# Computational Blueprints: Generating Isomorphic Mathematics Problems with Large Language Models

arXiv: https://arxiv.org/abs/2511.07932 · HTML: https://mlsanity.com/paper/2511.07932/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [A Neural Network Solves, Explains, and Generates University Math Problems by Program Synthesis and Few-Shot Learning at Human Level](https://mlsanity.com/paper/2112.15594/) (2021)
- [Math Word Problem Generation with Mathematical Consistency and Problem Context Constraints](https://mlsanity.com/paper/2109.04546/) (2021)
- [Neuro-Symbolic Data Generation for Math Reasoning](https://mlsanity.com/paper/2412.04857/) (2024)
- [Mathematical Word Problem Generation from Commonsense Knowledge Graph and Equations](https://mlsanity.com/paper/2010.06196/) (2020)

## Abstract (arXiv)

Personalized mathematics education is growing rapidly, creating a strong demand for large sets of similar practice problems. Yet existing studies on mathematics problem generation have focused on data augmentation for training neural language models rather than on direct educational deployment. To bridge this gap, we define a new task, Isomorphic Math Problem Generation (IMPG), designed to produce structurally consistent variants of source problems. Subsequently, we explored LLM-based frameworks for automatic IMPG through successive refinements, and established Computational Blueprints for Isomorphic Twins (CBIT). With meta-level generation and template-based selective variation, CBIT achieves high mathematical correctness and structural consistency while reducing the cost of generation. Empirical results across refinements demonstrate that CBIT is superior on generation accuracy and cost-effectiveness at scale. Most importantly, CBIT-generated problems exhibited an error rate 17.8% lower than expert-authored items, with deployment to 6,732 learners on a commercial education platform yielding 186,870 interactions.