Abstract: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, $x \mapsto ax+b$, 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 $S_U$ transform with two shape parameters $(\delta,\varepsilon)$ that control tailedness and skewness; the linear $Z$-score used by RevIN is recovered only in the limit $\delta \to \infty$. Training $(\delta,\varepsilon)$ 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: $(\delta,\varepsilon)$ 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 $(\delta^\star,\varepsilon^\star)$ 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.
| Comments: | 8 pages, 2 figures |
| Subjects: | Machine Learning (cs.LG) |
| ACM classes: | I.2.6 |
| Cite as: | arXiv:2605.10823 [cs.LG] |
| (or arXiv:2605.10823v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.10823 arXiv-issued DOI via DataCite (pending registration) |
From: Shun Zhang [view email]
[v1]
Mon, 11 May 2026 16:42:52 UTC (702 KB)
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