14.10. Pretraining BERT¶ Open the notebook in SageMaker Studio Lab
With the BERT model implemented in Section 14.8 and the pretraining examples generated from the WikiText-2 dataset in Section 14.9, we will pretrain BERT on the WikiText-2 dataset in this section.
from mxnet import autograd, gluon, init, np, npx
from d2l import mxnet as d2l
npx.set_np()
import torch
from torch import nn
from d2l import torch as d2l
To start, we load the WikiText-2 dataset as minibatches of pretraining examples for masked language modeling and next sentence prediction. The batch size is 512 and the maximum length of a BERT input sequence is 64. Note that in the original BERT model, the maximum length is 512.
batch_size, max_len = 512, 64
train_iter, vocab = d2l.load_data_wiki(batch_size, max_len)
batch_size, max_len = 512, 64
train_iter, vocab = d2l.load_data_wiki(batch_size, max_len)
14.10.1. Pretraining BERT¶
The original BERT has two versions of different model sizes (). The base model (\(\text{BERT}_{\text{BASE}}\)) uses 12 layers (transformer encoder blocks) with 768 hidden units (hidden size) and 12 self-attention heads. The large model (\(\text{BERT}_{\text{LARGE}}\)) uses 24 layers with 1024 hidden units and 16 self-attention heads. Notably, the former has 110 million parameters while the latter has 340 million parameters. For demonstration with ease, we define a small BERT, using 2 layers, 128 hidden units, and 2 self-attention heads.
net = d2l.BERTModel(len(vocab), num_hiddens=128, ffn_num_hiddens=256,
num_heads=2, num_layers=2, dropout=0.2)
devices = d2l.try_all_gpus()
net.initialize(init.Xavier(), ctx=devices)
loss = gluon.loss.SoftmaxCELoss()
net = d2l.BERTModel(len(vocab), num_hiddens=128, norm_shape=[128],
ffn_num_input=128, ffn_num_hiddens=256, num_heads=2,
num_layers=2, dropout=0.2, key_size=128, query_size=128,
value_size=128, hid_in_features=128, mlm_in_features=128,
nsp_in_features=128)
devices = d2l.try_all_gpus()
loss = nn.CrossEntropyLoss()
Before defining the training loop, we define a helper function
_get_batch_loss_bert. Given the shard of training examples, this
function computes the loss for both the masked language modeling and
next sentence prediction tasks. Note that the final loss of BERT
pretraining is just the sum of both the masked language modeling loss
and the next sentence prediction loss.
#@save
def _get_batch_loss_bert(net, loss, vocab_size, tokens_X_shards,
segments_X_shards, valid_lens_x_shards,
pred_positions_X_shards, mlm_weights_X_shards,
mlm_Y_shards, nsp_y_shards):
mlm_ls, nsp_ls, ls = [], [], []
for (tokens_X_shard, segments_X_shard, valid_lens_x_shard,
pred_positions_X_shard, mlm_weights_X_shard, mlm_Y_shard,
nsp_y_shard) in zip(
tokens_X_shards, segments_X_shards, valid_lens_x_shards,
pred_positions_X_shards, mlm_weights_X_shards, mlm_Y_shards,
nsp_y_shards):
# Forward pass
_, mlm_Y_hat, nsp_Y_hat = net(
tokens_X_shard, segments_X_shard, valid_lens_x_shard.reshape(-1),
pred_positions_X_shard)
# Compute masked language model loss
mlm_l = loss(
mlm_Y_hat.reshape((-1, vocab_size)), mlm_Y_shard.reshape(-1),
mlm_weights_X_shard.reshape((-1, 1)))
mlm_l = mlm_l.sum() / (mlm_weights_X_shard.sum() + 1e-8)
# Compute next sentence prediction loss
nsp_l = loss(nsp_Y_hat, nsp_y_shard)
nsp_l = nsp_l.mean()
mlm_ls.append(mlm_l)
nsp_ls.append(nsp_l)
ls.append(mlm_l + nsp_l)
npx.waitall()
return mlm_ls, nsp_ls, ls
#@save
def _get_batch_loss_bert(net, loss, vocab_size, tokens_X,
segments_X, valid_lens_x,
pred_positions_X, mlm_weights_X,
mlm_Y, nsp_y):
# Forward pass
_, mlm_Y_hat, nsp_Y_hat = net(tokens_X, segments_X,
valid_lens_x.reshape(-1),
pred_positions_X)
# Compute masked language model loss
mlm_l = loss(mlm_Y_hat.reshape(-1, vocab_size), mlm_Y.reshape(-1)) *\
mlm_weights_X.reshape(-1, 1)
mlm_l = mlm_l.sum() / (mlm_weights_X.sum() + 1e-8)
# Compute next sentence prediction loss
nsp_l = loss(nsp_Y_hat, nsp_y)
l = mlm_l + nsp_l
return mlm_l, nsp_l, l
Invoking the two aforementioned helper functions, the following
train_bert function defines the procedure to pretrain BERT (net)
on the WikiText-2 (train_iter) dataset. Training BERT can take very
long. Instead of specifying the number of epochs for training as in the
train_ch13 function (see Section 13.1), the
input num_steps of the following function specifies the number of
iteration steps for training.
def train_bert(train_iter, net, loss, vocab_size, devices, num_steps):
trainer = gluon.Trainer(net.collect_params(), 'adam',
{'learning_rate': 0.01})
step, timer = 0, d2l.Timer()
animator = d2l.Animator(xlabel='step', ylabel='loss',
xlim=[1, num_steps], legend=['mlm', 'nsp'])
# Sum of masked language modeling losses, sum of next sentence prediction
# losses, no. of sentence pairs, count
metric = d2l.Accumulator(4)
num_steps_reached = False
while step < num_steps and not num_steps_reached:
for batch in train_iter:
(tokens_X_shards, segments_X_shards, valid_lens_x_shards,
pred_positions_X_shards, mlm_weights_X_shards,
mlm_Y_shards, nsp_y_shards) = [gluon.utils.split_and_load(
elem, devices, even_split=False) for elem in batch]
timer.start()
with autograd.record():
mlm_ls, nsp_ls, ls = _get_batch_loss_bert(
net, loss, vocab_size, tokens_X_shards, segments_X_shards,
valid_lens_x_shards, pred_positions_X_shards,
mlm_weights_X_shards, mlm_Y_shards, nsp_y_shards)
for l in ls:
l.backward()
trainer.step(1)
mlm_l_mean = sum([float(l) for l in mlm_ls]) / len(mlm_ls)
nsp_l_mean = sum([float(l) for l in nsp_ls]) / len(nsp_ls)
metric.add(mlm_l_mean, nsp_l_mean, batch[0].shape[0], 1)
timer.stop()
animator.add(step + 1,
(metric[0] / metric[3], metric[1] / metric[3]))
step += 1
if step == num_steps:
num_steps_reached = True
break
print(f'MLM loss {metric[0] / metric[3]:.3f}, '
f'NSP loss {metric[1] / metric[3]:.3f}')
print(f'{metric[2] / timer.sum():.1f} sentence pairs/sec on '
f'{str(devices)}')
def train_bert(train_iter, net, loss, vocab_size, devices, num_steps):
net = nn.DataParallel(net, device_ids=devices).to(devices[0])
trainer = torch.optim.Adam(net.parameters(), lr=0.01)
step, timer = 0, d2l.Timer()
animator = d2l.Animator(xlabel='step', ylabel='loss',
xlim=[1, num_steps], legend=['mlm', 'nsp'])
# Sum of masked language modeling losses, sum of next sentence prediction
# losses, no. of sentence pairs, count
metric = d2l.Accumulator(4)
num_steps_reached = False
while step < num_steps and not num_steps_reached:
for tokens_X, segments_X, valid_lens_x, pred_positions_X,\
mlm_weights_X, mlm_Y, nsp_y in train_iter:
tokens_X = tokens_X.to(devices[0])
segments_X = segments_X.to(devices[0])
valid_lens_x = valid_lens_x.to(devices[0])
pred_positions_X = pred_positions_X.to(devices[0])
mlm_weights_X = mlm_weights_X.to(devices[0])
mlm_Y, nsp_y = mlm_Y.to(devices[0]), nsp_y.to(devices[0])
trainer.zero_grad()
timer.start()
mlm_l, nsp_l, l = _get_batch_loss_bert(
net, loss, vocab_size, tokens_X, segments_X, valid_lens_x,
pred_positions_X, mlm_weights_X, mlm_Y, nsp_y)
l.backward()
trainer.step()
metric.add(mlm_l, nsp_l, tokens_X.shape[0], 1)
timer.stop()
animator.add(step + 1,
(metric[0] / metric[3], metric[1] / metric[3]))
step += 1
if step == num_steps:
num_steps_reached = True
break
print(f'MLM loss {metric[0] / metric[3]:.3f}, '
f'NSP loss {metric[1] / metric[3]:.3f}')
print(f'{metric[2] / timer.sum():.1f} sentence pairs/sec on '
f'{str(devices)}')
We can plot both the masked language modeling loss and the next sentence prediction loss during BERT pretraining.
train_bert(train_iter, net, loss, len(vocab), devices, 50)
MLM loss 7.357, NSP loss 0.820
6876.3 sentence pairs/sec on [gpu(0), gpu(1)]
train_bert(train_iter, net, loss, len(vocab), devices, 50)
MLM loss 5.652, NSP loss 0.778
4370.1 sentence pairs/sec on [device(type='cuda', index=0), device(type='cuda', index=1)]
14.10.2. Representing Text with BERT¶
After pretraining BERT, we can use it to represent single text, text
pairs, or any token in them. The following function returns the BERT
(net) representations for all tokens in tokens_a and
tokens_b.
def get_bert_encoding(net, tokens_a, tokens_b=None):
tokens, segments = d2l.get_tokens_and_segments(tokens_a, tokens_b)
token_ids = np.expand_dims(np.array(vocab[tokens], ctx=devices[0]),
axis=0)
segments = np.expand_dims(np.array(segments, ctx=devices[0]), axis=0)
valid_len = np.expand_dims(np.array(len(tokens), ctx=devices[0]), axis=0)
encoded_X, _, _ = net(token_ids, segments, valid_len)
return encoded_X
def get_bert_encoding(net, tokens_a, tokens_b=None):
tokens, segments = d2l.get_tokens_and_segments(tokens_a, tokens_b)
token_ids = torch.tensor(vocab[tokens], device=devices[0]).unsqueeze(0)
segments = torch.tensor(segments, device=devices[0]).unsqueeze(0)
valid_len = torch.tensor(len(tokens), device=devices[0]).unsqueeze(0)
encoded_X, _, _ = net(token_ids, segments, valid_len)
return encoded_X
Consider the sentence “a crane is flying”. Recall the input
representation of BERT as discussed in
Section 14.8.4. After inserting special tokens
“<cls>” (used for classification) and “<sep>” (used for separation), the
BERT input sequence has a length of six. Since zero is the index of the
“<cls>” token, encoded_text[:, 0, :] is the BERT representation of
the entire input sentence. To evaluate the polysemy token “crane”, we
also print out the first three elements of the BERT representation of
the token.
tokens_a = ['a', 'crane', 'is', 'flying']
encoded_text = get_bert_encoding(net, tokens_a)
# Tokens: '<cls>', 'a', 'crane', 'is', 'flying', '<sep>'
encoded_text_cls = encoded_text[:, 0, :]
encoded_text_crane = encoded_text[:, 2, :]
encoded_text.shape, encoded_text_cls.shape, encoded_text_crane[0][:3]
((1, 6, 128),
(1, 128),
array([-0.8070753 , 0.10175605, -2.2340913 ], ctx=gpu(0)))
tokens_a = ['a', 'crane', 'is', 'flying']
encoded_text = get_bert_encoding(net, tokens_a)
# Tokens: '<cls>', 'a', 'crane', 'is', 'flying', '<sep>'
encoded_text_cls = encoded_text[:, 0, :]
encoded_text_crane = encoded_text[:, 2, :]
encoded_text.shape, encoded_text_cls.shape, encoded_text_crane[0][:3]
(torch.Size([1, 6, 128]),
torch.Size([1, 128]),
tensor([1.4623, 1.4245, 0.9124], device='cuda:0', grad_fn=<SliceBackward0>))
Now consider a sentence pair “a crane driver came” and “he just left”.
Similarly, encoded_pair[:, 0, :] is the encoded result of the entire
sentence pair from the pretrained BERT. Note that the first three
elements of the polysemy token “crane” are different from those when the
context is different. This supports that BERT representations are
context-sensitive.
tokens_a, tokens_b = ['a', 'crane', 'driver', 'came'], ['he', 'just', 'left']
encoded_pair = get_bert_encoding(net, tokens_a, tokens_b)
# Tokens: '<cls>', 'a', 'crane', 'driver', 'came', '<sep>', 'he', 'just',
# 'left', '<sep>'
encoded_pair_cls = encoded_pair[:, 0, :]
encoded_pair_crane = encoded_pair[:, 2, :]
encoded_pair.shape, encoded_pair_cls.shape, encoded_pair_crane[0][:3]
((1, 10, 128),
(1, 128),
array([-0.80707246, 0.10177543, -2.2340825 ], ctx=gpu(0)))
tokens_a, tokens_b = ['a', 'crane', 'driver', 'came'], ['he', 'just', 'left']
encoded_pair = get_bert_encoding(net, tokens_a, tokens_b)
# Tokens: '<cls>', 'a', 'crane', 'driver', 'came', '<sep>', 'he', 'just',
# 'left', '<sep>'
encoded_pair_cls = encoded_pair[:, 0, :]
encoded_pair_crane = encoded_pair[:, 2, :]
encoded_pair.shape, encoded_pair_cls.shape, encoded_pair_crane[0][:3]
(torch.Size([1, 10, 128]),
torch.Size([1, 128]),
tensor([-0.5468, 1.4655, 1.1686], device='cuda:0', grad_fn=<SliceBackward0>))
In Section 15, we will fine-tune a pretrained BERT model for downstream natural language processing applications.
14.10.3. Summary¶
The original BERT has two versions, where the base model has 110 million parameters and the large model has 340 million parameters.
After pretraining BERT, we can use it to represent single text, text pairs, or any token in them.
In the experiment, the same token has different BERT representation when their contexts are different. This supports that BERT representations are context-sensitive.
14.10.4. Exercises¶
In the experiment, we can see that the masked language modeling loss is significantly higher than the next sentence prediction loss. Why?
Set the maximum length of a BERT input sequence to be 512 (same as the original BERT model). Use the configurations of the original BERT model such as \(\text{BERT}_{\text{LARGE}}\). Do you encounter any error when running this section? Why?