IRDS: Interpretable RLVR Data Selection via Verifier-Coupled Sparse Autoencoder Coverage
Authors: Yuhan Li, Mingxu Zhang, Dazhong Shen, Ying Sun
Organizations: The Hong Kong University of Science and Technology (Guangzhou) · Nanjing University of Aeronautics and Astronautics · The 63rd Research Institute, National University of Defense Technology, Nanjing
Abstract
Reinforcement learning with verifiable rewards (RLVR) has become a key technique for en- hancing LLM reasoning, yet its data ineffi- ciency remains a major bottleneck. Existing methods address this problem only partially, each missing at least one of subset-level cov- erage, verifier signal use, or interpretability. To address this gap, we present IRDS (Inter- pretable RLVR Data Selection), which selects RLVR training instances on a sparse autoen- coder (SAE) cluster basis so the selection itself is auditable on recognizable problem motifs. To select instances the model both fails on and can still learn from, we introduce a verifier- coupled coverage objective on the SAE basis and solve it by greedy log-determinant max- imization. Experiments on three instruction- tuned models and six math reasoning bench- marks show that IRDS achieves the highest overall accuracy, exceeding the strongest base- line by +3.9/+4.0 pp on the two Qwen models and by +0.5 pp on Llama-3.1-8B, while run- ning an order of magnitude cheaper than the trajectory-based baseline.
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) is sensitive to which problems a model trains on, yet existing selection criteria--difficulty filtering, hand-curation, reward-trajectory scoring--assess data value as an intrinsic property of problems, independent of the model that will learn from them. We introduce Circuit Reasoning Score (CRS), a selection signal derived from 46 reasoning-sensitive attention heads identified via contrastive ablation, computed in a single forward pass on the frozen base model without reward labels or rollouts. CRS runs against the intuitive hypothesis that stronger reasoning-circuit engagement produces better training data: on Qwen2.5-Math-7B, the lowest-engagement decile improves over random selection on three medium-difficulty benchmarks (GSM8K +2.0 pp, OlympiadBench +1.6 pp, Minerva +2.9 pp), while the highest-engagement decile gains less and is indistinguishable from the middle decile. The advantage has boundary conditions: on a domain-curated pool no selection method separates from the others; at 1.5B scale the useful direction differs; and the lowest-reward training condition produces the strongest downstream generalization. Within the Qwen2.5-Math settings tested, RLVR data selection appears regime-dependent rather than reducible to a static ranking of problem quality.
Reinforcement learning with verifiable rewards (RLVR) optimizes LLMs using sparse verifiable final-answer rewards. This sparse anchor reliably verifies whether a trajectory succeeds but provides no direct feedback on the reasoning path that produced it. Before success, prerequisite progress on hard problems receives no reward signal; after success, outcome rewards cannot distinguish well-organized correct trajectories from redundant or locally flawed ones. We introduce SCOPE-RL (Scaffolded Chain Optimization with Process Efficiency), a two-stage framework that densifies this anchor while retaining the GRPO update: Adaptive Scaffolded RL adds prefix-decomposed verifiable rewards on answer-hidden sub-question chains before success, and Quality-Aware Process RL applies correctness-gated process-shape rewards to refine correct trajectories after success. An expert-validated Step-Quality Evaluation Protocol evaluates useful-step density, error localization, and token efficiency beyond final-answer accuracy. On Qwen3-8B-Instruct trained on DAPO-Math and Big-Math, SCOPE-RL improves average accuracy by up to 11.2 pp and reduces reasoning tokens by up to 27.1% over outcome-only GRPO; the gains hold under GSPO and on Qwen3-0.6B-Instruct, indicating that reward-signal densification is complementary to policy-update-level RLVR advances. Code and data are available at https://github.com/tokencraft-lab/SCOPE-RL.