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Fix notation and clarification of Puzzle 9 #16

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@alexzhang13 alexzhang13 commented Jul 17, 2024

The notation for the softmax in Puzzle 9 is confusing. The current indexing is not representative of the outer product, and also the inclusion of an extra variable B1 is a bit ambiguous. I think the new description (minor change) is more clear.

The new notation also makes it clear the relationship between the k vector and v vector, which is important for understanding how the full flash attention is done.

The notation for the softmax in Puzzle 9 is both confusing and wrong. The indexing is not the outer product, and also the inclusion of an extra variable B1 is a bit ambiguous. I think the new description (minor change) is more clear.
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