Abstract
Entity tracking requires maintaining and updating latent states for entities and attributes over long sequences. Recent task-specific attention operators can compress deep Transformer stacks into a few layers by performing multi-hop state propagation within a single layer, but their dense evaluation remains expensive. We show that in this setting, learned attention is strongly structured: most mass concentrates in local block-diagonal neighborhoods with a light cross-block residue. Exploiting this, we derive a blockwise evaluation of a resolvent-style operator that keeps within-block interactions exact and routes cross-block interactions through a reduced system. The resulting evaluation is subquadratic in sequence length (and when ). On controlled tracking benchmarks, our method matches the dense operator's accuracy while reducing wall-clock time by under a standardized measurement protocol, and is up to faster than a compact dense Transformer at comparable exact-match accuracy. We further provide ablations over block size and model capacity, and identify a limitation: performance collapses when the number of simultaneously evolving properties exceeds the number of attention heads.