Cautious Weight Decay

'Tim' Lizhang Chen, Jonathan Li, Kaizhao Liang, Baiyu Su, Cong Xie, Nuo Wang Pierse, Chen Liang, Ni Lao, Qiang Liu

Cautious Weight Decay: 10 upvotes on Hugging Face Daily Papers, #28 of 47 papers on 2025-10-15. Day-by-day upvote history.

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.

Paper page on Hugging Face · arXiv

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