Someone suggested this comment was inscrutable so here’s a summary:
I don’t think that how argmax-y softmax is being is a crux between us—we think our picture makes the most sense when softmax acts like argmax or top-k so we hope you’re right that softmax is argmax-ish. Instead, I think the property that enables your efficient solution is that the set of features ‘this token is token (i)’ is mutually exclusive, ie. only one of these features can activate on an input at once. That means that in your example you don’t have to worry about how to recover feature values when multiple features are present at once. For more general tasks implemented by an attention head, we do need to worry about what happens when multiple features are present at the same time, and then we need the f-vectors to form a nearly orthogonal basis and your construction becomes a special case of ours I think.
Someone suggested this comment was inscrutable so here’s a summary:
I don’t think that how argmax-y softmax is being is a crux between us—we think our picture makes the most sense when softmax acts like argmax or top-k so we hope you’re right that softmax is argmax-ish. Instead, I think the property that enables your efficient solution is that the set of features ‘this token is token (i)’ is mutually exclusive, ie. only one of these features can activate on an input at once. That means that in your example you don’t have to worry about how to recover feature values when multiple features are present at once. For more general tasks implemented by an attention head, we do need to worry about what happens when multiple features are present at the same time, and then we need the f-vectors to form a nearly orthogonal basis and your construction becomes a special case of ours I think.