Spectral-Driven Adaptive-Rank Optimizer for Large Language Model Reinforcement Learning with Verifiable Rewards

arXiv:2610.16533 · cs.CL, cs.LG · Submitted 2026-10-12 · Read on arXiv

cs.CL, cs.LG

Submitted: 2026-10-12

Updated: 2026-10-12

Comments: 23 pages, 11 figures, 8 tables. Working in progress

Code: https://github.com/RUCAIBox/Ares

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

Terminology

• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Verifiable Rewards — 1× in this paper · explained in 2 episodes

Sources

• Low-rank Optimization Trajectories Modeling for LLM RLVR Acceleration
• DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning
• Rethinking Muon Beyond Pretraining: Spectral Failures and High-Pass Remedies for VLA and RLVR
• Gradient Descent Happens in a Tiny Subspace
• REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization
• Adam: A Method for Stochastic Optimization
• Tulu 3: Pushing Frontiers in Open Language Model Post-Training
• GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimization
• OpenAI o1 System Card
• Proximal Policy Optimization Algorithms
• DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
• Qwen3 Technical Report

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