Warped Selective State Spaces: Reusable Computation and Anchor Selection

Selective state-space recurrences preserve input-dependent dynamics but complicate reusable computation. This paper connects an exact anchored representation of the unchanged recurrence to two execution decisions: which dynamic transition-summary computations can be removed, and which blocks admit a positive constant anchor under a coordinate-span budget. Feasible-anchor intervals and temporal certificates distinguish repairable failures from failures under every constant anchor. A sharp mean-anchor span bound yields a sharp budget-augmentation guarantee for fixed-tree partitions; a complementary counterexample rules out a width-independent leaf-count approximation at unchanged budget. On 16,384 sampled public-checkpoint roots, block means recover 96.58–99.41% of oracle leaf-count headroom and improve on width-two-only rescue. Matched GPU experiments separate anchor policy from affine/source-only execution. A subsequent evaluation on eight new documents, 130M- and 370M-parameter models, and three layers per model finds that the block-mean policy reduces preparation-inclusive packed-affine latency by 31.3% and 19.5%, respectively, relative to deployed anchors within the same custom executor at the prespecified primary setting. Improvements occur in all 48 model–document–layer cases, with all cases passing full-output numerical checks. Source-only removes specified local-tree arithmetic, while its total-time benefit depends on partition and preparation. These results connect exact coordinate conditions, reusable propagation, and measured policy benefits within the tested execution families.