Researchers propose Isospectral Optimization (ISO), a framework for Reinforcement Learning with Verifiable Rewards (RLVR) that addresses the missing optimization layer by keeping model weight spectra fixed while optimizing input and output singular frames.
The approach includes ISO-Merger, which combines specialist capabilities into a single model without post-merge data or gradient updates, and ISO-Optimizer, which applies standard optimizers like AdamW to frame variables. On Qwen3-8B-Base, ISO-AdamW matched an aggregate accuracy of 0.495 in just 100 training steps compared to 270 for standard AdamW, eventually reaching 0.509 after 210 steps.
ISO provides a concrete method for post-training adaptation by inheriting the base model's spectrum and optimizing only the frames associated with reward-driven changes.