When Does Learned Normalization Actually Adapt? A Diagnostic Analysis of Adaptive Centring in Time Series Forecasting

Adaptive normalization schemes for time series forecasting introduce learnable coefficients intended to let models discover data-dependent centring behavior, but it is rarely established whether these coefficients capture genuine structure or merely reparameterize training around their initialization. We study one such mechanism, Adaptive Cross-Scale Normalisation (ACSN), across a factorial benchmark of 3,200 runs spanning four forecasting architectures, five datasets, four forecast horizons, and ten random seeds. The learned coefficient departs from its initialization in an architecture- and dataset-specific manner: on Electricity and Weather it shifts meaningfully, while on Exchange Rate and National Illness it remains close to initialization. Where the coefficient fails to move, a fixed normalization baseline reliably outperforms the adaptive variant; where it moves, adaptive normalization is more often competitive. Because the coefficient is sigmoid-parameterised and restricted to $(0,1)$, it can approach but never equal the Fixed baseline ($\alpha =1$). This constraint induces an inherent adaptive-versus-fixed performance gap whenever Fixed is near-optimal, complicating a direct interpretation of that comparison. Pooled performance comparisons show extreme heterogeneity ($I^2$ up to 99.9%), so we report conditional, dataset- and horizon-specific effects rather than a single aggregate number. On the evidence gathered here – one controlled-centring scalar, five datasets, and ten seeds per configuration – we do not claim ACSN is a general-purpose normalization improvement; we present it, and the analysis pipeline built around it, as a diagnostic method for identifying when a normalization coefficient is and is not doing meaningful work.