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arXiv · 2605.10119

Refresh-Scaling the Memory of Balanced Adam

Alberto Fernández-Hernández·Cristian Pérez-Corral·Jose I. Mestre·Manuel F. Dolz·Enrique S. Quintana-Ortí
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Abstract

Recent evidence suggests that Adam performs robustly when its momentum parameters are tied, $β_1=β_2$, reducing the optimizer to a single remaining parameter. However, how this parameter should be set remains poorly understood. We argue that, in balanced Adam, $β$ should not be treated as a dimensionless constant: it defines a statistical memory horizon $H_β=(1-β)^{-1}$. In terms of the effective learning horizon $T_{\mathrm{ES}}$, estimated from the validation trajectory, we study the refresh count $R_β=(1-β)T_{\mathrm{ES}}$, which measures how many times Adam renews its internal statistics during the useful phase of training. Across 11 vision and language experiments, we find that choosing $β$ so that $R_β\approx1000$ selects different $β$ values depending on the training scale, yet improves robustness over the best fixed-beta baseline. Compared with the strongest fixed choice $β=0.944$, the refresh rule improves worst-case robustness, reducing the maximum relative gap in validation loss by 33.4\%, while bringing all 11 runs within 1\% of their validation oracle. These results suggest that the remaining hyperparameter of balanced Adam is more naturally viewed as a memory-scale variable than as a fixed constant. This provides a simple budget-aware perspective on optimizer scaling and opens a path toward treating Adam's momentum as part of the learning dynamics rather than as a static default.

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Alberto Fernández-Hernández, Cristian Pérez-Corral, Jose I. Mestre, Manuel F. Dolz, Enrique S. Quintana-Ortí. 2026-05-12. Refresh-Scaling the Memory of Balanced Adam. https://arxiv.org/abs/2605.10119

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