Refresh-Scaling the Memory of Balanced Adam

• URL: http://arxiv.org/abs/2605.10119v2
• Date: Tue, 12 May 2026 07:05:18 GMT
• Title: Refresh-Scaling the Memory of Balanced Adam
• Abstract summary: We argue that in balanced Adam, $$ should not be treated as a dimensionless constant.<n>We study the refresh count $R_= (1-)T_mathrmES$, which measures how many times Adam renews its internal statistics during the useful phase of training.
• Score: 1.1145952934885128
• License: http://creativecommons.org/licenses/by/4.0/
• 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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