轻量级时序预测模型，通过自适应归一化与频段分解提升长期预测精度。
FreqLite: A Lightweight Frequency-Decomposed Linear Model with Adaptive Reversible Normalization for Robust Long-Term Time-Series Forecasting
- 频域分解+可学习滤波器，按频段独立建模，保留高频成分。
- 在长周期预测中误差低于Transformer（0.3244 vs 0.3587 MSE），参数少4倍。
- 自适应可逆归一化，在非平稳数据上表现更优，适合真实场景部署。
长期时间序列预测需兼顾精度与效率。轻量级线性模型表现优异，但仍存在两处缺陷：可逆实例归一化（RevIN）用单一历史统计量反归一化整个预测时序，在非平稳情况下不准确；时域趋势/季节性分解依赖固定、非自适应滤波器。本文提出FreqLite，一种超轻量、通道无关的频率分解线性预测器：可学习、无损、单位分解的谱滤波器将输入划分为频带，各频带由独立线性头建模，不同于低通截断方法，高频部分被保留并建模。FreqLite在标准长周期预测基准上表现最佳，当长回溯长度为336时，平均误差低于PatchTST Transformer（0.3244 vs 0.3587 MSE），参数量减少4倍，内存降低2.2倍，每轮训练耗时减少2.2倍，且在单块4GB笔记本显卡上即可完成。所有改进在配对威尔科克森检验中均具显著性（p < 1e-5）。此外引入自适应可逆实例归一化（A-RevIN），其在非平稳环境下动态激活，平稳数据下退化为标准RevIN，性能无损。在真实非平稳数据（ILI）和受控合成漂移实验中，其性能提升随非平稳程度单调上升。组件均可独立验证，所有结果在消费级硬件上可复现。
原文摘要 · Abstract (English)
Long-term time-series forecasting needs models that are accurate yet efficient enough for commodity hardware. Lightweight linear forecasters are remarkably strong in this regime, yet they leave two openings: reversible instance normalization (RevIN) de-normalizes the entire horizon with a single lookback statistic, which is inaccurate under non-stationarity, and time-domain trend/seasonal decomposition relies on a fixed, non-adaptive filter. We present FreqLite, an ultra-lightweight, channel-independent frequency-decomposed linear forecaster: a learnable, lossless, partition-of-unity spectral filter splits the input into bands that are forecast by per-band linear heads and, unlike low-pass-truncation approaches, the high-frequency band is retained and modeled. FreqLite is the best lightweight model on the standard long-term forecasting benchmarks and, at long lookback (L=336), attains a lower average error than a PatchTST Transformer (0.3244 vs. 0.3587 MSE) while using 4x fewer parameters, 2.2x less memory, and 2.2x less time per epoch on a single 4 GB laptop GPU; although modest in magnitude, its improvements are statistically significant under paired Wilcoxon tests across all matched cells (p < 1e-5). We further introduce Adaptive Reversible Instance Normalization (A-RevIN), a regime-adaptive reversible normalization that strictly generalizes RevIN (recovered exactly when its gate is closed), engages under non-stationarity, and reduces to RevIN without harm on stationary data. We validate this on both a real strongly non-stationary dataset (ILI, up to ~5% MSE reduction) and a controlled synthetic drift sweep in which A-RevIN's benefit and its learned gate both rise monotonically with injected non-stationarity. Every component is independently ablatable (Linear and RLinear are special cases of FreqLite), and all results are reproducible on commodity hardware.
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