Efficient RLVR Training via Weighted Mutual Information Data Selection

Reinforcement learning with verifiable rewards (RLVR) has greatly advanced large reasoning models (LRMs), but it requires timely training on a huge fully-annotated dataset. To this end, data-efficient RLVR methods have been widely studied from two perspectives: (i) data selection methods identify a small subset of "golden" samples that yield near-full-data performance, but they rely on a pre-existing pool of labeled data. (ii) unsupervised RLVR methods train the model using its own internal supervision signals on large-scale unlabeled data, yet they exhibit suboptimal performance. Accordingly, we investigate the "pick in the dark" setup for RLVR, which aims to select, without prior supervision, unlabeled samples that are most beneficial for training and worthy of annotation. Through systematic analysis, we demonstrate that smart picks hinge on a well-calibrated uncertainty estimator to enable strategic partitioning of data for adaptive training regimes. Building on this insight, we propose PivotTrace, a three-way data triage framework that leverages attention dynamics to trace metacognitive pivots during reasoning. By precisely quantifying uncertainty through pivot density, PivotTrace achieves automated data routing to synergistically maximize both annotation and training efficiency. Empirically, PivotTrace surpasses the fully supervised LRM with only 29.3% annotated samples and 2.75 faster convergence.

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.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a prominent paradigm for training reasoning models, but its computational cost makes efficient data selection increasingly important. Since training examples contribute unequally to learning, selecting a small, informative subset can offer a more efficient alternative to using the entire data pool. The training-free selection method estimates prompt value with hidden states from complete greedy rollouts. However, in our datasets, $26$--$32\%$ of these rollouts fail to terminate within the generation budget. We introduce LIFT, a training-free data selector that identifies impactful prompts using only partial reasoning rollouts. At its core, LIFT uses Partial Rollout Context Lift (PRCL), a score inspired by pointwise $\mathcal{V}$-information that accumulates token-level log-likelihood ratios between a question-conditioned context and a null context with the question removed. This enables prompt scoring from a short rollout prefix rather than a complete trajectory. Across Qwen2.5-Math-1.5B and DeepSeek-R1-Distill-1.5B, prefixes retaining at least 90% and 95% of the full-rollout PRCL score, respectively, require only 26% and 4.7% of the tokens generated by full rollouts. Compared with SHIFT, LIFT reduces selection cost by 3.7--9.1$\times$ while achieving competitive downstream RLVR performance, with the highest six-benchmark average in three of six settings.