研究对比乘法与加法状态耦合对学习式优化器调度的影响
Multiplicative vs. Additive State Coupling in Learned Optimizer Schedules
一篇优化器调度的架构对比实验：乘法耦合的调度能泛化到大 15 个种子验证的分布外实例，加法版不行，做学习式优化的人可以看看。
论文通过反传经过展开的经典求解器，学习 MAX-CUT 连续惩罚松弛的调度策略。状态自适应的双线性调度在 15 个种子上泛化到分布外，t=4.1 显著优于未训练基线；而输入和输出头相同的加法消融版在分布内与之统计上不可区分，分布外却比自身基线更差（t=-11.7）。该差异无需正则化，在 30 轮 weight-decay 扫描的每个取值上均保持显著。结论指向求解器状态进入调度的乘法方式本身，而非状态自适应，是与分布外迁移相关的架构区别。
Multiplicative vs. Additive State Coupling in Learned Optimizer Schedules
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.