# Sharpen Before You Adapt: Data-Free Entry-State Sharpening for Test-Time Reinforcement Learning

arXiv: https://arxiv.org/abs/2610.00903 · HTML: https://mlsanity.com/paper/2610.00903/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL training of language and agent models, one of 15 directions in Deep reinforcement learning methods.
- Builds on 33 of its 37 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Placed in

- Deep reinforcement learning methods / [RL training of language and agent models](https://mlsanity.com/deeprl/rl-training-of-language-and-agent-models/)

## Builds on (most cited first, 30 of 33)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Don't Stop Pretraining: Adapt Language Models to Domains and Tasks](https://mlsanity.com/paper/2004.10964/) (2020)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [Right Question is Already Half the Answer: Fully Unsupervised LLM Reasoning Incentivization](https://mlsanity.com/paper/2504.05812/) (2025)
- [OctoThinker: Mid-training Incentivizes Reinforcement Learning Scaling](https://mlsanity.com/paper/2506.20512/) (2025)
- [Self-Improvement in Language Models: The Sharpening Mechanism](https://mlsanity.com/paper/2412.01951/) (2024)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [Preserving Diversity in Supervised Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2408.16673/) (2024)
- [SeRL: Self-Play Reinforcement Learning for Large Language Models with Limited Data](https://mlsanity.com/paper/2505.20347/) (2025)
- [ETTRL: Balancing Exploration and Exploitation in LLM Test-Time Reinforcement Learning Via Entropy Mechanism](https://mlsanity.com/paper/2508.11356/) (2025)
- [One-shot Entropy Minimization](https://mlsanity.com/paper/2505.20282/) (2025)
- [SPINE: Token-Selective Test-Time Reinforcement Learning with Entropy-Band Regularization](https://mlsanity.com/paper/2511.17938/) (2025)
- [What If Consensus Lies? Selective-Complementary Reinforcement Learning at Test Time](https://mlsanity.com/paper/2603.19880/) (2026)
- [On-Policy Self-Distillation with Sampled Demonstrations Reduces Output Diversity](https://mlsanity.com/paper/2606.26091/) (2026)
- [Reinforcement Mid-Training](https://mlsanity.com/paper/2509.24375/) (2025)

## Abstract (arXiv)

Test-time reinforcement learning (TTRL) adapts language models on unlabeled test problems using supervision derived from their own samples. This makes the checkpoint's entry state consequential: a diffuse policy provides noisier self-supervision and may spend much of a limited adaptation budget merely concentrating probability mass before reliably expressing capability it already possesses. We propose entry-state sharpening: use data-free training before TTRL to prepare a general-purpose checkpoint in a state that subsequent label-free adaptation can exploit more efficiently. The idea is not tied to one training recipe; different data-free objectives can move the same base model to different entry states. Across five data-free checkpoints derived from Qwen3-4B and evaluated under an identical 15-step TTRL protocol, entry policy entropy strongly rank-orders endpoint conversion efficiency, a reliability-to-reachability measure (Spearman ρ=-0.90; ρ=-0.99 after controlling for entry reachability). The contrast across objectives is striking: R-Zero remains diffuse at 3.39 nats and finishes below the untuned base in 6/6 matched comparisons across MATH, GPQA, and AMC, whereas SPIRAL reaches 0.07 nats and achieves the highest post-TTRL accuracy on MATH and GPQA despite its self-play stage using no math training data. An in-domain label-free self-distillation intervention further shows that the entry state can be deliberately sharpened. These results motivate treating checkpoint preparation as a state-control problem: use data-free training to improve TTRL readiness, with entry entropy as a label-free control signal and reachable capability as the constraint.