# IRDS: Interpretable RLVR Data Selection via Verifier-Coupled Sparse Autoencoder Coverage

arXiv: https://arxiv.org/abs/2605.28247 · HTML: https://mlsanity.com/paper/2605.28247/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 27 May 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- Mechanistic interpretability / [Steering and interpreting LLM reasoning](https://mlsanity.com/mechinterp/steering-and-interpreting-llm-reasoning/)

## Builds on (most cited first, 21 of 21)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [ReClor: A Reading Comprehension Dataset Requiring Logical Reasoning](https://mlsanity.com/paper/2002.04326/) (2020)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [Perplexed by Perplexity: Perplexity-Based Data Pruning With Small Reference Models](https://mlsanity.com/paper/2405.20541/) (2024)
- [Improving Data Efficiency for LLM Reinforcement Fine-tuning Through Difficulty-targeted Online Data Selection and Rollout Replay](https://mlsanity.com/paper/2506.05316/) (2025)
- [Prompt Curriculum Learning for Efficient LLM Post-Training](https://mlsanity.com/paper/2510.01135/) (2025)
- [Towards High Data Efficiency in Reinforcement Learning with Verifiable Reward](https://mlsanity.com/paper/2509.01321/) (2025)
- [Data-Efficient RLVR via Off-Policy Influence Guidance](https://mlsanity.com/paper/2510.26491/) (2025)
- [Do Sparse Autoencoders Identify Reasoning Features in Language Models?](https://mlsanity.com/paper/2601.05679/) (2026)
- [Prioritized Replay for RL Post-training](https://mlsanity.com/paper/2601.02648/) (2026)
- [Learn More with Less: Uncertainty Consistency Guided Query Selection for RLVR](https://mlsanity.com/paper/2601.22595/) (2026)
- [Rethinking Representativeness and Diversity in Dynamic Data Selection](https://mlsanity.com/paper/2603.04981/) (2026)

## Built on by (most cited first, 1 of 1)

- [Per-Matrix Optimality Is Not Enough: Three-Level Optimization for Low-Rank LLM Compression](https://mlsanity.com/paper/2609.15838/) (2026)

## Abstract (arXiv)

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.