U-centered relational attention

Integrate this into a graph neural network or transformer attention block immediately after computing pairwise scores and before masking and softmax. For a batch of n valid tokens, compute symmetric logits A_{ij}=(q_i^T k_j+q_j^T k_i)/(2 sqrt(d)) for i unequal to j, set A_{ii}=0, and exclude padding tokens from every sum. Compute row sums r_i=sum_{j not equal to i} A_{ij} and total t=sum_i r_i. Form R_{ij}=A_{ij}-(r_i+r_j)/(n-2)+t/((n-1)(n-2)). Use R directly as the relational logit, or add a gated term to ordinary attention: L_{ij}=L^{vanilla}_{ij}+gamma R_{ij}, with gamma initialized to zero and learned. Apply the usual mask after constructing R. The paper's exact computation is the residualization formula and its zero-row-sum guarantee; no pseudoinverse is needed for pairwise arrays. Estimate only gamma, the temperature, and network parameters by backpropagation. First test a six-layer small ViT on CIFAR-10 or a graph-attention model on Cora, comparing vanilla attention, ordinary row-centering, and U-centering at matched FLOPs. Track validation accuracy, attention entropy, gradient-norm variance, and performance under duplicated or high-degree tokens. Success means improved accuracy or robustness at equal compute, fewer dominant-token failures, and stable loss without pathological attention concentration.