# MedCalc-R1: Knowledge-Guided Reward Framework for Medical Mathematical Reasoning

arXiv: https://arxiv.org/abs/2608.08623 · HTML: https://mlsanity.com/paper/2608.08623/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Clinical and biomedical applications, one of 17 directions in LLM reasoning.
- Builds on 19 of its 47 references that are in the map.
- First posted on arXiv 9 Aug 2026.

## Placed in

- LLM reasoning / [Clinical and biomedical applications](https://mlsanity.com/lr/clinical-and-biomedical-applications/)

## Builds on (most cited first, 19 of 19)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [HuatuoGPT-o1, Towards Medical Complex Reasoning with LLMs](https://mlsanity.com/paper/2412.18925/) (2024)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [Crossing the Reward Bridge: Expanding RL with Verifiable Rewards Across Diverse Domains](https://mlsanity.com/paper/2503.23829/) (2025)
- [Med-R1: Reinforcement Learning for Generalizable Medical Reasoning in Vision-Language Models](https://mlsanity.com/paper/2503.13939/) (2025)
- [Reinforcement Learning Enhanced LLMs: A Survey](https://mlsanity.com/paper/2412.10400/) (2024)
- [Logical Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2502.09100/) (2025)
- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [Relevant or Random: Can LLMs Truly Perform Analogical Reasoning?](https://mlsanity.com/paper/2404.12728/) (2024)

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

- [Towards a Deterministic Math Solver for Clinical Language Models](https://mlsanity.com/paper/2609.10728/) (2026)

## Abstract (arXiv)

In Reinforcement Learning with Verifiable Rewards (RLVR) frameworks for mathematical reasoning tasks, floating-point results are typically evaluated using a tolerance-based reward. However, this strategy suffers from challenges such as difficulty in threshold calibration, unstable training dynamics, and limited accuracy, especially in clinical scenarios. To address these limitations, we propose a knowledge-guided hybrid reward framework (textscMedCalc-R1). Specifically, we introduce a knowledge verification reward mechanism that enforces explicit generation of computational formulas, which are further validated by an external verifier to enhance interpretability and reasoning reliability. Furthermore, we design a hybrid soft-hard reward scheme combining a hard constraint based on clinical safety thresholds with a soft, precision-sensitive reward that progressively guides learning within the acceptable range. Experimental results demonstrate that our method significantly outperforms existing baselines in both reasoning accuracy and generalization capability, validating the effectiveness and applicability in safety-critical domains.