The contraction is the ranking signal

Recommendation and search systems rank items by the dot product between a user vector and every item vector. That is one user against millions of items, many times per second.

That contraction is the ranking signal. Sum over the wrong axis and every user gets wrong results — and, as everywhere else in this workshop, nothing raises an error.

It is also why the digit similarity matrix from this section is worth building by hand: the toy and the production system are the same expression at different sizes.