On the Role of Reversible Instance Normalization

Gaspard Berthelier; Tahar Nabil; Etienne Le Naour; Richard Niamke; Samir Perlaza; Giovanni Neglia

cs.LGMar 12, 2026

On the Role of Reversible Instance Normalization

Authors: Gaspard Berthelier, Tahar Nabil, Etienne Le Naour, Richard Niamke, Samir Perlaza, Giovanni Neglia

Organizations: EDF R&D & Inria Sophia-Antipolis · EDF R&D · Inria Sophia-Antipolis

Abstract

Data normalization is a crucial component of deep learning models, yet its role in time series forecasting remains insufficiently understood. In this paper, we identify three central challenges for normalization in time series forecasting: temporal input distribution shift, spatial input distribution shift, and conditional output distribution shift. In this context, we revisit the widely used Reversible Instance Normalization (RevIN), by showing through ablation studies that several of its components are redundant or even detrimental. Based on these observations, we draw new perspectives to improve RevIN's robustness and generalization.

Figures & tables

Panel of Figure 1 — Figure 1: Illustration of the three distribution shifts: (a) temporal shift between training and test periods (rolling average of a Traffic sensor), (b) spatial shift between users (two Solar sensors), (c) conditional shift (different horizons for similar look-back windows, from one Electricity user).

Figure 2: Illustration of the RevIN process on three synthetic examples.

				RevIN (w/o $\alpha,\beta$ )		RevIN
	L-H	None	Standard Normalization	Standard BP	Normalized BP	Standard BP	Normalized BP
Electricity	168-24	61.16	23.55	0.93	0.59	0.93	0.59
	504-24	60.82	22.32	0.92	0.52	0.92	0.52
	504-168	60.27	21.33	1.02	0.67	1.01	0.67
	504-504	60.82	23.04	1.23	0.87	1.22	0.87
Solar	168-24	2.74	2.35	1.31	1.30	1.31	1.30

Table 1: Ablation of RevIN components on PatchTST (MSE on new dates and new users). Average improvements are expressed relative to the first column. BP stands for “backpropagation".

Appendix figures & tables35 assets

Supplementary material from the paper’s appendix.

Appendix

Normalization	Citations
DAIN	301
RevIN	1322
DishTS	173
SAN	142

Appendix

Table 2: Citations of TSF normalization papers, according to Google Scholar (06/03/26)

Split	Description	Users	Period
Train	Training distribution	$\mathcal{I}_{in}$	$\mathcal{T}_{train}$
Valid1	Validation (new period)	$\mathcal{I}_{in}$	$\mathcal{T}_{valid}$
Valid2	Validation (new users)	$\mathcal{I}_{out}$	$\mathcal{T}_{train}$
Valid3	Validation (new period & new users)	$\mathcal{I}_{out}$	$\mathcal{T}_{valid}$
Test1	Testing (new period)	$\mathcal{I}_{in}$	$\mathcal{T}_{test}$
Test2	Testing (new period & new users)	$\mathcal{I}_{out}$	$\mathcal{T}_{test}$

Appendix

Table 3: 6-way dataset split

	L-H	Instance	RevIN	cmIN	cmIN(init)
Synthetic	40-10	427.42	427.30	425.17	356.03
	100-20	366.02	365.36	364.70	328.54
	100-100	425.38	425.22	424.97	346.45
Improvements		0.0 %	0.08 %	0.33 %	15.16 %

Appendix

Table 4: Results of cmIN (on PatchTST) for the synthetic dataset (nMSE, Test1 split).

Figure 3: Values of $\delta$ for a given user in time. Modulation stationarity does not hold.

Figure 4: Distribution of sampled $(\delta,\lambda)$ . In red from a single user, in blue from the whole set of users. Modulation stationarity does not hold.

Figure 5: Example of a signal with saturation. A model with instance normalization cannot distinguish both blue windows nor both green windows. Yet the expected outputs are different for each.

Panel of Figure 6 — Figure 6: Example synthetic windows. Up: cluster 1 ( $a=10^{-1},b=10\pm 1$ ), Down: cluster 2 ( $a=-10^{-1},b=100\pm 10$ ). For all, we set $A=1,T=10,\sigma=5*10^{-2}$ .

Panel of Figure 7 — Figure 7: Synthetic dataset’s statistics. We notice the two distinct clusters. Individuals are recreated randomly at each run.

				RevIN (w/o $\alpha,\beta$ )		RevIN
	L-H	None	Standard Normalization	Standard BP	Normalized BP	Standard BP	Normalized BP
Electricity	168-24	349.83	20.56	8.52	4.91	8.52	4.92
	504-24	348.14	19.68	8.36	4.09	8.34	4.09
	504-168	347.21	28.28	11.00	7.09	10.94	7.09
	504-504	358.70	33.18	16.70	12.54	16.65	12.53
Solar	168-24	3.05	2.30	1.47	1.46	1.47	1.47

Appendix

Table 5: Ablation of RevIN components on PatchTST (MSE test1 results).

				RevIN (w/o $\alpha,\beta$ )		RevIN
	L-H	None	Standard Normalization	Standard BP	Normalized BP	Standard BP	Normalized BP
Electricity	168-24	61.16	23.55	0.93	0.59	0.93	0.59
	504-24	60.82	22.32	0.92	0.52	0.92	0.52
	504-168	60.27	21.33	1.02	0.67	1.01	0.67
	504-504	60.82	23.04	1.23	0.87	1.22	0.87
Solar	168-24	2.74	2.35	1.31	1.30	1.31	1.30

Appendix

Table 6: Ablation of RevIN components on PatchTST (MSE test2 results).

				RevIN (w/o $\alpha,\beta$ )		RevIN
	L-H	None	Standard Normalization	Standard BP	Normalized BP	Standard BP	Normalized BP
Electricity	168-24	49.28	4.7 $\times 10^{11}$	0.44	0.28	0.44	0.28
	504-24	39.93	4.8 $\times 10^{11}$	0.34	0.19	0.34	0.19
	504-168	52.56	5.4 $\times 10^{11}$	0.42	0.28	0.42	0.28
	504-504	47.95	2.2 $\times 10^{1}1$	0.60	0.45	0.60	0.45
Solar	168-24	1.72	120.62	1.00	0.86	1.00	0.86

Appendix

Table 7: Ablation of RevIN components on PatchTST (nMSE test1 results).

				RevIN (w/o $\alpha,\beta$ )		RevIN
	L-H	None	Standard Normalization	Standard BP	Normalized BP	Standard BP	Normalized BP
Electricity	168-24	38.27	2.4 $\times 10^{12}$	0.48	0.30	0.48	0.30
	504-24	32.35	1.0 $\times 10^{12}$	0.36	0.19	0.36	0.19
	504-168	35.99	4.4 $\times 10^{11}$	0.43	0.27	0.43	0.27
	504-504	37.31	6.1 $\times 10^{11}$	0.61	0.43	0.61	0.43
Solar	168-24	1.88	132.03	1.09	0.93	1.09	0.93

Appendix

Table 8: Ablation of RevIN components on PatchTST (nMSE test2 results).

				RevIN (w/o $\alpha,\beta$ )		RevIN
	L-H	None	Standard Normalization	Standard BP	Normalized BP	Standard BP	Normalized BP
Electricity	168-24	88.15	78.28	45.01	22.04	45.01	22.04
	504-24	20.92	18.55	17.00	11.18	17.00	11.19
	504-168	17.82	15.72	16.04	8.89	16.04	8.90
	504-504	23.06	20.34	21.09	14.54	21.08	14.63
Solar	168-24	5.43	6.29	3.83	3.74	3.83	3.75

Appendix

Table 9: Ablation of RevIN components on DLinear (MSE test1 results).

				RevIN (w/o $\alpha,\beta$ )		RevIN
	L-H	None	Standard Normalization	Standard BP	Normalized BP	Standard BP	Normalized BP
Electricity	168-24	9.14	60.96	2.74	1.49	2.74	1.49
	504-24	1.70	12.44	1.43	0.96	1.43	0.96
	504-168	1.39	10.67	1.29	0.83	1.29	0.83
	504-504	1.57	11.72	1.43	1.02	1.43	1.03
Solar	168-24	4.84	6.32	3.44	3.36	3.44	3.36

Appendix

Table 10: Ablation of RevIN components on DLinear (MSE test2 results).

				RevIN (w/o $\alpha,\beta$ )		RevIN
	L-H	None	Standard Normalization	Standard BP	Normalized BP	Standard BP	Normalized BP
Electricity	168-24	5.78	4.1 $\times 10^{12}$	0.83	0.57	0.83	0.57
	504-24	0.60	2.9 $\times 10^{11}$	0.54	0.34	0.54	0.34
	504-168	0.63	4.2 $\times 10^{10}$	0.56	0.34	0.56	0.34
	504-504	0.79	4.8 $\times 10^{10}$	0.72	0.50	0.72	0.50
Solar	168-24	1.98	237.45	1.67	1.64	1.67	1.64

Appendix

Table 11: Ablation of RevIN components on DLinear (nMSE test1 results).

				RevIN (w/o $\alpha,\beta$ )		RevIN
	L-H	None	Standard Normalization	Standard BP	Normalized BP	Standard BP	Normalized BP
Electricity	168-24	4.92	2.2 $\times 10^{12}$	0.87	0.60	0.87	0.60
	504-24	0.63	7.4 $\times 10^{10}$	0.57	0.34	0.57	0.34
	504-168	0.64	3.1 $\times 10^{10}$	0.58	0.32	0.58	0.32
	504-504	0.82	4.5 $\times 10^{10}$	0.74	0.49	0.74	0.49
Solar	168-24	2.11	254.75	1.80	1.77	1.80	1.77

Appendix

Table 12: Ablation of RevIN components on DLinear (nMSE test2 results).

Figure 8: Electricity , temporal setting

Figure 10: Electricity , Overall setting

	None		Standard		Instance
	Temporal	Spatial	Temporal	Spatial	Temporal	Spatial
Electricity	7.09	57.16	0.05	0.42	0.64	1.01
Solar	3.48	0.98	1.05	0.3	0.78	0.29
Traffic	0.32	0.99	1.39	4.29	0.92	0.45
Synthetic	15.97	39.51	2.53	6.26	0.9	3.76
Difference	0%	0%	-20.27%	-20.13%	18.86%	78.42%

Appendix

Table 13: Energy distances between shifted distributions (inputs).

	None		Standard		Instance
	Temporal	Spatial	Temporal	Spatial	Temporal	Spatial
Electricity	7.31	59.13	0.05	0.43	0.67	1.05
Solar	3.56	1.05	1.08	0.32	0.88	0.32
Traffic	0.32	1.02	1.4	4.43	0.93	0.47
Synthetic	16.51	40.77	2.62	6.46	0.93	4.38
Difference	0%	0%	-21.1%	-20.34%	17.46%	77.73%

Appendix

Table 14: Energy distances between shifted distributions (windows).

	None		Standard		Instance
	Temporal	Spatial	Temporal	Spatial	Temporal	Spatial
Electricity	3.01	20.66	0.02	0.15	0	0
Solar	1.18	0.3	0.36	0.09	0	0
Traffic	0.08	0.4	0.36	1.72	0	0
Synthetic	4.51	10.99	0.71	1.74	0	0
Difference	0%	0%	-24.23%	-19.14%	100%	100%

Appendix

Table 15: Energy distances between shifted distributions (statistics).

	None		Standard		Instance
	Temporal	Spatial	Temporal	Spatial	Temporal	Spatial
Electricity	0.08	0.57	0.08	0.57	0.08	0.57
Solar	0.29	0.10	0.29	0.10	0.29	0.10
Traffic	0.16	0.17	0.17	0.15	0.16	0.17
Synthetic	0.10	2.04	0.10	2.04	0.10	2.04
Difference	0%	0%	-1.56%	2.94%	0%	0%

Appendix

Table 16: Energy distances between shifted distributions (modulations).

Figure 20: Example prediction from Electricity

(L-H)=(168-24)

. Without normalization, PatchTST does not converge. RevIN(nMSE) corresponds to RevIN trained with normalized backpropagation. It fits the ground-truth more smoothly than RevIN(MSE).

Figure 21: Solar sensors’ statistics (Left: Train and Test1, Right: Test 1 and Test2).

Figure 22: Traffic sensors’ statistics (Left: Train and Test1, Right: Test 1 and Test2).

Time Series Forecasting

Time series forecasting predicts future values from ordered observations using statistical, neural, and probabilistic models to support decisions under uncertainty.

See all 858 papers

NoRIN: Backbone-Adaptive Reversible Normalization for Time-Series Forecasting
May 11, 2026Shun Zhang, Yuyang XiaoTime Series Forecasting
Graduate School of China Academy of Engineering Physics, Beijing 100193, China · Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
FreqLite: A Lightweight Frequency-Decomposed Linear Model with Adaptive Reversible Normalization for Robust Long-Term Time-Series Forecasting
May 31, 2026Mirza Samad Ahmed Baig, Syeda Anshrah GillaniLong-Term Time Series Forecasting Frequency-Domain Feature Learning
Fandaqah, Al Khobar, Saudi Arabia · Hamdard University, Karachi, Pakistan
Reversible Residual Normalization Alleviates Spatio-Temporal Distribution Shift
Apr 17, 2026Zhaobo Hu, Vincent Gauthier, Mehdi NaimaInvertible Neural Networks Distribution Shift Robustness
SAMOVAR, Télécom SudParis · Institut Polytechnique de Paris · CNRS – LIP6 +1

May 11, 2026J/K move · Enter open · S save

NoRIN: Backbone-Adaptive Reversible Normalization for Time-Series Forecasting

Shun Zhang, Yuyang Xiao

Graduate School of China Academy of Engineering Physics, Beijing 100193, China · Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

Time Series Forecasting

Open paper AskPDF arXiv

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

(δ,\varepsilon)

that control tailedness and skewness; the linear

Z

-score used by RevIN is recovered only in the limit

δ\to \infty

. Training

(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,\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^\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.

Abstract

Time Series Forecasting

Explore similar work

NoRIN: Backbone-Adaptive Reversible Normalization for Time-Series Forecasting

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

Reversible Residual Normalization Alleviates Spatio-Temporal Distribution Shift