Proposition 414 of 39 in the corpus
A static embedding gives one vector per token, so context has to supply the rest.
The embedding table cannot distinguish two senses of a word, because it is indexed by the token alone. Everything that separates them is done by the layers above.
Depends on
Demonstration
The river bank flooded. The central bank raised rates. The token bank is
the same integer in both, so it retrieves the same row of E in both. At the
input to the network the two are indistinguishable — not approximately, but
exactly, bit for bit.
This is a hard limit on the embedding table and it cannot be trained away. A single vector must serve every sense of the token, so what it converges to is something like a frequency-weighted compromise between them: close to neither sense, and closest to whichever dominated the corpus.
What resolves it is everything above the table. One layer of attention lets each
position read its neighbours and add what it finds to its own representation, so
after that layer the two copies of bank occupy different points — the first
having absorbed something from river, the second from central. The vector at
layer k is a function of the whole context, and this is the precise sense in
which a transformer’s representations are contextual while its embeddings are
not.
The historical order is worth keeping. word2vec and GloVe produced static vectors, one per word type, and they were a genuine advance over one-hot encodings. ELMo produced vectors that depended on the sentence, using a bidirectional LSTM. BERT and its successors made the contextual representation the object of interest and the static table merely the starting point. The progression is not from worse embeddings to better ones but from embedding as the representation to embedding as the first row of a computation.
Corollary
Asking what a transformer “thinks a word means” is under-specified until a layer is named. At layer zero the answer is a corpus-wide average that belongs to the token. At the last layer it is a point that belongs to this occurrence in this sentence and to nothing else.