When Does RevIN Hurt? A Statistical Analysis of Reversible Normalization

Reversible Instance Normalization (RevIN) has become widely adopted in time series forecasting. However, we show that mean-only normalization can match or outperform full RevIN across a substantial fraction of configurations. To understand this counterintuitive phenomenon, we develop a statistical framework that characterizes the effect of normalization through two competing factors, a structural floor induced by information loss and a transfer distance arising from shifts in the learned mapping between training and deployment. This formulation reveals an inherent tradeoff: normalization can reduce transfer distance by discarding distributional information, but the same information loss introduces a structural floor. Based on this framework, we derive a closed-form characterization of the performance gap between mean normalization and raw data, yielding an exact criterion for mean removal. For variance scaling, whose nonlinear effect precludes an exact characterization, we introduce proxy statistics that capture the corresponding structural floor and transfer distance, and validate their causal roles through controlled experiments on real datasets. Together, these results provide a unified theoretical characterization of RevIN and criteria for determining when its two components are effective.