Question

Why must the scaled dot-product attention mechanism divide the product of the queries and keys by the square root of the dimension of the keys?

Accepted Answer

In the scaled dot-product attention mechanism, queries and keys are vectors representing pieces of information, and their dot product measures how much focus to place on specific parts of the input. When the dimension of these vectors is large, the magnitude of the dot product tends to grow significantly. This large value pushes the output of the subsequent softmax function into regions where the gradient is extremely small, a phenomenon known as vanishing gradients. The softmax function converts a vector of numbers into probabilities that sum to one by exponentiating the inputs. If the input values to the softmax are too large, the function produces a distribution where one value is nearly one and the others are nearly zero. During backpropagation, which is the process used to train neural networks by calculating how much each weight contributed to an error, these tiny gradients prevent the model from learning effectively because the weight updates become negligible. By dividing the dot product by the square root of the dimension of the keys, the mechanism scales down the variance of the product to approximately one. This stabilization ensures that the inputs to the softmax function remain in a range where the gradient is large enough to allow for efficient and stable learning during the training process.

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Why must the scaled dot-product attention mechanism divide the product of the queries and keys by the square root of the dimension of the keys?