Softmax function

In Anthropic's mathematical framework for transformer circuits, they introduced QK and OV circuits.

They stop there because you can't compose other parts of the model together due to non-linearity such as Softmax or GELU.

With a tensor transformer, you can compose everything with everything, such as embedding.

Right arrow.

Attention has that structure, and not merely by analogy.

Every earlier word is scored, and the softmax forces the scores into a distribution summing to 1, so the candidates are in literal zero-sum competition for a fixed budget, exactly as q's are in Bates' model.

What the query and key lenses learn is the functional equivalent of q-strength.

How much a given kind of match counts, tuned by training toward whatever predicts well.

You know, the application drives certain requirements, right? You have gems, you're gonna need some matrix multiply units.

You have, you know, softmax and, and norms, you're gonna need some vector units and, and things that can do transcendental functions.

You need a certain amount of memory capacity and a certain amount of memory bandwidth.

You need a certain amount of communication bandwidth.

Which is totally realistic.

To get that, we cap the network off with a special function called softmax.

Softmax.

It looks at all the final scores and mathematically forces them to add up to exactly 100%.

It gives us a clear, distinct distribution of probabilities we can actually read.

Jürgen Schmidhuber published IDEN 1992 as a scheme for programming fast weights, a quarter of a century before attention existed, and a 2021 paper proved the two are formally the same idea in different notation.

Softmax's attention is not the original design.

It is the deviation, nor is it unbuilt, which is the part he finds funny.

Go back to the model cards from the last chapter and read the architectures instead of the licenses.