Finite-Horizon Fisher Memory in Two-Sided Power-Bounded Recurrent Systems

תקציר מקורי באנגליתarXiv:2609.39800v1 Announce Type: new Abstract: We analyse allocation, admission and post-write retention in finite-horizon linear-Gaussian noisy recurrent memories. At every horizon, the directional Fisher memory $M_n$ satisfies $\operatorname{tr}M_n=N$: non-normality redistributes information but cannot raise its spherical average, while normal carriers satisfy $M_n=I$. For bi-power-bounded carriers, we derive uniform $1/n$ lag bounds, identify the limit of $M_n$ with the inverse of the classical Ces\`aro asymptotic limit of $W^\top$, and give finite-horizon error bounds. A time-varying coupling defines an end-to-end store operator. The writer-optimal direction need not be store-optimal. After writing ends, an invertible hold preserves the full stored Fisher matrix. Additive contaminatio