When Reversible Normalization Changes What Equivariant Forecasters Can Express

Finite-sample calibration can change which architecture a forecasting experiment recommends, even with the physical task and supervised data fixed. In Lorenz–96, position inputs (POS) and a parameter-matched equivariant-feature control (SHAM) receive the same three-rate validation search. On 128 test trajectories generated after locking selection, POS lowers horizon-32 error from 0.796 to 0.330 with four site-wise calibration trajectories. Increasing only the calibration pool to 256 reverses the mean ranking. With global normalization, the same architecture search favors SHAM and attains 0.084 using four calibration trajectories. Metric certificates preserve all four mean rankings under raw and global-scale errors. A separate five-block centering study repeats the calibration-dependent mean ranking across a sixteen-fold supervision range at fixed training budgets. An equal-dimensional construction distinguishes symmetry compatibility from statistical model choice, although its predicted supervision effect has the opposite sign in the jointly trained CNN. Gray–Scott FNO supplies a second small-pool POS benefit; CNN and long-horizon results delimit transfer. The practical consequence is that a position-input gain within one preprocessing protocol does not establish a need for position-dependent physics. Calibration choices should be controlled when interpreting architecture ablations.