QORLA: A MEASURE-AWARE STATISTICAL SE- QUENCE OPERATOR WITH EXACT FAST EVALUATION AND INNOVATION MEMORY

Transformer-based sequence models rely on dense pairwise interactions whose computa- tional cost grows rapidly with context length. QORLA replaces dense query-key scoring with measure-aware statistical estimation over learned scalar geometry, while preserving full-vector values through Laplacian localization and local-linear correction. Its struc- tured formulation admits exact efficient evaluation without materializing the full pairwise interaction matrix, and innovation memory preserves information beyond the statistical predictor. Across diverse sequence-modeling domains, QORLA shows competitive predictive performance, strong transfer across architectures, and favorable long-context computational scaling. These properties position QORLA as an efficient statistical sequence-modeling primitive for scalable alternatives to dense pairwise attention.