# Curriculum Reinforcement Learning Can Incentivize Reasoning Capacity in LLMs Beyond the Base Model

arXiv: https://arxiv.org/abs/2606.22317 · HTML: https://mlsanity.com/paper/2606.22317/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 49 references that are in the map.
- First posted on arXiv 21 Jun 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 22 of 22)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [Seed1.5-Thinking: Advancing Superb Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.13914/) (2025)
- [Mitigating Catastrophic Forgetting in Large Language Models with Self-Synthesized Rehearsal](https://mlsanity.com/paper/2403.01244/) (2024)
- [Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models](https://mlsanity.com/paper/2503.21380/) (2025)
- [Spurious Forgetting in Continual Learning of Language Models](https://mlsanity.com/paper/2501.13453/) (2025)
- [Mitigating Catastrophic Forgetting in Large Language Models with Forgetting-aware Pruning](https://mlsanity.com/paper/2509.08255/) (2025)
- [Trust Region Preference Approximation: A simple and stable reinforcement learning algorithm for LLM reasoning](https://mlsanity.com/paper/2504.04524/) (2025)
- [Enhancing Long-Chain Reasoning Distillation through Error-Aware Self-Reflection](https://mlsanity.com/paper/2505.22131/) (2025)
- [TACLer: Tailored Curriculum Reinforcement Learning for Efficient Reasoning](https://mlsanity.com/paper/2601.21711/) (2026)

## Built on by (most cited first, 5 of 5)

- [Question Begets Question: Self-Evolving Curriculum for Reinforcement Fine-Tuning on Competition Mathematics](https://mlsanity.com/paper/2608.01522/) (2026)
- [BODHI: Do LLMs Branch Out and Discover Heterogeneous Inferences?](https://mlsanity.com/paper/2608.02867/) (2026)
- [Reachability Is Not Realization: Tracing the Sources of LLM Benchmark Gains](https://mlsanity.com/paper/2608.03219/) (2026)
- [Moving the Mean Toward the Known Good, Not Beyond It: What Inference-Time Interventions and Weight Consolidation Buy in Open-Ended Generation](https://mlsanity.com/paper/2608.28886/) (2026)
- [When Terminal-Agent Training Stalls: Demystifying Data Generation and Verification Challenge](https://mlsanity.com/paper/2610.02405/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) is widely viewed as a promising path toward continuously improving large language models. Recent works, however, suggest that mainstream RLVR often reallocates sampling probabilities among trajectories already present in the base model: it can improve sampling efficiency, reflected by higher pass@1 scores, but yields limited gains, and can even decrease pass@k scores when k is large, and therefore may fail to expand the base model's reasoning capacity boundary. In this paper, we present a boundary-aware Curriculum RL approach to move beyond the base model's reasoning capacity boundary. Our approach first uses pass@k sampling to locate the current reasoning capacity boundary, then applies targeted teacher guidance to examples near or beyond that boundary, and finally uses RL to consolidate the newly introduced reasoning patterns. Across Qwen, Llama, and DeepSeek base models, boundary-aware Curriculum RL improves both pass@1 scores and pass@256 scores, with pass@1 reflecting one-attempt performance and pass@256 serving as an empirical proxy for the reasoning capacity boundary. In our experiments, average pass@256 improves by 9.8 percentage points over the base models and by 10.3 percentage points over Vanilla RLVR. These results suggest that boundary-aware Curriculum RL can provide a scalable route for LLMs to continuously improve beyond the base model's empirical reasoning capacity boundary.