Infinite Problem Generator: Verifiably Scaling Physics Reasoning Data with Agentic Workflows

Advancing physics reasoning in large language models requires scalable training data that connect physical laws, concrete problem scenarios, and verifiable numerical answers. Expert-designed problems offer top-down control over physical laws, conditions, and scenarios, but require costly human effort. LLM-based synthesis from texts scales efficiently, but model-generated answers and assessments leave supervision vulnerable to hallucinations. We introduce TIRE, a framework for Top-Down Formula Instantiation with Reliable Execution that brings knowledge-driven problem construction to large-scale data generation. Top-down instantiation uses reusable physical formulas and their applicability conditions to control the physical relations and numerical configurations of generated problems. Reliable execution establishes reference answers before problem generation, providing a common numerical foundation for problem construction and teacher distillation. Together, these mechanisms combine control over problem content with execution-grounded supervision for both supervised fine-tuning and reinforcement learning. Using TIRE, we construct TIRE-19k, spanning nine subfields of physics. Across 3 backbone LLMs and 4 benchmarks, TIRE-19k outperforms 5 representative datasets with equal amounts of SFT data, exceeding the strongest baseline by 2.86 percentage points on average. Further GRPO raises Qwen3-8B's average accuracy by 1.52 percentage points over its TIRE-19k SFT checkpoint. These results demonstrate the value of generating physics training data from explicit physical knowledge with reliable execution.

Data synthesis for training large reasoning models offers a scalable alternative to limited, human-curated datasets, enabling the creation of high-quality data. However, existing approaches face several challenges: (i) indiscriminate generation that ignores the solver's ability and yields low-value problems, or reliance on complex data pipelines to balance problem difficulty; and (ii) a lack of reasoning in problem generation, leading to shallow problem variants. In this paper, we develop a problem generator that reasons explicitly to plan problem directions before synthesis and adapts difficulty to the solver's ability. We recover problem-design CoT from human-authored multi-part questions, using later subquestions as targets to infer the design rationale. These traces initialize the generator, which is then optimized with a seed-conditioned reward based on solver answer consistency. The reward guides difficulty adjustment relative to each seed while favoring problems near the solver's competence boundary. Across 10 mathematical and general reasoning benchmarks, our method outperforms seed-only training by 2.69 and 3.39 percentage points after one and three rounds, respectively. The framework also extends to vision-language models. Our code is publicly available at https://github.com/WalkerWorldPeace/Reasoning-Synthesis.

As large language models (LLMs) advance their mathematical capabilities toward the IMO and research level, the scarcity of challenging, high-quality problems has become a significant bottleneck for training, evaluation and self-evolution of LLMs. Simultaneously, recent code agents have demonstrated sophisticated skills in agentic coding and reasoning, suggesting that code execution can serve as a scalable environment for mathematical experimentation. In this paper, we investigate the potential of code agents to autonomously evolve existing math problems into more complex variations. We introduce a multi-agent framework designed to perform problem evolution while validating the solvability and increased difficulty of the generated problems. Our experiments demonstrate that, given sufficient test-time exploration, code agents can synthesize new, solvable problems that are structurally distinct from and more challenging than the originals. This work provides empirical evidence that code-driven agents can serve as a viable mechanism for synthesizing high-difficulty mathematical reasoning problems within scalable computational environments. Code and data is available at https://github.com/TarferSoul/Code2Math.