Multiplicative vs. Additive State Coupling in Learned Optimizer Schedules
Abstract
We learn schedules for a continuous penalty relaxation of MAX-CUT by backpropagating through an unrolled classical solver. A state-blind schedule generalizes to instances substantially larger than those used for training. A state-adaptive bilinear schedule also generalizes out of distribution, outperforming its untrained baseline across 15 seeds (t=4.1). By contrast, an additive ablation with identical inputs and output heads is statistically indistinguishable from the bilinear model in distribution but performs worse than its own baseline out of distribution (t=−11.7). This separation appears without regularization and persists across a $30$ round weight-decay sweep: the bilinear advantage remains significant at every tested value, whereas the additive model never recovers. The results in this setting isolate how solver state enters the schedule, rather than state adaptivity alone, as the architectural distinction associated with out-of-distribution transfer.
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BibTeX
@misc{langston2026multiplicative,
title = {{Multiplicative vs. Additive State Coupling in Learned Optimizer Schedules}},
author = {M. Harper Langston and Pierre-David Letourneau and Dalton Jones and Roland Memisevic and Peter Scott and Mingu Lee and Richard A. Lethin and Christopher Lott and Fatih Porikli and Harris Teague},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32801},
eprint = {2610.32801},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32801},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Multiplicative vs. Additive State Coupling in Learned Optimizer Schedules
AU - M. Harper Langston
AU - Pierre-David Letourneau
AU - Dalton Jones
AU - Roland Memisevic
AU - Peter Scott
AU - Mingu Lee
AU - Richard A. Lethin
AU - Christopher Lott
AU - Fatih Porikli
AU - Harris Teague
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32801
UR - https://arxiv.org/abs/2610.32801
AB - We learn schedules for a continuous penalty relaxation of MAX-CUT by backpropagating through an unrolled classical solver. A state-blind schedule generalizes to instances substantially larger than those used for training. A state-adaptive bilinear schedule also generalizes out of distribution, outperforming its untrained baseline across 15 seeds (t=4.1). By contrast, an additive ablation with identical inputs and output heads is statistically indistinguishable from the bilinear model in distribution but performs worse than its own baseline out of distribution (t=−11.7). This separation appears without regularization and persists across a $30$ round weight-decay sweep: the bilinear advantage remains significant at every tested value, whereas the additive model never recovers. The results in this setting isolate how solver state enters the schedule, rather than state adaptivity alone, as the architectural distinction associated with out-of-distribution transfer.
ER -