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Large Language Models (LLMs) have shown promise in highly-specialized domains, however challenges are still present in aspects of accuracy and costs. These limitations restrict the usage of existing models in domain-specific tasks. While…

Large Language Models (LLMs) have demonstrated strong reasoning capabilities in solving complex problems. However, current approaches primarily enhance reasoning through the elaboration of thoughts while neglecting the diversity of…

Dynamic programming (DP) is a fundamental method in operations research, but formulating DP models has traditionally required expert knowledge of both the problem context and DP techniques. Large Language Models (LLMs) offer the potential…

The growing disparity between the exponential scaling of computational resources and the finite growth of high-quality text data now constrains conventional scaling approaches for large language models (LLMs). To address this challenge, we…

Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…

Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…

Large language models (LLMs) empowered by chain-of-thought reasoning have achieved impressive accuracy on complex tasks but suffer from excessive inference costs and latency when applied uniformly to all problems. We propose SABER…

Recent advances in Large Language Models (LLMs) have shown that their reasoning capabilities can be significantly improved through Reinforcement Learning with Verifiable Reward (RLVR), particularly in domains like mathematics and…

Large Language Models (LLMs) have revolutionized various domains but encounter substantial challenges in tackling optimization modeling tasks for Operations Research (OR), particularly when dealing with complex problem. In this work, we…

Large Language Models (LLMs) are increasingly adopted as evaluators, offering a scalable alternative to human annotation. However, existing supervised fine-tuning (SFT) approaches often fall short in domains that demand complex reasoning.…

Training large language models (LLMs) with synthetic reasoning data has become a popular approach to enhancing their reasoning capabilities, while a key factor influencing the effectiveness of this paradigm is the quality of the generated…

Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…

Recent studies have demonstrated the effectiveness of LLM test-time scaling. However, existing approaches to incentivize LLMs' deep thinking abilities generally require large-scale data or significant training efforts. Meanwhile, it remains…

As Vision-Language Models (VLMs) grow in sophistication, their ability to perform reasoning is coming under increasing supervision. While they excel at many tasks, their grasp of fundamental scientific principles, such as physics, remains…

Recent studies demonstrate that multimodal large language models (MLLMs) can proficiently evaluate visual quality through interpretable assessments. However, existing approaches typically treat quality scoring and reasoning descriptions as…

Multimodal large language models (MLLMs) have shown promising reasoning abilities, yet evaluating their performance in specialized domains remains challenging. STEM reasoning is a particularly valuable testbed because it provides highly…

Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…

We present Fox-1, a series of small language models (SLMs) consisting of Fox-1-1.6B and Fox-1-1.6B-Instruct-v0.1. These models are pre-trained on 3 trillion tokens of web-scraped document data and fine-tuned with 5 billion tokens of…

Reinforcement Learning (RL) has shown promise in improving the reasoning abilities of Large Language Models (LLMs). However, the specific challenges of adapting RL to multimodal data and formats remain relatively unexplored. In this work,…

Large Language Models (LLMs) have revolutionized natural language processing, yet they struggle with inconsistent reasoning, particularly in novel domains and complex logical sequences. This research introduces Proof of Thought, a framework…