# Single-Rollout Hidden-State Dynamics for Training-Free RLVR Data Selection

arXiv: https://arxiv.org/abs/2605.28631 · HTML: https://mlsanity.com/paper/2605.28631/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 51 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 30 of 36)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [PubMedQA: A Dataset for Biomedical Research Question Answering](https://mlsanity.com/paper/1909.06146/) (2019)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Textbooks Are All You Need](https://mlsanity.com/paper/2306.11644/) (2023)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [MedMCQA : A Large-scale Multi-Subject Multi-Choice Dataset for Medical domain Question Answering](https://mlsanity.com/paper/2203.14371/) (2022)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Learning Loss for Active Learning](https://mlsanity.com/paper/1905.03677/) (2019)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [MedXpertQA: Benchmarking Expert-Level Medical Reasoning and Understanding](https://mlsanity.com/paper/2501.18362/) (2025)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [Consistency-based Semi-supervised Active Learning: Towards Minimizing Labeling Cost](https://mlsanity.com/paper/1910.07153/) (2019)
- [Estimating Example Difficulty Using Variance of Gradients](https://mlsanity.com/paper/2008.11600/) (2020)
- [Sequential Graph Convolutional Network for Active Learning](https://mlsanity.com/paper/2006.10219/) (2020)
- [Active Learning by Feature Mixing](https://mlsanity.com/paper/2203.07034/) (2022)
- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [Semi-Supervised Active Learning with Temporal Output Discrepancy](https://mlsanity.com/paper/2107.14153/) (2021)
- [Learning without training: The implicit dynamics of in-context learning](https://mlsanity.com/paper/2507.16003/) (2025)
- [Think Twice Before Selection: Federated Evidential Active Learning for Medical Image Analysis with Domain Shifts](https://mlsanity.com/paper/2312.02567/) (2023)
- [Bi3D: Bi-domain Active Learning for Cross-domain 3D Object Detection](https://mlsanity.com/paper/2303.05886/) (2023)
- [OPUS: Towards Efficient and Principled Data Selection in Large Language Model Pre-training in Every Iteration](https://mlsanity.com/paper/2602.05400/) (2026)

## Built on by (most cited first, 2 of 2)

- [What Matters in On-Policy Distillation? A Perspective on Data Efficiency and Data Selection](https://mlsanity.com/paper/2609.05198/) (2026)
- [SelectTTRL: Representation-Guided Data Selection for Efficient Test-Time Reinforcement Learning](https://mlsanity.com/paper/2610.16104/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) can yield large reasoning gains from very few training instances, yet its strong sensitivity to which instances are used makes data selection a central bottleneck. Most existing selection pipelines rely on training-time optimization signals and/or require access to verifiable rewards or ground-truth answers over large candidate pools, which is costly and often infeasible in specialized domains. We study RLVR data selection in a setting where selection must be performed before any RL training and without labels or reward evaluation on the full pool. We propose SHIFT, a one-shot, training-free selector based solely on inference-time hidden-state dynamics. For each candidate instance, SHIFT runs a single deterministic reasoning rollout and computes a reasoning-induced representation shift (RIRS) as the start-to-end hidden-state delta. SHIFT uses the RIRS magnitude as a lightweight proxy for instance utility and enforces coverage via a quality-weighted farthest-first CoreSet procedure in an RIRS-augmented feature space, producing compact subsets that scale to large unlabeled pools. Across mathematical reasoning and medical QA benchmarks under ultra-low budgets, SHIFT consistently outperforms training-free diversity and difficulty/uncertainty baselines, improving both in-domain accuracy and transfer to harder evaluation settings. Ablations show that RIRS-based coverage and quality-weighting contribute complementary gains, and analyses indicate that RIRS is not explained by simple input/output length statistics. Code is available at github.com/JianghaoWu/SHIFT.