LSTM（Long Short-Term Memory，长短时记忆网络）是一种特殊的循环神经网络（RNN），由Hochreiter和Schmidhuber在1997年提出。它旨在解决传统RNN在处理长距离依赖问题时出现的梯度消失和梯度爆炸问题。以下是LSTM的一些主要特点：

1. 细胞状态（Cell State）：LSTM的核心是细胞状态，它贯穿整个LSTM网络，使得信息可以在网络中长时间传递。

2. 门结构（Gates）：LSTM通过门结构来控制信息的流入、流出和遗忘。主要包括以下三个门：

   • 遗忘门（Forget Gate）：决定从细胞状态中丢弃什么信息。
   • 输入门（Input Gate）：决定哪些新的信息被存储在细胞状态中。
   • 输出门（Output Gate）：决定从细胞状态中输出什么信息。

3. 梯度消失和梯度爆炸问题的缓解：由于LSTM的门结构，它能够在长序列中保持稳定的梯度，从而有效地缓解梯度消失和梯度爆炸问题。

CRF（Conditional Random Field，条件随机场）是一种概率图模型，常用于自然语言处理（NLP）中的序列标注任务，如词性标注、命名实体识别（NER）等。CRF模型能够考虑上下文信息，对序列中的每个元素（如词语）进行标注，使得整个序列的标注结果尽可能合理。

以下是CRF的一些关键特点：

1. 无向图：CRF是一种无向图模型，它假设序列中的每个元素与其相邻元素之间存在依赖关系。

2. 条件概率：CRF模型定义了一个条件概率分布，它表示在给定输入序列的情况下，输出标签序列的概率。

3. 特征函数：CRF模型使用特征函数来描述输入与输出之间的关系。特征函数可以是基于输入序列和输出标签的任意函数，例如当前词、前后词、词性等。

4. 全局最优标注：CRF在预测时会考虑整个序列的信息，寻找全局最优的标签序列，而不是单独对每个元素进行最优标注。

5. 训练与解码：CRF的训练通常使用最大似然估计，而解码（即预测）时通常使用维特比算法（Viterbi algorithm）来找到最有可能的标签序列。

CRF模型的结构通常包括以下两个部分：

• 发射特征（Emission Features）：这些特征与输入序列中的每个元素相关，描述了输入元素与其对应标签的关系。
• 转移特征（Transition Features）：这些特征描述了标签序列中相邻标签之间的关系。

CRF模型的优势在于它能够有效地利用上下文信息，并且能够通过特征函数灵活地定义输入与输出之间的关系。这使得CRF在处理序列标注问题时通常比其他模型（如基于规则的模型或简单的概率模型）表现得更好。

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

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

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

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

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
embedding_dim = 16
hidden_dim = 32training_data = [("清 华 大 学 ".split(),"B I I I ".split()
), ("重 庆 ".split(),"B I ".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}len(word_to_idx)
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
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)
data, label, seq_length = prepare_sequence(training_data, word_to_idx, tag_to_idx)
data.shape, label.shape, seq_length.shape
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)
score, history = model(data, seq_length)
score
predict = post_decode(score, history, seq_length)
predict
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 outputs
sequence_to_tag(predict, idx_to_tag)