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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2605.09126 |
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| _version_ | 1866911667387891712 |
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| author | Shah, Vatsal Sun, Jiahao |
| author_facet | Shah, Vatsal Sun, Jiahao |
| contents | Asynchronous DiLoCo systems may receive pseudo-gradients computed several outer rounds earlier, yet the standard Nesterov outer optimizer does not explicitly condition its update on per-update age. This can make the outer momentum buffer brittle under large controlled delays. We propose Cosine Gated Adam Decay (CGAD), a simple, drop-in, age-aware outer optimizer that scales each incoming pseudo-gradient by $σ(τ) = γ(τ) e^{-ατ}$ before it enters Adam's first- and second-moment buffers; the exponential models information decay and the cosine gate $γ(τ)$ smoothly zeroes contributions past a chosen cutoff. CGAD reduces to plain Adam at $τ=0$, adds two hyperparameters whose defaults transfer across scales, and extends to partial-sync schedulers via a per-fragment age-aware variant (PA-CGAD). For an idealized gated-adaptive update on smooth non convex objectives, we prove a non-asymptotic convergence bound whose staleness-bias term depends on $α$ alone, rather than on the realized maximum delay $τ_{\max}$; standard analyses of asynchronous momentum-SGD instead carry a $τ_{\max}^2$ factor. Empirically, on Llama style language model pretraining at 25M, 1B, and 7B parameters, CGAD trains stably across the controlled delays we sweep. The cosine cutoff acts as scale insurance: the closest baseline, Adam Decay (CGAD without the cutoff), is competitive at 25M but its seed-to-seed $σ$ at $τ=8$ grows 27x from 25M to 7B, pushing its single-shot risk (mean + $σ$) above the chance-level loss while CGAD's stays well below. The published Nesterov recipe is the least stable method on the full sweep. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09126 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cosine-Gated Adam-Decay: Drop-In Staleness-Aware Outer Optimization for Decoupled DiLoCo Shah, Vatsal Sun, Jiahao Machine Learning Asynchronous DiLoCo systems may receive pseudo-gradients computed several outer rounds earlier, yet the standard Nesterov outer optimizer does not explicitly condition its update on per-update age. This can make the outer momentum buffer brittle under large controlled delays. We propose Cosine Gated Adam Decay (CGAD), a simple, drop-in, age-aware outer optimizer that scales each incoming pseudo-gradient by $σ(τ) = γ(τ) e^{-ατ}$ before it enters Adam's first- and second-moment buffers; the exponential models information decay and the cosine gate $γ(τ)$ smoothly zeroes contributions past a chosen cutoff. CGAD reduces to plain Adam at $τ=0$, adds two hyperparameters whose defaults transfer across scales, and extends to partial-sync schedulers via a per-fragment age-aware variant (PA-CGAD). For an idealized gated-adaptive update on smooth non convex objectives, we prove a non-asymptotic convergence bound whose staleness-bias term depends on $α$ alone, rather than on the realized maximum delay $τ_{\max}$; standard analyses of asynchronous momentum-SGD instead carry a $τ_{\max}^2$ factor. Empirically, on Llama style language model pretraining at 25M, 1B, and 7B parameters, CGAD trains stably across the controlled delays we sweep. The cosine cutoff acts as scale insurance: the closest baseline, Adam Decay (CGAD without the cutoff), is competitive at 25M but its seed-to-seed $σ$ at $τ=8$ grows 27x from 25M to 7B, pushing its single-shot risk (mean + $σ$) above the chance-level loss while CGAD's stays well below. The published Nesterov recipe is the least stable method on the full sweep. |
| title | Cosine-Gated Adam-Decay: Drop-In Staleness-Aware Outer Optimization for Decoupled DiLoCo |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.09126 |