Bi-directionality in BERT model I am reading the paper BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding that can be found here. 

It looks to me that the crux of the paper is using masked inputs to achieve bidirectionally.

This is an excerpt from the Google AI blog here which states:


  "However, it is not possible to train bidirectional models by simply
  conditioning each word on its previous and next words, since this
  would allow the word that’s being predicted to indirectly “see itself”
  in a multi-layer model.  To solve this problem, we use the
  straightforward technique of masking out some of the words in the
  input and then condition each word bidirectionally to predict the
  masked words."


Can someone please help me understand how does bidirectionally allow the words to see themselves and how masking solves this problem?

Thanks.
Let's take an example : "I went to the shop."

Let's say you want to predict "to" and "the". With bidirectionality, you will predict :

p(to | I, went, the, shop) : No problem here.

p(the | I, went, to, shop) : Here we have a problem, because we already saw the word 'the' while predicting 'to'. It's trivial for the model to predict 'the'.



With MLM, if we take the same example :

p(to | I, went, [MASK], [MASK], shop)
p(the | I, went, [MASK], [MASK], shop)

There is no more problem because the word cannot see itself in other predictions. It's more difficult to predict, but anyway only 15% of the time the word is masked.



Edit

In MLM, BERT will see all the words of the sentence, including the word to predict itself. 
This is because BERT will create representations not only for the [MASK] token, but also for the other tokens of the sentence (but in this case we are interested only in [MASK]). 

Note : It is also because BERT will create representations of all tokens that we need to replace [MASK] sometimes by the original token, sometimes by a random token.

You can find more detailed information in this blog in the "Pretraining" section.