cs.LGMay 31, 2026

FreqLite: A Lightweight Frequency-Decomposed Linear Model with Adaptive Reversible Normalization for Robust Long-Term Time-Series Forecasting

Authors: Mirza Samad Ahmed Baig, Syeda Anshrah Gillani

Abstract

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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Reversible instance normalization (RevIN) and its successors (Dish-TS, SAN, FAN) have become the de facto plug-in for time-series forecasting, yet the map they apply to each data point is strictly affine, x↦ax+bx \mapsto ax+b, so they cannot reshape the underlying distribution -- heavy tails remain heavy and skewness remains uncorrected. We propose NoRIN, a non-linear reversible normalization based on the arcsinh-form Johnson SUS_U transform with two shape parameters (δ,ε)(δ,\varepsilon) that control tailedness and skewness; the linear ZZ-score used by RevIN is recovered only in the limit δ→∞δ\to \infty. Training (δ,ε)(δ,\varepsilon) jointly with the backbone via gradient descent reliably pushes them toward this linear limit within a few epochs -- a phenomenon we name the degeneration problem: the forecasting loss is locally indifferent to shape, and the high-capacity backbone compensates for any monotone reparameterization of its input. NoRIN escapes the degeneration by decoupling shape selection from gradient training: (δ,ε)(δ,\varepsilon) are initialized by a closed-form Slifker-Shapiro quantile fit and refined by Bayesian optimization on the validation objective, while the inner training loop is identical to standard RevIN-style training. Across six representative backbones x five real-world datasets x three prediction horizons (90 configurations), decoupled shape optimization recovers (δ⋆,ε⋆)(δ^\star,\varepsilon^\star) that sit systematically far from the linear limit, with values that vary in a backbone-dependent way. This empirically supports the central thesis: different backbones genuinely require different normalization parameters to reach their best performance.
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