Imagine you have two lists of numbers (like two small piles of blocks) that you want to compare to see how similar they are.
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Normal dot product: You line up the lists side by side, multiply the pairs of numbers, and then add them all up. For example:
- List A: [2, 3, 4]
- List B: [5, 1, 2]
Dot product = (2 × 5) + (3 × 1) + (4 × 2) = 10 + 3 + 8 = 21.
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Scaled dot product: Sometimes, especially if these lists are very long, the dot product can become a large (or at least a tricky) number to work with. So, we scale it by dividing by something, usually the square root of the number of items in each list. This keeps the result from getting too big as the lists grow.
- In other words, instead of just adding up the products, you shrink the total by some factor. It’s like saying, “Yes, your piles of blocks match up this much, but let’s keep the final score from exploding if we compare huge piles.”
This “scaling” helps keep the results in a stable range and makes it easier for certain mathematical operations—like those in machine learning and Transformers (where scaled dot product is a key part of “attention”)—to handle big lists of numbers without the results becoming unwieldy.