Delayed Optimizer-State Transport Shapes Short-Horizon Training Decisions

• URL: http://arxiv.org/abs/2608.24593v1
• Date: Tue, 25 Aug 2026 14:18:29 GMT
• Title: Delayed Optimizer-State Transport Shapes Short-Horizon Training Decisions
• Abstract summary: We examine whether a delayed transport is large enough to change prospective short-horizon decisions.<n>On committed future-minibatch sequences, we differentiate eight-step AdamW through the complete model-optimizer state.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Adaptive optimizers retain gradient history in moment variables, allowing a local change in loss weighting to alter later updates. We examine whether this delayed transport is large enough to change prospective short-horizon decisions. On committed future-minibatch sequences, we differentiate eight-step AdamW trajectories through the complete model--optimizer state and select exposure-matched Math--Code loss schedules before independent evaluation. Across 12 unused 0.3M Transformer histories, full transport lowers token-disjoint loss relative to an optimizer-aware immediate derivative in 10/12 histories (mean benefit $4.71\times10^{-4}$; exact one-sided sign test, $p=0.0193$). The two controllers act equally often but select different schedules in 60/96 windows. Crossed checkpoint--future-path tests attribute this reordering to the interaction between optimizer state and near-future data, while an independent Ising--CNN experiment shows that deleting moment-state transport destroys accurate response prediction. Full-transport scores also concentrate exact-rollout winners in larger candidate libraries, focusing finite-amplitude evaluation on a shortlist. On these committed short paths, optimizer memory and near-future data order are therefore actionable components of the training state, providing a mechanism-based criterion for when finite-horizon rather than one-step intervention is required.

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