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This research introduces Terminal Shrinkage Averaging (TSA), a technique that decouples learning-rate schedules from model estimators to simultaneously optimize training progress and reduce parameter variance during LLM pretraining. By interpolating between the final iterate and recent checkpoint averages, TSA enables faster convergence to GPT-2 quality benchmarks while improving validation performance on larger models like NanoChat. The findings offer a concrete methodological advance for refining pretraining pipelines without altering fundamental architecture or data strategies.
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Terminal Shrinkage Averaging Reveals a Schedule-Estimator Interaction in LLM Pretraining

arXiv2 min read

arXiv:2609.25482v1 Announce Type: cross Abstract: Large language model (LLM) pretraining conventionally returns the raw final iterate. This couples two design choices: the learning-rate schedule that generates the parameter trajectory and the estimator that constructs the deployed model (e.g. the raw final iterate or a checkpoint average). A schedule that promotes optimization progress may differ from one that minimizes variation in the raw final iterate. Separating these choices creates an opportunity to maintain progress late in training while reducing variation in the returned model. To this end, we propose \emph{Terminal Shrinkage Averaging (TSA)}, which interpolates between the raw final iterate and the average of recent checkpoints to balance recent progress against terminal variation. We analyze how TSA changes the preferred terminal learning-rate schedule under a local quadratic approximation and test this interaction through a sequence of controlled NanoChat experiments. Finally, we demonstrate that the resulting gains transfer to depth-22 NanoChat, where the combined schedule and estimator improve validation quality. A qualifying time-to-GPT-2 run also finishes faster than the public baseline used in our experiments, providing preliminary evidence of benchmark acceleration.

Abstract:Large language model (LLM) pretraining conventionally returns the raw final iterate. This couples two design choices: the learning-rate schedule that generates the parameter trajectory and the estimator that constructs the deployed model (e.g. the raw final iterate or a checkpoint average). A schedule that promotes optimization progress may differ from one that minimizes variation in the raw final iterate. Separating these choices creates an opportunity to maintain progress late in training while reducing variation in the returned model. To this end, we propose \emph{Terminal Shrinkage Averaging (TSA)}, which interpolates between the raw final iterate and the average of recent checkpoints to balance recent progress against terminal variation. We analyze how TSA changes the preferred terminal learning-rate schedule under a local quadratic approximation and test this interaction through a sequence of controlled NanoChat experiments. Finally, we demonstrate that the resulting gains transfer to depth-22 NanoChat, where the combined schedule and estimator improve validation quality. A qualifying time-to-GPT-2 run also finishes faster than the public baseline used in our experiments, providing preliminary evidence of benchmark acceleration.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2609.25482 [cs.LG]

(or arXiv:2609.25482v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.25482 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Full text under the publisher's open licence · 271 words

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