TK Transformer-Kernel Neural Re-Ranking Model

An interpretable, time-budget-constrained neural re-ranking architecture that independently contextualizes query and document sequences by blending lookup word embeddings t_i with l-layer (l in {1, 2, 3}) sinusoidal-positional Transformer outputs via a learned interpolation weight alpha (hat{t}_i = t_i * alpha + context(t_{1:n})_i * (1 - alpha)), computes a single pairwise cosine interaction match-matrix M_{i,j} = cos(hat{q}_i, hat{d}_j), transforms M_{i,j} with Gaussian RBF kernels K_{i,j}^k = exp(-(M_{i,j} - mu_k)^2 / (2 * sigma^2)), and combines log-normalized kernel pooling (s_log^k = sum_i log_b(sum_j K_{i,j}^k)) with document-length-normalized kernel pooling (s_len^k = sum_i (sum_j K_{i,j}^k) / d_len) into a weighted relevance score s = s_log * beta + s_len * gamma.