BIOE label:
B start of an entity; O background; I other parts of an entity
We first compute a certain score.
python
def compute_score(emissions, tags, seq_ends, mask, trans, start_trans, end_trans):
seq_length, batch_size = tag.shape
mask = mask.astype(emissions.dtype)
score = start_trans[tags[0]]
score += emissions[0, mnp.arange(batch_size),tags[0]]
for i in range(1, seq_length):
score += trans[tags[i-1], tags[i]] * mask[i]
score += emissions[i, mnp.arange(batch_size), tags[i]] * mask[i]
last_tags = tags[seq_ends, mnp.arange(batch_size)]
score += end_trans[last_tags]
return scorehow to understand the score?
Just two thing:
- When we consider a input seq: x = {x1, x2, x3...} and
a label y = {y1, y2, y3 ...} correspondingly, there exists a transportation probablity
where score(x, y) can represent the probablity from x to generate y.
- Okay, so we need to acculumate probablity of x_i to y_i, and y_(i-1) to y_i since it is important to generate a reasonable next label after one has been generated.
so the former probablity is called emission probablity , and the next is called transportation probablity
, and we can define a kind of score by:
Next we define a concept called normalizer., which represents the denominator of the formula below:
python
def compute_normalizer(emissions, mask, trans, start_trans, end_trans):
seq_length = emissions.shape[0]
score = start_trans + emissions[0]
for i in range(1, seq_length):
broadcast_emissions = emissions[i].expand_dims(1)
next_score = broadcast_score + trans + broadcast_emissions
next_score = ops.logsumexp(next_score, axis = 1)
score = mnp.where(mask[i].expand_dims(1), next_score, score)
score += end_trans
return ops.logsumexp(score, axis = 1)Viterbi算法
python
def viterbi_decode(emissions, mask, trans, start_trans, end_trans):
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
indices = next_score.argmax(axis=1)
history += (indeices, )
next_score = next_score.max(axis = 1)
score = mnp.where(mask[i].expand_dims(1), next_score, score)
score += end_trans
return score, history
reasons:
Here is a decoder to get the best sequence predicted.
python
def post_decode(score, history,seq_length):
batch_size = seq_length.shape[0]
seq_ends = seq_length - 1
best_tags_list = []
for idx in range(batch_size):
batch_last_tag = score[idx].argmax(axis = 0)
best_tags = [int(best_last_tag.asnumpy())]
for hist in reversed(history[:seq_ends[idx]]):
best_last_tag = hist[idx][best_tags[-1]]
best_tags.append(int(best_last_tag.asnumpy()))
best_tags.reverse()
best_tags_list.append(best_tags)
return best_tags_list
python
def sequence_mask(seq_length, max_length, batch_first=False):
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)
numerator = compute_score(emissions, tags, seq_length- 1, mask, self.transitions, self.start_transitions, self.end_transitions)
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)sequence_mask is mean to generate mask_matrix.
Next we construct a BiLSTM CRF model.
the architure is :
nn.Embedding -> nn.LSTM -> nn.Dense -> CRF
where LSTM is mean to get the feature and get the emission matrix after Dense layer , finally into CRF layer.
python
class BiLSTM_CRF(nn.Cell):
def __init__(self, vocab_size, embbeding_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, bidirection=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_outsNow an example is given.
python
enbedding_dim = 16
hidden_dim = 32
training_data = [(
'清华大学坐落在首都北京'.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, '0': 2}we instantialize the model and choose optimizers into wrapper together.
python
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 lossprocess the data by patching data into batch and pad those sequence not enough long ,
python
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['0'] 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)
python
data, label, seq_length = prepare_sequence(training_data, word_to_idx, tag_to_idx)we visualize the training.
python
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)
python
score, history = model(data, seq_length)
predict = post_decode(score, history, seq_length)
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
python
sequence_to_tag(predict,idx_to_tag)