RLVR landscapes for iterated multiplications can be benign: Insights from spin-glass theory

arXiv:2609.28625 · cs.LG, cond-mat.dis-nn, stat.ML · Submitted 2026-09-23 · Read on arXiv

cs.LG, cond-mat.dis-nn, stat.ML

Submitted: 2026-09-23

Updated: 2026-09-23

Terminology

• Transformer — 36× in this paper · explained in 2 episodes
• Reinforcement Learning — 24× in this paper · explained in 4 episodes
• Monte Carlo — 13× in this paper
• Accuracy — 3× in this paper · explained in 1 episode
• Deep Reinforcement Learning — 3× in this paper · explained in 2 episodes
• Actor — 2× in this paper · explained in 3 episodes
• In International Conference on Learning Representations — 2× in this paper
• International Conference on Machine Learning — 2× in this paper
• Symmetry Breaking — 2× in this paper · explained in 3 episodes
• Verifiable Rewards — 2× in this paper · explained in 2 episodes
• Action Space — 1× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Animat — 1× in this paper · explained in 1 episode
• Calibration — 1× in this paper · explained in 7 episodes
• Credit assignment — 1× in this paper · explained in 3 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Distribution Shift — 1× in this paper · explained in 5 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• First-Order Transition — 1× in this paper · explained in 2 episodes
• GRPO — 1× in this paper · explained in 6 episodes
• Gibbs State — 1× in this paper · explained in 2 episodes
• Hypergraph — 1× in this paper · explained in 2 episodes
• Multi-Agent System — 1× in this paper · explained in 5 episodes
• Quantization — 1× in this paper · explained in 12 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Transformer Architecture — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• On the Theory of Policy Gradient Methods: Optimality, Approximation, and Distribution Shift
• Global Optimality Guarantees For Policy Gradient Methods
• The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models
• DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning
• Revisiting Policy Gradients for Restricted Policy Classes: Escaping Myopic Local Optima with $k$-step Policy Gradients
• Non-Uniform Noise-to-Signal Ratio in the REINFORCE Policy-Gradient Estimator
• VCRL: Variance-based Curriculum Reinforcement Learning for Large Language Models
• Revisiting Entropy in Reinforcement Learning for Large Reasoning Models
• Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review
• Sequential Group Composition: A Window into the Mechanics of Deep Learning
• The Quantization Model of Neural Scaling
• The Primacy Bias in Deep Reinforcement Learning
• Hybrid Reinforcement: When Reward Is Sparse, It's Better to Be Dense
• Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning
• RAGEN: Understanding Self-Evolution in LLM Agents via Multi-Turn Reinforcement Learning
• PAEC: Position-Aware Entropy Calibration for LLM Reasoning in RLVR
• DAPO: An Open-Source LLM Reinforcement Learning System at Scale
• Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?

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