What Must Survive a Subspace Refresh? Optimizer Memory, Calibration, and Instability

Refresh-based low-rank optimizers periodically change the low-dimensional representation in which they maintain gradient statistics. When this representation changes, must the accumulated statistics be preserved, or can they be rebuilt from new gradients? We vary the statistical age used in Adam's standard second-moment bias correction. At each refresh, we erase the second-moment statistic $v$ while retaining the first moment $m$, which smooths gradients. We compare two reconstructions that discard the same pre-refresh history and differ only in whether the correction age is global or restarted. The global-age reconstruction raises final perplexity to roughly $64\times$ the no-reset baseline on average across three GaLore-1B runs. Using the rebuilt statistic's own age recovers carry-level quality across GaLore scales up to 1B parameters, and in PLUMAGE and Fira runs at 60M, despite discarding all pre-refresh $v$ history at every refresh. The failure of the global-age ablation therefore cannot be attributed to history loss alone: preserving pre-refresh $v$ history is not necessary to recover carry-level quality in these settings. We also show that calibrated reconstruction can become hazardous from some training states, and trace one mechanism by which this occurs. In GaLore-60M, repeated oversized updates can drive attention concentration and highly intermittent gradients, causing a freshly rebuilt second moment to misrepresent the scale of retained momentum. Targeted interventions support this feedback mechanism. A late switch to correctly aged reconstruction progressively improves the gradient regime and training quality. A correct statistical age is therefore sufficient along the healthy trajectories tested, but calibration alone does not make reconstruction state-invariant: safe reconstruction also depends on the state training has reached.