14.10. Pretraining BERT
Open the notebook in Colab
Open the notebook in Colab

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 d2l import mxnet as d2l
from mxnet import autograd, gluon, init, np, npx

npx.set_np()

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)

14.10.1. Pretraining BERT

The original BERT has two versions of different model sizes [Devlin et al., 2018]. 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)
ctx = d2l.try_all_gpus()
net.initialize(init.Xavier(), ctx=ctx)
loss = gluon.loss.SoftmaxCELoss()

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

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.

#@save
def train_bert(train_iter, net, loss, vocab_size, ctx, log_interval,
               num_steps):
    trainer = gluon.Trainer(net.collect_params(), 'adam',
                            {'learning_rate': 1e-3})
    step, timer = 0, d2l.Timer()
    animator = d2l.Animator(xlabel='step', ylabel='loss',
                            xlim=[1, num_steps], legend=['mlm', 'nsp'])
    # Masked language modeling loss, next sentence prediction loss,
    # 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, ctx, 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()
            if (step + 1) % log_interval == 0:
                animator.add(step + 1,
                             (metric[0] / metric[3], metric[1] / metric[3]))
            step += 1
            if step == num_steps:
                num_steps_reached = True
                break

    print('MLM loss %.3f, NSP loss %.3f'
          % (metric[0] / metric[3], metric[1] / metric[3]))
    print('%.1f sentence pairs/sec on %s' % (metric[2] / timer.sum(), ctx))

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), ctx, 1, 50)
MLM loss 7.909, NSP loss 0.728
9185.2 sentence pairs/sec on [gpu(0), gpu(1)]
../_images/output_bert-pretraining_41429c_11_1.svg

14.10.2. Representing Text with BERT

After pretraing 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)
    ctx = d2l.try_gpu()
    token_ids = np.expand_dims(np.array(vocab[tokens], ctx=ctx), axis=0)
    segments = np.expand_dims(np.array(segments, ctx=ctx), axis=0)
    valid_len = np.expand_dims(np.array(len(tokens), ctx=ctx), axis=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([ 1.0541121,  1.0278355, -0.8073532], ctx=gpu(0)))

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([ 1.0320886 ,  1.0663296 , -0.81589526], ctx=gpu(0)))

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 pretraing 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

  1. In the experiment, we can see that the masked language modeling loss is significantly higher than the next sentence prediction loss. Why?

  2. 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?

14.10.5. Discussions

image0