# Agentic Retrieval and Reinforcement Learned Equation Chains: A Controlled Generation Framework for Complex and Novel Physics Word Problems

arXiv: https://arxiv.org/abs/2606.15591 · HTML: https://mlsanity.com/paper/2606.15591/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Educational agents and math problem solving, one of 16 directions in LLM agents and tool use.
- Builds on 14 of its 36 references that are in the map.
- First posted on arXiv 14 Jun 2026.

## Placed in

- LLM agents and tool use / [Educational agents and math problem solving](https://mlsanity.com/agents/educational-agents-and-math-problem-solving/)

## Builds on (most cited first, 14 of 14)

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- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
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- [A Survey of Knowledge-Enhanced Text Generation](https://mlsanity.com/paper/2010.04389/) (2020)
- [Math Word Problem Generation with Mathematical Consistency and Problem Context Constraints](https://mlsanity.com/paper/2109.04546/) (2021)
- [Using Large Language Model to Solve and Explain Physics Word Problems Approaching Human Level](https://mlsanity.com/paper/2309.08182/) (2023)
- [Machine Translation: A Literature Review](https://mlsanity.com/paper/1901.01122/) (2018)

## Abstract (arXiv)

Generating high-quality Physics Word Problems (PWPs) that are novel, complex, and solvable remains a challenging and underexplored problem in educational content generation. Existing approaches, many adapted from Math Word Problem (MWP) generation, often produce ambiguous, unsolvable, or structurally simple questions with limited linguistic diversity. We introduce ARVRE (Agentic Retrieval Value Reinforced Equation-chain), a two-stage framework for generating diverse and mathematically valid PWPs. In the first stage, a form of offline temporal-difference learning is used to construct valid chains of physics equations, while an agentic retrieval-augmented generation (RAG) framework dynamically selects topic-specific concepts and vocabulary. This design enables explicit control over problem structure and difficulty. In the second stage, a Large Language Model (LLM) converts the equation chain and retrieved concepts into a natural-language physics question. By grounding generation in valid equation chains, our method preserves mathematical correctness while promoting linguistic diversity and contextual richness. Human and automated evaluations demonstrate that ARVRE generates PWPs that are more complex, novel, and solvable than those produced by existing approaches. These results highlight the potential of combining reinforcement learning, retrieval, and LLMs for reliable generation of educational physics content.