One Weighted Average Is Not Enough
Last timeSoftmax Over Scores
A single attention head produces one mixture per token, and a mixture destroys information. Heads are how the mechanism keeps several answers at once.
Everything so far has described one head: one set of three projections, one
score matrix, one softmax, one weighted sum. That mechanism works. The question
this lesson answers is why no real model uses only one of them.
The limit of a single head
A head produces, for each token, one vector: a weighted average of the values,
with the weights summing to one.
The problem is in the word average. Averaging is not invertible. Given the
result, you cannot recover what went in. If the weights land half on one token
and half on another, what comes out is the midpoint of two value vectors, and
the midpoint of two meanings is generally not a meaning at all.
Take a sentence where one token needs two different things at once:
The researcher who wrote the paper said it was wrong.
For said, a useful representation depends on at least two relationships. Its
subject is researcher, four tokens back and separated by a relative clause.
Its complement is the clause beginning at it. These are different questions
with different answers.
One head must answer both with one set of weights. The options are all bad: put
the weight on the subject and lose the complement, split it and get a blend of
two unrelated vectors, or spread it thin and get mush.
Two heads dissolve the problem. One puts nearly all its weight on the subject,
the other on the complement, and both results survive into the output because
they occupy different coordinates.
The lesson stops here
7 more paragraphs to go
You have read the opening. The rest of the argument, the problems that check whether it landed, and the lines worth keeping at the end all come with a plan.
The first lesson of every course in the library reads the whole way through, free, so you can see exactly what the rest of them are.
See the planThe contentsThis is the reading half
Starting the course gives you your own copy of it. Every idea on every page has problems standing under it, marked with a reason rather than a tick, and any sentence you do not believe can be opened and argued with. None of that can happen on a page nobody owns.
The contents