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

TL;DR

This paper introduces the Infinite Problem Generator, an agentic framework that creates verifiable physics problems with guaranteed solutions, facilitating scalable and high-quality data for training reasoning models.

Contribution

The paper presents the IPG framework that synthesizes physics problems as executable code, ensuring mathematical consistency and enabling controllable curriculum generation.

Findings

Created ClassicalMechanicsV1 dataset with 1,335 problems

Established a strong correlation (R^2 ≈ 0.95) between formula count and code length

Demonstrated high structural diversity in generated problems

Abstract

Training large language models for complex reasoning is bottlenecked by the scarcity of verifiable, high-quality data. In domains like physics, standard text augmentation often introduces hallucinations, while static benchmarks lack the reasoning traces required for fine-tuning. We introduce the Infinite Problem Generator (IPG), an agentic framework that synthesizes physics problems with guaranteed solvability through a Formula-as-Code paradigm. Unlike probabilistic text generation, IPG constructs solutions as executable Python programs, enforcing strict mathematical consistency. As a proof-of-concept, we release ClassicalMechanicsV1, a high-fidelity corpus of 1,335 classical mechanics problems expanded from 165 expert seeds. The corpus demonstrates high structural diversity, spanning 102 unique physical formulas with an average complexity of 3.05 formulas per problem. Furthermore, we identify a Complexity Blueprint, demonstrating a strong linear correlation ($R^2 \approx 0.95$) between formula count and verification code length. This relationship establishes code complexity as a precise, proxy-free metric for problem difficulty, enabling controllable curriculum generation. We release the full IPG pipeline, the ClassicalMechanicsV1 dataset, and our evaluation report to support reproducible research in reasoning-intensive domains.