Does Scaling Reinforcement Learning Really Require More Training?

Bangji Yang, Jiajun Fan, Hongbo Ma, Ruihan Guo, Ge Liu

Scaling reasoning typically spends more compute on reinforcement learning (RL) or on inference. We show that a completed RL training history can yield policies stronger than the checkpoints visited by its optimizer. We call this policy-space scaling: expanding the deployable policy set accessible from a fixed RL history, without extending training or increasing per-query inference computation. We instantiate it with SURGE (Scaling Up RL Gradient-free via Eigenspace fusion). SURGE combines two checkpoints from the same RL run: a high-accuracy anchor and a competitive donor that generates shorter responses. It expresses both checkpoints as changes from their shared initialization, then spectrally decomposes the anchor's update to retain its dominant component and incorporate the donor's complementary component. With a fixed target for how much of the anchor update to retain, SURGE determines the block size from the weights without testing candidate policies. We evaluate two 1.5B mathematical-reasoning histories, DeepSeek and Nemotron, and one 7B coding history, OLMo. SURGE improves benchmark-average accuracy over both input checkpoints while using fewer reasoning tokens than the…