泄漏积分器重构：免训练修复时序预测递归误差累积
Leaky-integrator reconstruction: taming error accumulation in recursive differenced time-series forecasting
长时程时序预测越算越偏？arXiv 这篇给了个两行代码的免训练修复，336 步平均误差降 51%。
论文诊断出，对差分预测做累积求和的标准做法等价于极点在单位圆上的离散积分器，会让非线性模型递归外推发散，336 步归一化 MAE 达 1.6-3.8，而正常预测器约 0.8。修复方法是用 H(z)=1/(1-γz^-1)、γ=0.9 的泄漏积分器把极点移入单位圆内，可证明能约束累积误差方差。该重构无需重训练，只改两行代码即可套用在已部署的一步预测或基础模型预测器上。在 7 种架构、20 个数据集上，平均增益从 H=24 的约 3% 增至 H=96 的 23%、H=192 的 37%、H=336 的 51%（各架构区间 43-74%，oracle 极点下达 78%）。对无病理的稳定预测器可证明不影响结果，因此可作为通用默认配置。
Leaky-integrator reconstruction: taming error accumulation in recursive differenced time-series forecasting
We introduce leaky-integrator reconstruction, a training-free method that cures the error accumulation of recursive differenced forecasting. Our first contribution is diagnostic: predicting one-step changes and integrating them by cumulative summation, the standard remedy for non-stationarity, is a discrete integrator with a pole on the unit circle, and we show this makes recursive rollout of a nonlinear model diverge, its 336-step error reaching several times that of a well-behaved forecaster (normalised MAE 1.6-3.8 versus about 0.8) across every neural architecture tested. Our second, central contribution is the fix: move the pole inside the unit circle with a leaky integrator H(z) = 1/(1 - gamma z^-1), gamma < 1, which provably bounds the accumulated error variance. Applied at reconstruction time with a single fixed gamma=0.9 (no retraining, a two-line change to any deployed one-step or foundation-model forecaster), it shrinks error at every horizon, the mean gain over seven diverging architectures and twenty datasets growing from ~3% at H=24 to 23% at H=96, 37% at H=192 and 51% (43-74% across those architectures) at H=336 (78% with an oracle pole). Crucially, it is provably inert where no pathology exists (stable or joint predictors already at the irreducible rate), making it a safe, general default.