ISO shows that RLVR training can be 2-3x more efficient by freezing a model's weight spectra and only optimizing the directional components, suggesting a fundamental principle for how language models should adapt to reward signals.
This paper introduces Isospectral Optimization (ISO), a new optimization framework for reinforcement learning with verifiable rewards (RLVR) that improves how language models learn from reward feedback. Instead of changing a model's entire weight structure during training, ISO keeps the base weight spectra fixed and only updates the singular frames—the directional components of weights.