Cautious Weight Decay

• URL: http://arxiv.org/abs/2510.12402v1
• Date: Tue, 14 Oct 2025 11:32:55 GMT
• Title: Cautious Weight Decay
• Authors: Lizhang Chen, Jonathan Li, Kaizhao Liang, Baiyu Su, Cong Xie, Nuo Wang Pierse, Chen Liang, Ni Lao, Qiang Liu,
• Abstract summary: Cautious Weight Decay (CWD) is a one-line, agnostic modification that applies weight decay only to parameter whose signs align with update.<n>CWD is a drop-in change for coordinates such as AdamW, Lion and Muon.<n>For language model pre-training and ImageNet classification, CWD consistently improves final loss and accuracy.
• Score: 23.198565281737896
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce Cautious Weight Decay (CWD), a one-line, optimizer-agnostic modification that applies weight decay only to parameter coordinates whose signs align with the optimizer update. Unlike standard decoupled decay, which implicitly optimizes a regularized or constrained objective, CWD preserves the original loss and admits a bilevel interpretation: it induces sliding-mode behavior upon reaching the stationary manifold, allowing it to search for locally Pareto-optimal stationary points of the unmodified objective. In practice, CWD is a drop-in change for optimizers such as AdamW, Lion, and Muon, requiring no new hyperparameters or additional tuning. For language model pre-training and ImageNet classification, CWD consistently improves final loss and accuracy at million- to billion-parameter scales.

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