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：
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。
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。
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：
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。
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。
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。
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。
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.shape
mask = 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_trans
return score, history
def 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_listCRF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, Uniform
def 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_tags
self.batch_first = batch_first
self.reduction = reduction
self.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.shape
emissions = emissions.swapaxes(0, 1)
tags = tags.swapaxes(0, 1)
else:
max_length, batch_size = tags.shape
if 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 - numerator
if self.reduction == 'none':
return llh
if 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 = 32
training_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 tqdm
steps = 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)
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