# K2-Think: A Parameter-Efficient Reasoning System

arXiv: https://arxiv.org/abs/2509.07604 · HTML: https://mlsanity.com/paper/2509.07604/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 78 of its 98 references that are in the map.
- First posted on arXiv 9 Sep 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 78)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Jailbroken: How Does LLM Safety Training Fail?](https://mlsanity.com/paper/2307.02483/) (2023)
- [HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusal](https://mlsanity.com/paper/2402.04249/) (2024)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)

## Built on by (most cited first, 11 of 11)

- [DRPO: Efficient Reasoning via Decoupled Reward Policy Optimization](https://mlsanity.com/paper/2510.04474/) (2025)
- [Learning to Simulate Human Dialogue](https://mlsanity.com/paper/2601.04436/) (2026)
- [Are Large Reasoning Models Interruptible?](https://mlsanity.com/paper/2510.11713/) (2025)
- [Neural Theorem Proving for Verification Conditions: A Real-World Benchmark](https://mlsanity.com/paper/2601.18944/) (2026)
- [Best-of-∞ -- Asymptotic Performance of Test-Time LLM Ensembling](https://mlsanity.com/paper/2509.21091/) (2025)
- [Reasoning's Razor: Reasoning Improves Accuracy but Can Hurt Recall at Critical Operating Points in Safety and Hallucination Detection](https://mlsanity.com/paper/2510.21049/) (2025)
- [K2-V2: A 360-Open, Reasoning-Enhanced LLM](https://mlsanity.com/paper/2512.06201/) (2025)
- [XL-SafetyBench: A Country-Grounded Cross-Cultural Benchmark for LLM Safety and Cultural Sensitivity](https://mlsanity.com/paper/2605.05662/) (2026)
- [Group Pattern Selection Optimization: Let LRMs Pick the Right Pattern for Reasoning](https://mlsanity.com/paper/2601.07238/) (2026)
- [Themis: Training Robust Multilingual Code Reward Models for Flexible Multi-Criteria Scoring](https://mlsanity.com/paper/2605.00754/) (2026)
- [One More Turn, Less Regret: A Regret-Based Multi-Turn Benchmark for LLMs' Clarification Policies](https://mlsanity.com/paper/2607.21143/) (2026)

## Abstract (arXiv)

K2-Think is a reasoning system that achieves state-of-the-art performance with a 32B parameter model, matching or surpassing much larger models like GPT-OSS 120B and DeepSeek v3.1. Built on the Qwen2.5 base model, our system shows that smaller models can compete at the highest levels by combining advanced post-training and test-time computation techniques. The approach is based on six key technical pillars: Long Chain-of-thought Supervised Finetuning, Reinforcement Learning with Verifiable Rewards (RLVR), Agentic planning prior to reasoning, Test-time Scaling, Speculative Decoding, and Inference-optimized Hardware, all using publicly available open-source datasets. K2-Think excels in mathematical reasoning, achieving state-of-the-art scores on public benchmarks for open-source models, while also performing strongly in other areas such as Code and Science. Our results confirm that a more parameter-efficient model like K2-Think 32B can compete with state-of-the-art systems through an integrated post-training recipe that includes long chain-of-thought training and strategic inference-time enhancements, making open-source reasoning systems more accessible and affordable. K2-Think is freely available at k2think.ai, offering best-in-class inference speeds of over 2,000 tokens per second per request via the Cerebras Wafer-Scale Engine.