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

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 Cesàro 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 contamination bounded by $\alpha$ times the closure covariance retains at least $1/(1+\alpha)$ of that matrix; a covariance-aware decoder attains the corresponding accuracy. With recurrent carriers held fixed, training input masks and linear readouts approached the task-specific optimum in 160 runs, with median normalized Rayleigh efficiency above $0.998$. Binary accuracy matched the Gaussian prediction to mean absolute error below $0.002$ over more than four orders of magnitude in $J$. In a separate pre-specified study of 320 runs, trained masks followed the designated input-time objective in both carrier types, in 16 of 16 draws. These studies used development-seen carriers and are pre-specified validations, not blind holdouts. The same fixed design reproduced the objective-specific result in 16 of 16 draws on carriers unused before run commitment. Exact isolation preserved information, while a decoder fixed at its training horizon fell to chance; inverse-adjoint transport restored its sampled decisions to numerical precision.

34 pages, 7 figures. Reproducibility materials: this https URL (release v1.0)

Machine Learning (cs.LG)

arXiv:2609.39800 [cs.LG]

(or arXiv:2609.39800v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.39800 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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