昇思25天学习打卡营第19天|LSTM+CRF序列标注

概述

序列标注指给定输入序列，给序列中每个Token进行标注标签的过程。序列标注问题通常用于从文本中进行信息抽取，包括分词(Word Segmentation)、词性标注(Position Tagging)、命名实体识别(Named Entity Recognition, NER)等。

条件随机场（CRF）

对序列进行标注，实际上是对序列中每个Token进行标签预测，可以直接视作简单的多分类问题。但是序列标注不仅仅需要对单个Token进行分类预测，同时相邻Token直接有关联关系。

设 $x=\begin{Bmatrix} x_0,...,x_n \end{Bmatrix}$ 为输入序列， $y=\begin{Bmatrix} y_0,...,y_n \end{Bmatrix}$ 为输出的标注序列，输出序列y的概率为：

$P(y|x)=\frac{exp(Score(x,y))}{\sum_{y'\in Y}exp(Score(x,y'))}$

定义两个概率函数

1. 发射概率函数 $\psi _{EMIT}$ ：表示 $x_i\rightarrow y_i$ 的概率

2. 转移概率函数 $\psi _{TRANS}$ ：表示 $y_{i-1}\rightarrow y_i$ 的概率

于是可以得到Score的计算公式：

$Score(x,y)=\sum_ilog\psi _{EMIT}(x_i\rightarrow y_i)+log\psi_{TRANS}(y_{i-1}\rightarrow y_i)$

设标签集合为T，构造大小为 $\left | T \right |\times \left | T \right |$ 的矩阵P，用于存储标签间的转移概率。

实现CRF层的前向训练部分，将CRF和损失函数做合并，选择分类问题常用的负对数似然函数，则有：

$Loss=-log(P(y|x))$

$Loss=-log(\frac{exp(Score(x,y))}{\sum_{y'\in Y}exp(Score(x,y'))}) \newline=log(\sum_{y'\in Y}exp(Score(x,y'))-Score(x,y))$

Score计算

def compute_score(emissions, tags, seq_ends, mask, trans, start_trans, end_trans):# emissions: (seq_length, batch_size, num_tags)# tags: (seq_length, batch_size)# mask: (seq_length, batch_size)seq_length, batch_size = tags.shapemask = mask.astype(emissions.dtype)# 将score设置为初始转移概率# shape: (batch_size,)score = start_trans[tags[0]]# score += 第一次发射概率# shape: (batch_size,)score += emissions[0, mnp.arange(batch_size), tags[0]]for i in range(1, seq_length):# 标签由i-1转移至i的转移概率（当mask == 1时有效）# shape: (batch_size,)score += trans[tags[i - 1], tags[i]] * mask[i]# 预测tags[i]的发射概率（当mask == 1时有效）# shape: (batch_size,)score += emissions[i, mnp.arange(batch_size), tags[i]] * mask[i]# 结束转移# shape: (batch_size,)last_tags = tags[seq_ends, mnp.arange(batch_size)]# score += 结束转移概率# shape: (batch_size,)score += end_trans[last_tags]return score

Normalizer计算

Normalizer可以改写为以下形式：

$log(\sum_{y'_{0,i}\in Y}exp(Score_i))=log(\sum_{y'_{0,i-1}\in Y}exp(Score_{i-1}+h_i+P))$

Normalizer代码实现如下：

def compute_normalizer(emissions, mask, trans, start_trans, end_trans):# emissions: (seq_length, batch_size, num_tags)# mask: (seq_length, batch_size)seq_length = emissions.shape[0]# 将score设置为初始转移概率，并加上第一次发射概率# shape: (batch_size, num_tags)score = start_trans + emissions[0]for i in range(1, seq_length):# 扩展score的维度用于总score的计算# shape: (batch_size, num_tags, 1)broadcast_score = score.expand_dims(2)# 扩展emission的维度用于总score的计算# shape: (batch_size, 1, num_tags)broadcast_emissions = emissions[i].expand_dims(1)# 根据公式(7)，计算score_i# 此时broadcast_score是由第0个到当前Token所有可能路径# 对应score的log_sum_exp# shape: (batch_size, num_tags, num_tags)next_score = broadcast_score + trans + broadcast_emissions# 对score_i做log_sum_exp运算，用于下一个Token的score计算# shape: (batch_size, num_tags)next_score = ops.logsumexp(next_score, axis=1)# 当mask == 1时，score才会变化# shape: (batch_size, num_tags)score = mnp.where(mask[i].expand_dims(1), next_score, score)# 最后加结束转移概率# shape: (batch_size, num_tags)score += end_trans# 对所有可能的路径得分求log_sum_exp# shape: (batch_size,)return ops.logsumexp(score, axis=1)

Viterbi算法

在完成前向训练部分后，需要实现解码部分。Viterbi算法与计算Normalizer类似，使用动态规划求解所有可能的预测序列得分。不同的是在解码时同时需要将第i个Token对应的score取值最大的标签保存，供后续使用Viterbi算法求解最优预测序列使用。

取得最大概率得分ScoreScore，以及每个Token对应的标签历史HistoryHistory后，根据Viterbi算法可以得到公式：

$P_{0,i}=max(P_{0,i-1})+P_{i-1,i}$

代码实现：

def viterbi_decode(emissions, mask, trans, start_trans, end_trans):# emissions: (seq_length, batch_size, num_tags)# mask: (seq_length, batch_size)seq_length = mask.shape[0]score = start_trans + emissions[0]history = ()for i in range(1, seq_length):broadcast_score = score.expand_dims(2)broadcast_emission = emissions[i].expand_dims(1)next_score = broadcast_score + trans + broadcast_emission# 求当前Token对应score取值最大的标签，并保存indices = next_score.argmax(axis=1)history += (indices,)next_score = next_score.max(axis=1)score = mnp.where(mask[i].expand_dims(1), next_score, score)score += end_transreturn score, historydef post_decode(score, history, seq_length):# 使用Score和History计算最佳预测序列batch_size = seq_length.shape[0]seq_ends = seq_length - 1# shape: (batch_size,)best_tags_list = []# 依次对一个Batch中每个样例进行解码for idx in range(batch_size):# 查找使最后一个Token对应的预测概率最大的标签，# 并将其添加至最佳预测序列存储的列表中best_last_tag = score[idx].argmax(axis=0)best_tags = [int(best_last_tag.asnumpy())]# 重复查找每个Token对应的预测概率最大的标签，加入列表for hist in reversed(history[:seq_ends[idx]]):best_last_tag = hist[idx][best_tags[-1]]best_tags.append(int(best_last_tag.asnumpy()))# 将逆序求解的序列标签重置为正序best_tags.reverse()best_tags_list.append(best_tags)return best_tags_list

CRF层

CRF的输入需要考虑输入序列的真实长度，因此除发射矩阵和标签外，加入 seq_length 参数传入序列Padding前的长度，并实现生成mask矩阵的 sequence_mask 方法。

代码实现：

import mindspore as ms
import mindspore.nn as nn
import mindspore.ops as ops
import mindspore.numpy as mnp
from mindspore.common.initializer import initializer, Uniformdef sequence_mask(seq_length, max_length, batch_first=False):"""根据序列实际长度和最大长度生成mask矩阵"""range_vector = mnp.arange(0, max_length, 1, seq_length.dtype)result = range_vector < seq_length.view(seq_length.shape + (1,))if batch_first:return result.astype(ms.int64)return result.astype(ms.int64).swapaxes(0, 1)class CRF(nn.Cell):def __init__(self, num_tags: int, batch_first: bool = False, reduction: str = 'sum') -> None:if num_tags <= 0:raise ValueError(f'invalid number of tags: {num_tags}')super().__init__()if reduction not in ('none', 'sum', 'mean', 'token_mean'):raise ValueError(f'invalid reduction: {reduction}')self.num_tags = num_tagsself.batch_first = batch_firstself.reduction = reductionself.start_transitions = ms.Parameter(initializer(Uniform(0.1), (num_tags,)), name='start_transitions')self.end_transitions = ms.Parameter(initializer(Uniform(0.1), (num_tags,)), name='end_transitions')self.transitions = ms.Parameter(initializer(Uniform(0.1), (num_tags, num_tags)), name='transitions')def construct(self, emissions, tags=None, seq_length=None):if tags is None:return self._decode(emissions, seq_length)return self._forward(emissions, tags, seq_length)def _forward(self, emissions, tags=None, seq_length=None):if self.batch_first:batch_size, max_length = tags.shapeemissions = emissions.swapaxes(0, 1)tags = tags.swapaxes(0, 1)else:max_length, batch_size = tags.shapeif seq_length is None:seq_length = mnp.full((batch_size,), max_length, ms.int64)mask = sequence_mask(seq_length, max_length)# shape: (batch_size,)numerator = compute_score(emissions, tags, seq_length-1, mask, self.transitions, self.start_transitions, self.end_transitions)# shape: (batch_size,)denominator = compute_normalizer(emissions, mask, self.transitions, self.start_transitions, self.end_transitions)# shape: (batch_size,)llh = denominator - numeratorif self.reduction == 'none':return llhif self.reduction == 'sum':return llh.sum()if self.reduction == 'mean':return llh.mean()return llh.sum() / mask.astype(emissions.dtype).sum()def _decode(self, emissions, seq_length=None):if self.batch_first:batch_size, max_length = emissions.shape[:2]emissions = emissions.swapaxes(0, 1)else:batch_size, max_length = emissions.shape[:2]if seq_length is None:seq_length = mnp.full((batch_size,), max_length, ms.int64)mask = sequence_mask(seq_length, max_length)return viterbi_decode(emissions, mask, self.transitions, self.start_transitions, self.end_transitions)

BiLSTM+CRF模型

其中LSTM提取序列特征，经过Dense层变换获得发射概率矩阵，最后送入CRF层。具体实现如下：

class BiLSTM_CRF(nn.Cell):def __init__(self, vocab_size, embedding_dim, hidden_dim, num_tags, padding_idx=0):super().__init__()self.embedding = nn.Embedding(vocab_size, embedding_dim, padding_idx=padding_idx)self.lstm = nn.LSTM(embedding_dim, hidden_dim // 2, bidirectional=True, batch_first=True)self.hidden2tag = nn.Dense(hidden_dim, num_tags, 'he_uniform')self.crf = CRF(num_tags, batch_first=True)def construct(self, inputs, seq_length, tags=None):embeds = self.embedding(inputs)outputs, _ = self.lstm(embeds, seq_length=seq_length)feats = self.hidden2tag(outputs)crf_outs = self.crf(feats, tags, seq_length)return crf_outs

完成模型设计后，我们生成两句例子和对应的标签，并构造词表和标签表。

embedding_dim = 16
hidden_dim = 32training_data = [("清 华 大 学 坐 落 于 首 都 北 京".split(),"B I I I O O O O O B I".split()
), ("重 庆 是 一 个 魔 幻 城 市".split(),"B I O O O O O O O".split()
)]word_to_idx = {}
word_to_idx['<pad>'] = 0
for sentence, tags in training_data:for word in sentence:if word not in word_to_idx:word_to_idx[word] = len(word_to_idx)tag_to_idx = {"B": 0, "I": 1, "O": 2}

接下来实例化模型，选择优化器并将模型和优化器送入Wrapper。

model = BiLSTM_CRF(len(word_to_idx), embedding_dim, hidden_dim, len(tag_to_idx))
optimizer = nn.SGD(model.trainable_params(), learning_rate=0.01, weight_decay=1e-4)grad_fn = ms.value_and_grad(model, None, optimizer.parameters)def train_step(data, seq_length, label):loss, grads = grad_fn(data, seq_length, label)optimizer(grads)return loss

将生成的数据打包成Batch，按照序列最大长度，对长度不足的序列进行填充，分别返回输入序列、输出标签和序列长度构成的Tensor。

def prepare_sequence(seqs, word_to_idx, tag_to_idx):seq_outputs, label_outputs, seq_length = [], [], []max_len = max([len(i[0]) for i in seqs])for seq, tag in seqs:seq_length.append(len(seq))idxs = [word_to_idx[w] for w in seq]labels = [tag_to_idx[t] for t in tag]idxs.extend([word_to_idx['<pad>'] for i in range(max_len - len(seq))])labels.extend([tag_to_idx['O'] for i in range(max_len - len(seq))])seq_outputs.append(idxs)label_outputs.append(labels)return ms.Tensor(seq_outputs, ms.int64), \ms.Tensor(label_outputs, ms.int64), \ms.Tensor(seq_length, ms.int64)

对模型进行预编译后，训练500个step。

from tqdm import tqdmsteps = 500
with tqdm(total=steps) as t:for i in range(steps):loss = train_step(data, seq_length, label)t.set_postfix(loss=loss)t.update(1)

最后将预测的index序列转换为标签序列，打印输出结果，查看效果。

idx_to_tag = {idx: tag for tag, idx in tag_to_idx.items()}def sequence_to_tag(sequences, idx_to_tag):outputs = []for seq in sequences:outputs.append([idx_to_tag[i] for i in seq])return outputssequence_to_tag(predict, idx_to_tag)

得到输出标签

[['B', 'I', 'I', 'I', 'O', 'O', 'O', 'O', 'O', 'B', 'I'],['B', 'I', 'O', 'O', 'O', 'O', 'O', 'O', 'O']]

总结

LSTM用于提取序列特征，CRF用于序列标注，从而实现语义的切分。