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Language has long been conceived as an essential tool for human reasoning. The breakthrough of Large Language Models (LLMs) has sparked significant research interest in leveraging these models to tackle complex reasoning tasks. Researchers…

Recent Large Reasoning Models (LRMs), such as DeepSeek-R1 and OpenAI o1, have demonstrated strong performance gains by scaling up the length of Chain-of-Thought (CoT) reasoning during inference. However, a growing concern lies in their…

Upon its release in late 2022, ChatGPT has brought a seismic shift in the entire landscape of AI, both in research and commerce. Through instruction-tuning a large language model (LLM) with supervised fine-tuning and reinforcement learning…

The field of Artificial Intelligence (AI) continues to drive transformative innovations, with significant progress in conversational interfaces, autonomous vehicles, and intelligent content creation. Since the launch of ChatGPT in late…

Large language models (LLMs) have exhibited remarkable capabilities across various domains and tasks, pushing the boundaries of our knowledge in learning and cognition. The latest model, OpenAI's o1, stands out as the first LLM with an…

Large Language Models (LLMs) are highly proficient in language-based tasks. Their language capabilities have positioned them at the forefront of the future AGI (Artificial General Intelligence) race. However, on closer inspection, Valmeekam…

Large reasoning models (LRMs) like OpenAI o1 and DeepSeek R1 have demonstrated impressive performance on complex reasoning tasks like mathematics and programming with long Chain-of-Thought (CoT) reasoning sequences (slow-thinking), compared…

Large language models (LLMs) have shown significant potential to change how we write, communicate, and create, leading to rapid adoption across society. This dissertation examines how individuals and institutions are adapting to and…

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open…

Enabling Large Language Models (LLMs) to handle a wider range of complex tasks (e.g., coding, math) has drawn great attention from many researchers. As LLMs continue to evolve, merely increasing the number of model parameters yields…

The performance of large language models (LLMs) has recently improved to the point where models can perform well on many language tasks. We show here that--for the first time--the models can also generate valid metalinguistic analyses of…

Large Language Models (LLMs) are increasingly utilized in AI-driven educational instruction and assessment, particularly within mathematics education. The capability of LLMs to generate accurate answers and detailed solutions for math…

The recent advent of reasoning models like OpenAI's o1 was met with excited speculation by the AI community about the mechanisms underlying these capabilities in closed models, followed by a rush of replication efforts, particularly from…

In recent years, large language models (LLMs) have seen rapid advancements, significantly impacting various fields such as computer vision, natural language processing, and software engineering. These LLMs, exemplified by OpenAI's ChatGPT,…

The proliferation of open large language models (LLMs) is fostering a vibrant ecosystem of research and innovation in artificial intelligence (AI). However, the methods of collaboration used to develop open LLMs both before and after their…

Artificial intelligence is making spectacular progress, and one of the best examples is the development of large language models (LLMs) such as OpenAI's GPT series. In these lectures, written for readers with a background in mathematics or…

As the application of Large Language Models (LLMs) expands, the demand for reliable evaluations increases. Existing LLM evaluation benchmarks primarily rely on static datasets, making it challenging to assess model performance in dynamic…

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze…

The growing power of large language models (LLMs) has revolutionized how people access and utilize information. Notably, the LLMs excel at performing fine-grained data representation, which facilitates precise retrieval of information. They…

The ability to plan a course of action that achieves a desired state of affairs has long been considered a core competence of intelligent agents and has been an integral part of AI research since its inception. With the advent of large…