A developer is implementing an attention layer for a model that incorporates positional information by adding a learnable scalar bias based on the relative distance between tokens. Given a query vector q_i for a token at position i, a key vector k_j for a token at position j, a key dimension d_k, and the specific learnable bias u_{b(i-j)} for their relative position, which of the following expressions correctly computes the unnormalized attention score (the value passed into the softmax function) for this architectural design?

Analysis of T5 Attention Formula Modifications

Evaluating the Design of T5's Unscaled Attention Mechanism