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To the people dismissing the idea of binarising vectors: Fair criticism, but consider the fact that you can also train a model with a loss function that approaches a binary behaviour, i.e. so that the magnitude per dimension plays an insignificant role and only the sign of the dimension carries information. In that case you can use the binary vector for search and ranking.

in practice, learning_rate * grad(L) is mostly about the direction anyway.
But the direction is not at all binary, it's a direction in a very high-dimensional weight space.
But the vectors discussed can represent 2^3072 directions. It's close enough.

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