# Question Begets Question: Self-Evolving Curriculum for Reinforcement Fine-Tuning on Competition Mathematics

arXiv: https://arxiv.org/abs/2608.01522 · HTML: https://mlsanity.com/paper/2608.01522/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 24 of its 33 references that are in the map.
- First posted on arXiv 2 Aug 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)

## Builds on (most cited first, 24 of 24)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [Online Difficulty Filtering for Reasoning Oriented Reinforcement Learning](https://mlsanity.com/paper/2504.03380/) (2025)
- [Efficient Reinforcement Finetuning via Adaptive Curriculum Learning](https://mlsanity.com/paper/2504.05520/) (2025)
- [SwS: Self-aware Weakness-driven Problem Synthesis in Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.08989/) (2025)
- [Nudging the Boundaries of LLM Reasoning](https://mlsanity.com/paper/2509.25666/) (2025)
- [Teaching Models to Teach Themselves: Reasoning at the Edge of Learnability](https://mlsanity.com/paper/2601.18778/) (2026)
- [On the Emergence of Implicit Curriculum in RLVR Learning Dynamics](https://mlsanity.com/paper/2602.14872/) (2026)
- [Understanding Diversity Collapse in RLVR via the Lens of Overtraining](https://mlsanity.com/paper/2606.15455/) (2026)
- [Curriculum Reinforcement Learning Can Incentivize Reasoning Capacity in LLMs Beyond the Base Model](https://mlsanity.com/paper/2606.22317/) (2026)
- [Executable Functional Abstractions: Inferring Generative Programs for Advanced Math Problems](https://mlsanity.com/paper/2504.09763/) (2025)
- [Cog-DRIFT: Exploration on Adaptively Reformulated Instances Enables Learning from Hard Reasoning Problems](https://mlsanity.com/paper/2604.04767/) (2026)
- [Self-Improvement Can Self-Regress: The Rise-and-Collapse Failure Mode of LLM Self-Training](https://mlsanity.com/paper/2606.21090/) (2026)
- [EarthquakeNPP: A Benchmark for Earthquake Forecasting with Neural Point Processes](https://mlsanity.com/paper/2410.08226/) (2024)
- [CT Open: An Open-Access, Uncontaminated, Live Platform for the Open Challenge of Clinical Trial Outcome Prediction](https://mlsanity.com/paper/2604.16742/) (2026)
- [Do Larger Models Really Win in Drug Discovery? A Benchmark Assessment of Model Scaling in AI-Driven Molecular Property and Activity Prediction](https://mlsanity.com/paper/2604.26498/) (2026)
- [Learning from Synthetic Data without Model Collapse in Iterative Instruction Tuning](https://mlsanity.com/paper/2607.17043/) (2026)

## Built on by (most cited first, 2 of 2)

- [Save Your Saturated Data: Learning Beyond Reward Saturation in Group-Based RL](https://mlsanity.com/paper/2609.33126/) (2026)
- [Frontier Learning: Training LLM Reasoners at the Edge of Capability](https://mlsanity.com/paper/2609.35426/) (2026)

## Abstract (arXiv)

Teaching a language model a skill it has not mastered is obstructed by three recurring difficulties: training data is scarce, ground-truth reasoning traces are usually unavailable, and models often exhibit an apparent ceiling beyond which additional data yields no further improvement. We study these difficulties in a controlled setting, fine-tuning Qwen2.5-Math-7B on competition mathematics (AIME), a task on which it initially solves only 5.6% of problems (pass@1). To address data scarcity, we introduce Question-begets-Question (QbQ), a scalable procedure in which a teacher transforms existing problems into diverse variants that probe the same underlying skills; to model the absence of oracle reasoning, we train exclusively via reinforcement learning on problem statements and final answers, never on teacher reasoning traces. Static training on such data, however, plateaus well short of the task: real-plus-synthetic augmentation and non-curriculum QbQ generated synthetic data training cap pass@1 at 12.5% and 14.5% respectively, despite large increases in data. Our central finding is that this ceiling is not intrinsic to the model. We propose a self-evolving curriculum that, each round, evaluates the current checkpoint, seeds QbQ from the problems it can mostly get right, and trains on the resulting variants; under an identical data budget, this breaks the ceiling and lifts pass@1 to 16.5% with no sign of saturation after 20 rounds. Counterintuitively, we find that models improve when trained on variants of problems they can mostly get right, and that models trained this way go on to solve harder problems never seen during training.