Here is a concise summary of the document:

**Title:** DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning  
**Authors:** DeepSeek-AI  
**Key Points:**  

1. **Objective:** Improve reasoning capabilities in large language models (LLMs) using reinforcement learning (RL).  
2. **Models Introduced:**  
   - **DeepSeek-R1-Zero:** Trained purely via RL without supervised fine-tuning (SFT), showing strong reasoning but readability issues.  
   - **DeepSeek-R1:** Enhanced with multi-stage training (cold-start data + RL), achieving performance comparable to OpenAI’s o1-1217.  

3. **Methodology:**  
   - **RL Approach:** Used Group Relative Policy Optimization (GRPO) to optimize reasoning.  
   - **Cold-Start Data:** Improved readability and reasoning by fine-tuning with human-friendly CoT examples.  
   - **Distillation:** Transferred reasoning skills to smaller models (1.5B–70B parameters), outperforming competitors like QwQ-32B.  

4. **Results:**  
   - **DeepSeek-R1:** Matched OpenAI-o1-1217 on math (AIME: 79.8%, MATH-500: 97.3%) and coding (Codeforces: 96.3% percentile).  
   - **Distilled Models:** Smaller models (e.g., Qwen-7B) surpassed GPT-4o in math (AIME: 55.5%).  

5. **Challenges:**  
   - Language mixing, prompt sensitivity, and limited gains in software engineering tasks.  

6. **Future Work:**  
   - General capability expansion, multilingual support, and improved RL for engineering tasks.  

**Conclusion:** DeepSeek-R1 demonstrates RL’s potential to enhance reasoning without heavy reliance on SFT, with open-sourced models benefiting the research community.  

**Key Terms:** Reinforcement Learning (RL), Chain-of-Thought (CoT), Distillation, Benchmark Performance.  

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