In a standard attention mechanism, an attention score is computed from a query vector (q) and a key vector (k). Consider a modification where a learnable scalar bias is added directly to the query-key dot product before the result is scaled and passed through a Softmax function. The value of this bias is determined solely by the relative distance between the query and key. How does this specific modification influence the attention mechanism's behavior?

Calculating T5 Attention Score with Relative Position Bias

A researcher implements a modified attention mechanism where the learnable scalar bias, based on relative position, is applied after the query-key dot product is scaled. The formula used is: $\alpha(i, j) = \text{Softmax}\left( \frac{q_i^T k_j}{\sqrt{d}} + u_{b(i-j)} + \text{Mask}(i, j) \right)$ What is the most significant consequence of this specific modification compared to the standard approach of adding the bias before scaling?