InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning
Shanghai AI Laboratory（上海人工智能实验室）；Fudan University（复旦大学）；University of Southern California（南加州大学）；Shanghai Jiaotong University（上海交通大学）；Tsinghua University（清华大学）
The math abilities of large language models can represent their abstract reasoning ability. In this paper, we introduce and open-source our math reasoning LLMs InternLM-Math which is continue pre-trained from InternLM2. We unify chain-of-thought reasoning, reward modeling, formal reasoning, data augmentation, and code interpreter in a unified seq2seq format and supervise our model to be a versatile math reasoner, verifier, prover, and augmenter. These abilities can be used to develop the next math LLMs or self-iteration. InternLM-Math obtains open-sourced state-of-the-art performance under the setting of in-context learning, supervised fine-tuning, and code-assisted reasoning in various informal and formal benchmarks including GSM8K, MATH, Hungary math exam, MathBench-ZH, and MiniF2F. Our pre-trained model achieves 30.3 on the MiniF2F test set without fine-tuning. We further explore how to use LEAN to solve math problems and study its performance under the setting of multi-task learning which shows the possibility of using LEAN as a unified platform for solving and proving in math. Our models, codes, and data are released at \url{https://github.com/InternLM/InternLM-Math}.
Lean Workbook: A large-scale Lean problem set formalized from natural language math problems
Shanghai AI Laboratory（上海人工智能实验室）；Tsinghua University（清华大学）；Shanghai Jiao Tong University（上海交通大学）；Peking University（北京大学）；The Chinese University of Hong Kong（香港中文大学）
InternLM-XComposer2.5-Reward: A Simple Yet Effective Multi-Modal Reward Model
Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；The Chinese University of Hong Kong（香港中文大学）；Shanghai Jiao Tong University（上海交通大学）；Nanjing University（南京大学）；Fudan University（复旦大学）；Nanyang Technological University（南洋理工大学）
ReverseMath: Answer Inversion for Scalable and Verifiable Mathematical Problem Generation
Center for Information and Language Processing（信息与语言处理中心）；LMU Munich（慕尼黑大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心 (MCML)）；Saarland University（萨尔兰州大学）
Learning from Failures: Correction-Oriented Policy Optimization with Verifiable Rewards
Chinese Information Processing Laboratory, Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所信息处理实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Xiaohongshu Inc（小红书公司）
Correct Answers, Invalid Traces: What Verifiable Grade-School Math Reveals About Chain-of-Thought Traces
IT University of Copenhagen（哥本哈根信息技术大学）；Chennai Mathematical Institute（金奈数学研究所）；Indian Institute of Technology Jammu（印度理工学院贾姆穆分校）；Arizona State University（亚利桑那州立大学）
From Informal to Formal -- Incorporating and Evaluating LLMs on Natural Language Requirements to Verifiable Formal Proofs
The Hong Kong University of Science and Technology（香港科学与技术大学）；Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；Guangzhou Institute of Technology, Xidian University（西安电子科技大学广州研究院）；Chongqing University（重庆大学）；ICTT and ISN Laboratory, Xidian University（西安电子科技大学ICTT和ISN实验室）
Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles
ByteDance Seed（字节跳动种子）；Fudan University（复旦大学）；Institute for AI Industry Research (AIR), Tsinghua University（人工智能产业研究院（AIR），清华大学）；Nanjing University（南京大学）；Shanghai Jiao Tong University（上海交通大学）；SIA-Lab of Tsinghua AIR and ByteDance Seed（清华大学AIR实验室和字节跳动种子）
FinChain: A Symbolic Benchmark for Verifiable Chain-of-Thought Financial Reasoning
MBZUAI；Syllogia；The University of Tokyo（东京大学）；The Fin AI（Fin AI）；Cornell University（康奈尔大学）；The University of Melbourne（墨尔本大学）；IIT Delhi（德里理工学院）；The University of Manchester（曼彻斯特大学）
Correct Answers from Sound Reasoning: Verifiable Process Supervision for Language Models
KAIST AI（KAIST人工智能研究所）；University of Texas, Austin（德克萨斯大学奥斯汀分校）；Rice University（里士满大学）；Princeton University（普林斯顿大学）；University of Washington（华盛顿大学）；Sentient Labs（Sentient实验室）
