Paper 2604.12627
KnowRL: Boosting LLM Reasoning via Reinforcement Learning with Minimal-Sufficient Knowledge Guidance
- Published
- Apr 2026
- Research lab
- Independent
- Citations
- 8
- GitHub
- 58 stars
01 In brief
Summary
KnowRL is a reinforcement learning (RL) training framework that addresses reward sparsity in large language model (LLM) reasoning by treating hint design as a minimal-sufficient guidance problem.
Instead of injecting long solution prefixes or abstract templates, KnowRL decomposes guidance into atomic knowledge points (KPs) and selects compact, interaction-aware subsets.
The authors identify a critical-segment effect (performance jumps once a key hint segment appears) and a pruning interaction paradox (removing one KP may help, but removing multiple can hurt).
They propose Constrained Subset Search (CSS), which prunes candidates and then performs a global search, outperforming alternatives like Max-Score, Leave-One-Out, and Consensus-Based Robust Selection.
Trained from OpenMath-Nemotron-1.5B on the QuestA dataset, KnowRL-Nemotron-1.5B achieves 70.08 average accuracy across eight math reasoning benchmarks without KP hints at inference (surpassing Nemotron-1.5B by +9.63 points) and 74.16 with selected KPs, setting a new state of the art at the 1.5B scale.
The model, data, and code are publicly available.
02 From the paper
Abstract
RLVR improves reasoning in large language models, but its effectiveness is often limited by severe reward sparsity on hard problems. Recent hint-based RL methods mitigate sparsity by injecting partial solutions or abstract templates, yet they typically scale guidance by adding more tokens, which introduce redundancy, inconsistency, and extra training overhead. We propose \textbf{KnowRL} (Knowledge-Guided Reinforcement Learning), an RL training framework that treats hint design as a minimal-sufficient guidance problem. During RL training, KnowRL decomposes guidance into atomic knowledge points (KPs) and uses Constrained Subset Search (CSS) to construct compact, interaction-aware subsets for training. We further identify a pruning interaction paradox -- removing one KP may help while removing multiple such KPs can hurt -- and explicitly optimize for robust subset curation under this dependency structure. We train KnowRL-Nemotron-1.5B from OpenMath-Nemotron-1.5B. Across eight reasoning benchmarks at the 1.5B scale, KnowRL-Nemotron-1.5B consistently outperforms strong RL and hinting baselines. Without KP hints at inference, KnowRL-Nemotron-1.5B reaches 70.08 average accuracy, already surpassing Nemotron-1.5B by +9.63 points; with selected KPs, performance improves to 74.16, establishing a new state of the art at this scale. The model, curated training data, and code are publicly available at https://github.com/Hasuer/KnowRL.