Variance Control in Dot Product Attention
When calculating dot product attention, it is essential to manage the magnitude of the scores before they are processed by the exponential function (softmax) to avoid vanishing gradients. Assuming that all elements of a query vector and a key vector are independent and identically distributed random variables with a mean of and a variance of , their resulting dot product will have a mean of but a variance of . Because this variance scales linearly with the vector dimensionality , the raw dot product values can become excessively large, pushing the softmax function into saturated regions. To prevent this and ensure the variance of the dot product remains regardless of the vector length, the dot product is divided by . This critical stabilization step produces the scaled dot-product attention scoring function: .
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Variance Control in Dot Product Attention
DotProductAttention Implementation
In practical implementations of scaled dot-product attention, at which step is dropout applied for regularization?
In the general case where query and key vectors have differing vector lengths, how is the dot product calculation modified to bridge the two spaces?
Match each mathematical component of scaled dot-product attention to its correct definition and role in the attention mechanism.
Based on the mathematical formulation of scaled dot-product attention, determine the shape of the intermediate score matrix QK^T, the numerical value of the scaling divisor sqrt(d), and the shape of the final output matrix. Explain how each dimension and value is derived.
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Match each statistical property of dot product attention to its corresponding value, assuming vector elements are i.i.d. with a mean of 0 and a variance of 1.
Order the steps taken to compute a stabilized attention score between a query vector and a key vector.
Explain why unscaled dot products cause vanishing gradients in this model, and calculate the exact numerical scaling factor required to maintain a variance of 1.