# Knowledge or Reasoning? A Close Look at How LLMs Think Across Domains

arXiv: https://arxiv.org/abs/2506.02126 · HTML: https://mlsanity.com/paper/2506.02126/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Clinical and biomedical applications, one of 17 directions in LLM reasoning.
- Builds on 30 of its 49 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Placed in

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

## Builds on (most cited first, 30 of 30)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Capabilities of GPT-4 on Medical Challenge Problems](https://mlsanity.com/paper/2303.13375/) (2023)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [HuatuoGPT-o1, Towards Medical Complex Reasoning with LLMs](https://mlsanity.com/paper/2412.18925/) (2024)
- [MedXpertQA: Benchmarking Expert-Level Medical Reasoning and Understanding](https://mlsanity.com/paper/2501.18362/) (2025)
- [SFT or RL? An Early Investigation into Training R1-Like Reasoning Large Vision-Language Models](https://mlsanity.com/paper/2504.11468/) (2025)
- [ROSCOE: A Suite of Metrics for Scoring Step-by-Step Reasoning](https://mlsanity.com/paper/2212.07919/) (2022)
- [Llama-Nemotron: Efficient Reasoning Models](https://mlsanity.com/paper/2505.00949/) (2025)
- [Seed1.5-Thinking: Advancing Superb Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.13914/) (2025)
- [Verify-and-Edit: A Knowledge-Enhanced Chain-of-Thought Framework](https://mlsanity.com/paper/2305.03268/) (2023)
- [MedReason: Eliciting Factual Medical Reasoning Steps in LLMs via Knowledge Graphs](https://mlsanity.com/paper/2504.00993/) (2025)
- [ReCEval: Evaluating Reasoning Chains via Correctness and Informativeness](https://mlsanity.com/paper/2304.10703/) (2023)
- [Temporal Data Meets LLM -- Explainable Financial Time Series Forecasting](https://mlsanity.com/paper/2306.11025/) (2023)
- [STAR-1: Safer Alignment of Reasoning LLMs with 1K Data](https://mlsanity.com/paper/2504.01903/) (2025)
- [RCOT: Detecting and Rectifying Factual Inconsistency in Reasoning by Reversing Chain-of-Thought](https://mlsanity.com/paper/2305.11499/) (2023)
- [m1: Unleash the Potential of Test-Time Scaling for Medical Reasoning with Large Language Models](https://mlsanity.com/paper/2504.00869/) (2025)
- [A Preliminary Study of o1 in Medicine: Are We Closer to an AI Doctor?](https://mlsanity.com/paper/2409.15277/) (2024)
- [Chain of Logic: Rule-Based Reasoning with Large Language Models](https://mlsanity.com/paper/2402.10400/) (2024)
- [Benchmarking Large Language Models for Math Reasoning Tasks](https://mlsanity.com/paper/2408.10839/) (2024)

## Built on by (most cited first, 14 of 14)

- [What Characterizes Effective Reasoning? Revisiting Length, Review, and Structure of CoT](https://mlsanity.com/paper/2509.19284/) (2025)
- [Reasoning or Retrieval? A Study of Answer Attribution on Large Reasoning Models](https://mlsanity.com/paper/2509.24156/) (2025)
- [Tracing the Traces: Latent Temporal Signals for Efficient and Accurate Reasoning](https://mlsanity.com/paper/2510.10494/) (2025)
- [Correct Reasoning Paths Visit Shared Decision Pivots](https://mlsanity.com/paper/2509.21549/) (2025)
- [Learning from Mistakes: Negative Reasoning Samples Enhance Out-of-Domain Generalization](https://mlsanity.com/paper/2601.04992/) (2026)
- [Demystifying Scientific Problem-Solving in LLMs by Probing Knowledge and Reasoning](https://mlsanity.com/paper/2508.19202/) (2025)
- [ClinSeekAgent: Automating Multimodal Evidence Seeking for Agentic Clinical Reasoning](https://mlsanity.com/paper/2605.20176/) (2026)
- [Towards Efficient Medical Reasoning with Minimal Fine-Tuning Data](https://mlsanity.com/paper/2508.01450/) (2025)
- [Reasoning Fails Where Step Flow Breaks](https://mlsanity.com/paper/2604.06695/) (2026)
- [Prescriptive Scaling Reveals the Evolution of Language Model Capabilities](https://mlsanity.com/paper/2602.15327/) (2026)
- [TARo: Token-level Adaptive Routing for LLM Test-time Alignment](https://mlsanity.com/paper/2603.18411/) (2026)
- [Spatiotemporal Hidden-State Dynamics as a Signature of Internal Reasoning in Large Language Models](https://mlsanity.com/paper/2605.01853/) (2026)
- [CausalMix: Data Mixture as Causal Inference for Language Model Training](https://mlsanity.com/paper/2607.01104/) (2026)
- [WordPolo: Evaluating Language Models Through Iterative Semantic Feedback](https://mlsanity.com/paper/2609.19006/) (2026)

## Abstract (arXiv)

Recent advances in reasoning-enhanced Large Language Models such as OpenAI-o1/3 and DeepSeek-R1 have significantly improved performance on complex tasks. However, the quality and transparency of their internal reasoning processes remain underexplored. This work moves beyond the final-answer accuracy and investigates step-by-step reasoning in the medical and mathematical domains by explicitly decomposing the thinking trajectories into two parts: knowledge and reasoning. Specifically, we introduce a fine-grained evaluation framework that judges: (1) the correctness of knowledge used (measured by Knowledge Index (KI)) and (2) the quality of reasoning (measured by Information Gain (InfoGain)). Using this framework, we study R1-distilled and base Qwen models trained with supervised fine-tuning (SFT) and/or reinforcement learning (RL) in the medical and math domains. Three intriguing findings emerge: (1) The general reasoning abilities in R1-distilled models do not transfer effectively to the medical domain through either SFT or RL. (2) SFT raises final-answer accuracy in both domains, but often at the cost of reasoning quality: InfoGain drops by 38.9% on average compared with untrained models; In the medical domain, however, SFT remains crucial because domain knowledge is indispensable. (3) RL enhances medical reasoning by pruning inaccurate or irrelevant knowledge from reasoning paths, thereby improving both reasoning accuracy and knowledge correctness.