如果厌倦了RLVR微调慢慢跑，试试ISO：只用1/3的训练步数就能达到同等效果，Qwen3-8B上实测有效，代码开源。
ISO是一种专门为可验证奖励强化学习（RLVR）设计的优化框架。它通过保持基模型的权重谱不变，仅优化输入输出奇异帧来实现模型适配。离线版本ISO-Merger无需数据或梯度就能合并多个专家模型，在无数据合并方法中性能最强。在线版本ISO-Optimizer在Qwen3-8B-Base上，仅用100步就达到AdamW需270步的准确率（0.495），210步后进一步提升至0.509。实验覆盖1.5B到8B参数的推理与代码任务。
ISO: An RLVR-Native Optimization Stack
Reinforcement learning with verifiable rewards (RLVR) is rapidly advancing the reasoning capabilities of language models, yet the optimization layer that converts reward feedback into weight-space updates remains poorly understood. Building on our prior analysis (Zhu et al., 2025), we study this missing layer through the singular structure of model weights and identify spectral inheritance: RLVR can reuse the base model's weight spectra while acquiring new behavior through changes in the associated input and output singular frames. We operationalize spectral inheritance as Isospectral Optimization (ISO), an RLVR-native, fixed-spectrum optimization framework with complementary offline and online instantiations. Offline, ISO-Merger combines the frame changes of shared-base specialists into a single fixed-spectrum model, requiring no post-merge data, rollouts, gradient updates, or on-policy distillation (OPD). It recovers complementary specialist capabilities and achieves the strongest aggregate performance among the compared data-free merging methods. Online, ISO-Optimizer applies a chosen base optimizer, including AdamW and Muon, to the frame variables while keeping the base spectra fixed. Across reasoning and coding tasks ranging from 1.5B to 8B parameters, ISO-Optimizer improves accuracy in the reported runs and reaches matched scores with substantially fewer training steps. On Qwen3-8B-Base, AdamW reaches an aggregate accuracy of 0.495 after 270 training steps. ISO-AdamW reaches the same accuracy after only 100 training steps and improves further to 0.509 after 210 training steps. Together, ISO offers a concrete answer to RLVR's missing optimization layer: rather than inheriting pre-training optimization wholesale, design post-training around the structure of reward-driven adaptation: inherit the spectrum, optimize the frames.