# Mathematical Reasoning

Skywork-OR1 is a high-performance mathematical code reasoning model developed by Kunlun Wanwei's Tiangong team. This model series achieves industry-leading inference performance with comparable parameter scales, breaking through the bottleneck of large models in logical understanding and complex task solving. The Skywork-OR1 series includes three models: Skywork-OR1-Math-7B, Skywork-OR1-7B-Preview, and Skywork-OR1-32B-Preview, focusing on mathematical reasoning, general reasoning, and high-performance reasoning tasks, respectively. This open-source release not only includes model weights but also fully opens the training dataset and complete training code. All resources have been uploaded to GitHub and Hugging Face, providing the AI community with a fully reproducible practical reference. This comprehensive open-source strategy helps to promote the common progress of the entire AI community in reasoning ability research.

HunYuan T1 is a large-scale reasoning model launched by Tencent, based on reinforcement learning technology, significantly improving reasoning capabilities through extensive post-training. It excels in long text processing and context capture, while optimizing the consumption of computing resources, thus possessing efficient reasoning capabilities. It is suitable for various reasoning tasks, and particularly excels in mathematics and logical reasoning. This product is based on deep learning and continuously optimized with actual feedback, suitable for applications in various fields such as scientific research and education.

DeepSeek-R1-Distill-Qwen-7B is a reinforcement learning-optimized reasoning model distilled from Qwen-7B. It excels in mathematical, coding, and reasoning tasks, generating high-quality reasoning chains and solutions. This model significantly enhances reasoning capabilities and efficiency through large-scale reinforcement learning and data distillation techniques, making it suitable for scenarios requiring complex reasoning and logical analysis.

rStar-Math is a study aimed at demonstrating that small language models (SLMs) can match or even surpass the mathematical reasoning capabilities of OpenAI's o1 model without relying on more advanced models. This research employs Monte Carlo Tree Search (MCTS) to achieve 'deep thinking', allowing mathematical strategy SLMs to search based on a reward model guided by SLM. rStar-Math introduces three innovative approaches to address the challenge of training two SLMs, enhancing their mathematical reasoning abilities to a state-of-the-art level through four rounds of self-evolution and millions of synthetic solutions. The model significantly improved performance in the MATH benchmark tests and excelled in the AIME competition.

Eurus-2-7B-SFT is a large language model fine-tuned from the Qwen2.5-Math-7B model, aimed at enhancing mathematical reasoning and problem-solving abilities. The model learns reasoning patterns through imitation learning (supervised fine-tuning), effectively solving complex mathematical and programming tasks. Its main advantages lie in its powerful reasoning capabilities and accurate handling of mathematical problems, making it suitable for scenarios that require complex logical reasoning. Developed by the PRIME-RL team, the model aims to improve its reasoning capabilities through implicit rewards.

QVQ-72B-Preview is an experimental research model developed by the Qwen team, focusing on enhancing visual reasoning capabilities. The model demonstrates strong abilities in multidisciplinary understanding and reasoning, achieving significant advances especially in mathematical reasoning tasks. Although advancements have been made in visual reasoning, it does not completely replace the capabilities of Qwen2-VL-72B, and may gradually lose focus on image content in multi-step visual reasoning, leading to hallucinations. Furthermore, QVQ does not show significantly better performance in basic recognition tasks compared to Qwen2-VL-72B.

O1-Journey is a project initiated by the GAIR research group at Shanghai Jiao Tong University, aimed at replicating and reimagining the capabilities of OpenAI's O1 model. This project introduces a novel training paradigm called 'journey learning' and has successfully built the first model that integrates search and learning in mathematical reasoning. Through processes such as trial and error, correction, backtracking, and reflection, this model has become an effective method for tackling complex reasoning tasks.

DeepSeek-Coder-V2 is an open-source Mixture-of-Experts code language model, whose performance rivals that of GPT4-Turbo. It excels in code-specific tasks. Further pre-trained with an additional 60 billion tokens, it enhances coding and mathematical reasoning abilities while maintaining comparable performance on general language tasks. Compared to DeepSeek-Coder-33B, it shows significant improvements across code-related tasks, reasoning, and general capabilities. Moreover, it supports 338 programming languages (an expansion from 86) and boasts a context length extended to 128K from 16K.

InternLM-Math-Plus is a cutting-edge bilingual (English and Chinese) open-source large language model (LLM) focused on mathematical reasoning. It exhibits capabilities in solving, proving, validating, and augmenting mathematical problems. It demonstrates significant performance improvements in both informal mathematical reasoning (such as reasoning chains and code interpretation) and formal mathematical reasoning (such as LEAN 4 translation and proof).