# MedRule-KG: A Knowledge-Graph--Steered Scaffold for Mathematical Reasoning with a Lightweight Verifier

arXiv: https://arxiv.org/abs/2510.16309 · HTML: https://mlsanity.com/paper/2510.16309/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 6 of its 12 references that are in the map.
- First posted on arXiv 18 Oct 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 6 of 6)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Augmented Language Models: a Survey](https://mlsanity.com/paper/2302.07842/) (2023)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Autoformalization with Large Language Models](https://mlsanity.com/paper/2205.12615/) (2022)
- [MathSmith: Towards Extremely Hard Mathematical Reasoning by Forging Synthetic Problems with a Reinforced Policy](https://mlsanity.com/paper/2508.05592/) (2025)

## Built on by (most cited first, 1 of 1)

- [VeriBound: PAC-Bayesian Generalization Bounds for Process Reward Models Trained with Formal Verification Tools](https://mlsanity.com/paper/2606.20740/) (2026)

## Abstract (arXiv)

Large language models (LLMs) often produce fluent reasoning steps while violating simple mathematical or logical constraints. We introduce MedRule-KG, a compact typed knowledge graph coupled with a symbolic verifier, designed to enforce mathematically interpretable rules in reasoning tasks. MedRule-KG encodes entities, relations, and three domain-inspired rules, while the verifier checks predictions and applies minimal corrections to guarantee consistency. On a 90-example FDA-derived benchmark, grounding in MedRule-KG improves exact match (EM) from 0.767 to 0.900, and adding the verifier yields 1.000 EM while eliminating rule violations entirely. We demonstrate how MedRule-KG provides a general scaffold for safe mathematical reasoning, discuss ablations, and release code and data to encourage reproducibility.