):\n",
    "    print('X:',X,'\\nY:',Y)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 顺序分区\n",
    "def seq_data_iter_sequential(corpus, batch_size, num_steps): #@save\n",
    "    # 开始都是从随机偏移量划分\n",
    "    #   假设offset=0,batch_size=2,num_steps=5,corpus=35\n",
    "    offset = random.randint(0,num_steps)\n",
    "    # 将数据按 batch_size 划分后可以使用的总词元数\n",
    "    # 这个值确保划分后的数据可以整除 batch_size\n",
    "    #   num_tokens = (35-0-1)//2*2=34\n",
    "    num_tokens = ((len(corpus)-offset-1)//batch_size)*batch_size\n",
    "    # 获取X和Y要用到的所有词元\n",
    "    #   Xs=corpus[0:34],Ys=corpus[1:35]\n",
    "    Xs = torch.tensor(corpus[offset:offset+num_tokens])\n",
    "    Ys = torch.tensor(corpus[offset+1:offset+1+num_tokens])\n",
    "    # 按 batch_size 划分 X 和 Y，也即Xs和Ys中含有batch_size个序列\n",
    "    #   Xs.shape = (2,17), Ys.shape = (2,17)\n",
    "    Xs,Ys = Xs.reshape(batch_size,-1), Ys.reshape(batch_size,-1)\n",
    "    # 除以时间步长得到总batch数\n",
    "    #   num_batches = 17//5=3\n",
    "    num_batches = Xs.shape[1] // num_steps\n",
    "    for i in range(0,num_steps*num_batches,num_steps):\n",
    "        X = Xs[:,i:i+num_steps]\n",
    "        Y = Ys[:,i:i+num_steps]\n",
    "        yield X,Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: tensor([[ 0,  1,  2,  3,  4],\n",
      "        [17, 18, 19, 20, 21]]) \n",
      "Y: tensor([[ 1,  2,  3,  4,  5],\n",
      "        [18, 19, 20, 21, 22]])\n",
      "X: tensor([[ 5,  6,  7,  8,  9],\n",
      "        [22, 23, 24, 25, 26]]) \n",
      "Y: tensor([[ 6,  7,  8,  9, 10],\n",
      "        [23, 24, 25, 26, 27]])\n",
      "X: tensor([[10, 11, 12, 13, 14],\n",
      "        [27, 28, 29, 30, 31]]) \n",
      "Y: tensor([[11, 12, 13, 14, 15],\n",
      "        [28, 29, 30, 31, 32]])\n"
     ]
    }
   ],
   "source": [
    "for X,Y in seq_data_iter_sequential(my_seq,2,5):\n",
    "    print('X:',X,'\\nY:',Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "class SeqDataLoader: #@save\n",
    "    def __init__(self, batch_size, num_steps, use_random_iter, max_tokens):\n",
    "        # 把两个采样函数放到一个类里\n",
    "        if use_random_iter:\n",
    "            self.data_iter_fn = d2l.seq_data_iter_random\n",
    "        else:\n",
    "            self.data_iter_fn = d2l.seq_data_iter_sequential\n",
    "        # 统计词频（vocab），把词元转换成索引（corpus）\n",
    "        self.corpus,self.vocab = d2l.load_corpus_time_machine(max_tokens)\n",
    "        self.batch_size,self.num_steps = batch_size, num_steps\n",
    "    \n",
    "    def __iter__(self):\n",
    "        # 返回特征和标签的迭代器\n",
    "        return self.data_iter_fn(self.corpus, self.batch_size, self.num_steps)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_data_time_machine(batch_size, num_steps, #@save\n",
    "                           use_random_iter=False, max_tokens=10000):\n",
    "        data_iter = SeqDataLoader(\n",
    "                batch_size, num_steps, use_random_iter, max_tokens)\n",
    "        # 返回迭代器和词频表\n",
    "        return data_iter, data_iter.vocab"
   ]
  }
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