Accelerating LLM Pretraining with Zeroth-Order Curvature on Idle Serving Compute

LLM pretraining is increasingly compute-intensive, while substantial inference serving compute remains idle during off-peak periods. However, such serving hardware is difficult to use for conventional first-order training due to its memory, networking and other system requirements. Zeroth-order (ZO) optimization offers a natural interface to this forward-only compute resource, but its gradient estimates break down in pretraining. Unlike fine-tuning, which can confine updates to a small parameter subspace, pretraining must update every parameter, and the alignment of a ZO gradient estimate with the true gradient shrinks as the number of updated parameters grows. We make a different observation: noisy ZO estimates can still provide useful curvature information, even when they are too inaccurate to serve as gradients. Based on this insight, we propose ZO-Curv, which leverages idle forward-only devices to estimate curvature and uses it to adapt and refine the update used during first-order training, thereby accelerating the process. We provide convergence guarantees that characterize the effect of finite-query curvature estimation. Experiments on LLMs from 125M to 1.5B parameters show that ZO-Curv consistently accelerates pretraining. At 770M parameters, ZO-Curv reaches AdamW's 20K-step validation loss in 3.9 hours instead of 7.5 hours, while achieving a lower final loss of 2.70 versus 2.84 under the same step budget. These results show that idle model serving compute can accelerate LLM pretraining when zeroth-order queries are used to estimate curvature rather than gradients directly.