Revolutionizing difficult question generation for LRMs.
Large Reasoning Models (LRMs) benefit substantially from training on challenging competition-level questions. However, existing automated question synthesis methods lack precise difficulty control, incur high computational costs, and struggle to generate competition-level questions at scale. In this paper, we propose CoDiQ (Controllable Difficult Question Generation), a novel framework enabling fine-grained difficulty control via test-time scaling while ensuring question solvability. Specifically, first, we identify a test-time scaling tendency (extended reasoning token budget boosts difficulty but reduces solvability) and the intrinsic properties defining the upper bound of a model's ability to generate valid, high-difficulty questions. Then, we develop CoDiQ-Generator from Qwen3-8B, which improves the upper bound of difficult question generation, making it particularly well-suited for challenging question construction. Building on the CoDiQ framework, we build CoDiQ-Corpus (44K competition-grade question sequences). Human evaluations show these questions are significantly more challenging than LiveCodeBench/AIME with over 82% solvability. Training LRMs on CoDiQ-Corpus substantially improves reasoning performance, verifying that scaling controlled-difficulty training questions enhances reasoning capabilities. We open-source CoDiQ-Corpus, CoDiQ-Generator, and implementations to support related research.
CoDiQ scales question difficulty at inference time.
Maintains high solvability while increasing question complexity.
Improves Large Reasoning Model performance on benchmarks.
Currently limited to English math and code tasks.
Computationally intensive verification process.
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