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

Excerpt

arXiv: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 classi