Block-Coherent Delta

A Parallel Pairwise Fast-Weight Operator for Continuous Spatial Data Recall

Abstract

We consider spatial observations encoded so that nearby coordinates produce similar keys, regardless of access order. A query at the current coordinate can then combine information stored at that address with evidence from similar historical keys. Standard Delta memory corrects only one address per event. We introduce Block-Coherent Delta (BC-Delta), a fixed-capacity fast-weight rule that forms a two-key update block from the current and preceding keys, with the latter serving as causal context without implying spatial adjacency. A 2 x 2 Gram pseudoinverse separates their shared key component, while squared cosine coherence attenuates residual transport at low similarity. BC-Delta retains Delta’s single learning rate and adds no learned gate, window length, or decay parameter. Its rank-two affine update admits associative prefix evaluation. Under equal-budget tuning, both methods select eta = 0.025. Across six route–field conditions and three horizons from 16K to 262K events, BC-Delta lowers blind historical-recall MSE by 4.43% (95% confidence interval 4.11–4.82) and wins 90/90 primary comparisons. Tuned controls, coherence strata, and a signed key–value diagnostic distinguish residual transport from Gram preconditioning and expose the boundary of the spatial-continuity assumption. Code, frozen seeds, and evaluation records support reproducibility.