ISO says RLVR can keep the weight spectrum and learn 2.7× faster

UTEXAS · hf · 2026-07-22

ISO proposes fixed-spectrum optimization for RLVR and cuts training steps by 2.7×

This paper studies the optimization layer behind reinforcement learning with verifiable rewards (RLVR).

The authors argue that RLVR can preserve a base model's weight spectra while changing behavior through the associated input and output singular frames, a phenomenon they call spectral inheritance.
They formalize this as Isospectral Optimization (ISO), with both offline and online versions.
ISO-Merger combines specialists trained from the same base model into a single fixed-spectrum model, without post-merge data, rollouts, gradient updates, or on-policy distillation.
The merged model recovers complementary specialist abilities and performs best among the compared data-free merging methods.
ISO-Optimizer applies optimizers such as AdamW and Muon to the frame variables while keeping the base spectra fixed.
Across reasoning and coding tasks from 1.5B to 8B parameters, ISO-Optimizer improves accuracy in the reported runs and reaches the same score with far fewer steps.
On Qwen3-8B-Base, standard AdamW reaches 0.495 aggregate accuracy after 270 steps, while ISO-AdamW hits the same score after 100 steps and climbs to 0.509 after 210 steps.
The headline claim: RLVR post-training should inherit the spectrum but optimize the frames.

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