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Recent advances in large language models (LLMs) have shown impressive progress in mathematical reasoning tasks. However, current evaluation benchmarks predominantly focus on the accuracy of final answers, often overlooking the crucial…

Mathematical problem-solving is a key field in artificial intelligence (AI) and a critical benchmark for evaluating the capabilities of large language models (LLMs). While extensive research has focused on mathematical problem-solving, most…

Despite the remarkable advancements and widespread applications of deep neural networks, their ability to perform reasoning tasks remains limited, particularly in domains requiring structured, abstract thought. In this paper, we investigate…

Large Reasoning Models (LRMs) like o3 and DeepSeek-R1 have achieved remarkable progress in reasoning tasks with long cot. However, they remain computationally inefficient and struggle with accuracy when solving problems requiring complex…

Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…

Although demonstrating remarkable performance on reasoning tasks, Large Language Models (LLMs) still tend to fabricate unreliable responses when confronted with problems that are unsolvable or beyond their capability, severely undermining…

Large Language Models (LLMs) have been widely used to automate programming tasks. Their capabilities have been evaluated by assessing the quality of generated code through tests or proofs. The extent to which they can reason about code is a…

Large language models (LLMs) face challenges in solving complex mathematical problems that require comprehensive capacities to parse the statements, associate domain knowledge, perform compound logical reasoning, and integrate the…

In this thesis, I evaluate the performance of Large Language Models (LLMs) on the Law School Admissions Test (LSAT), specifically the Logic Games section of the test. I focus on this section because it presents a complex logical reasoning…

Students' handwritten math work provides a rich resource for diagnosing cognitive skills, as it captures intermediate reasoning beyond final answers. We investigate how current large language models (LLMs) perform in diagnosing cognitive…

Large Language Models (LLMs), such as OpenAI's o1 and DeepSeek's R1, excel at advanced reasoning tasks like math and coding via Reinforcement Learning with Verifiable Rewards (RLVR), but still struggle with puzzles solvable by humans…

Mathematical modeling is a cornerstone of scientific discovery and engineering practice, enabling the translation of real-world problems into formal systems across domains such as physics, biology, and economics. Unlike mathematical…

Large language models (LLMs) are increasingly explored as general-purpose reasoners, particularly in agentic contexts. However, their outputs remain prone to mathematical and logical errors. This is especially challenging in open-ended…

Large Language Models (LLMs) have emerged as powerful tools for software development tasks such as code completion, translation, and optimization. However, their ability to generate efficient and correct code, particularly in complex…

While state-of-the-art large language models (LLMs) demonstrate advanced reasoning capabilities-achieving remarkable performance on challenging competitive math and coding benchmarks-they also frequently fail on tasks that are easy for…

Achieving human-level intelligence requires refining the transition from the fast, intuitive System 1 to the slower, more deliberate System 2 reasoning. While System 1 excels in quick, heuristic decisions, System 2 relies on logical…

As Large Language Models (LLMs) are integrated into critical real-world applications, their strategic and logical reasoning abilities are increasingly crucial. This paper evaluates LLMs' reasoning abilities in competitive environments…

To reduce the need for human annotations, large language models (LLMs) have been proposed as judges of the quality of other candidate models. The performance of LLM judges is typically evaluated by measuring the correlation with human…

Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with the leading model, Gemini-2.5-Pro,…

Large Language Models (LLMs) have emerged with many intellectual capacities. While numerous benchmarks assess their intelligence, limited attention has been given to their ability to explore--an essential capacity for discovering new…