COIL Contextualized Inverted List

A contextualized exact lexical match retrieval architecture and inverted-list index structure that encodes document tokens offline with a pretrained Transformer language model into low-dimensional contextualized vectors v_j^d = W_tok LM(d, j) + b_tok in R^{n_t} grouped by surface token t in V into contextualized inverted lists I^t = {v_j^d | d_j = t, d in C}, and at query time encodes query tokens into v_i^q = W_tok LM(q, i) + b_tok to traverse only the inverted lists J = {I^t | t in q} of overlapping terms and compute the contextualized exact token match score s_tok(q, d) = sum_{q_i in q cap d} max_{d_j = q_i} (v_i^q)^T v_j^d (COIL-tok), optionally augmented with a projected [CLS] dot-product score s_full(q, d) = s_tok(q, d) + (v_cls^q)^T v_cls^d (COIL-full) to mitigate vocabulary mismatch.