双侧幂有界递归系统中的有限时域Fisher记忆
Finite-Horizon Fisher Memory in Two-Sided Power-Bounded Recurrent Systems
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中文总结 AI 辅助
本研究分析有限时域线性高斯递归记忆中的信息分配与保留，证明Fisher记忆的球面平均不变性，提出写后保留与污染界，并通过实验验证训练掩码接近最优，精度与理论预测高度一致。
中文摘要 AI 辅助
我们分析了有限时域线性高斯噪声递归记忆中的分配、准入和写后保留。在每个时域上，方向性Fisher记忆$M_n$满足$\operatorname{tr}M_n=N$：非正态性重新分配信息但不能提高其球面平均值，而正态载体满足$M_n=I$。对于双幂有界载体，我们推导了统一的$1/n$滞后界，将$M_n$的极限识别为$W^\top$的经典Cesàro渐近极限的逆，并给出了有限时域误差界。时变耦合定义了一个端到端存储算子。写者最优方向不必是存储最优方向。写入结束后，可逆保持保留完整的存储Fisher矩阵。由$\alpha$乘以闭包协方差限定的加性污染至少保留该矩阵的$1/(1+\alpha)$；协方差感知解码器达到相应的精度。在递归载体固定的情况下，训练输入掩码和线性读出在160次运行中接近任务特定最优，中位数归一化瑞利效率高于0.998。在$J$的四个数量级以上，二值精度与高斯预测的匹配平均绝对误差低于0.002。在另一项320次运行的预先指定研究中，训练掩码在16/16次抽取中遵循了两种载体类型的指定输入时间目标。这些研究使用了开发阶段见过的载体，是预先指定的验证，而非盲留出。相同的固定设计在运行承诺前未使用过的载体上，在16/16次抽取中重现了目标特定结果。精确隔离保留了信息，而在其训练时域固定的解码器降至随机水平；逆伴随传输将其采样决策恢复到数值精度。
英文摘要
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 $α$ times the closure covariance retains at least $1/(1+α)$ 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.
