Does Scaling Reinforcement Learning Really Require More Training?

arXiv:2610.01133 · cs.LG, cs.AI · Submitted 2026-10-01 · Read on arXiv

cs.LG, cs.AI

Submitted: 2026-10-01

Updated: 2026-10-06

Comments: Corrected a typo in an author's name. No changes to the paper content

Code: https://github.com/project-numina/aimo-progress-prize

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Reinforcement Learning — 1× in this paper · explained in 4 episodes

Sources

• DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
• DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning
• JustRL: Scaling a 1.5B LLM with a Simple RL Recipe
• AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset
• Olmo 3
• Understanding R1-Zero-Like Training: A Critical Perspective
• ResMerge: Residual-based Spectral Merging of Large Language Models
• On Predictability of Reinforcement Learning Dynamics for Large Language Models
• You Only Need Minimal RLVR Training: Extrapolating LLMs via Rank-1 Trajectories
• Low-rank Optimization Trajectories Modeling for LLM RLVR Acceleration
• Extrapolative Weight Averaging Reveals Correctness-Efficiency Frontiers in Code RL

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