RLVR is a Kernel, Not a Function: Statistical Inference for pass@ k Crossovers
stat.ML, cs.LG
Submitted: 2026-09-18
Updated: 2026-09-25
Comments: 37 pages, 5 figures
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- When More Sampling Hurts: The Modal Ceiling and Correlation Ceiling of Test-Time Scaling
- Large Language Monkeys: Scaling Inference Compute with Repeated Sampling
- Demystifying Reinforcement Learning Post-Training of Language Models
- Beyond Pass@k: Breadth-Depth Metrics for Reasoning Boundaries
- When Sharpening Becomes Collapse: Sampling Bias and Semantic Coupling in RL with Verifiable Rewards
- KL-Regularized Reinforcement Learning is Designed to Mode Collapse
- Self-Improvement in Language Models: The Sharpening Mechanism
- Efficient Prediction of Pass@k Scaling in Large Language Models
- Reinforcement Learning vs. Distillation: Understanding Accuracy and Capability in LLM Reasoning
- Adding Error Bars to Evals: A Statistical Approach to Language Model Evaluations
- Reinforcement Learning with Verifiable Rewards: GRPO's Effective Loss, Dynamics, and Success Amplification
- Teacher-Free Self-Training Amplifies but Does Not Compound: A Pass@$K$ Crossover on a Free-Verifier Domain
- Power Distribution Bridges Sampling, Self-Reward RL, and Self-Distillation
- Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs
- The Invisible Leash: Why RLVR May or May Not Escape Its Origin
- Tail-Shape Estimation in LLM Evaluation Is Fragile: A Protocol for Diagnosing False Positives
- When RLVR Shrinks the Reasoning Boundary: Diagnosing Pass@k Inversion
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