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Large Language Models (LLMs) represent a class of deep learning models adept at understanding natural language and generating coherent responses to various prompts or queries. These models far exceed the complexity of conventional neural…

Retrieval-augmented Large Language Models (LLMs) offer substantial benefits in enhancing performance across knowledge-intensive scenarios. However, these methods often face challenges with complex inputs and encounter difficulties due to…

Large Language Models (LLMs) have seen great advance in both academia and industry, and their popularity results in numerous open-source frameworks and techniques in accelerating LLM pre-training, fine-tuning, and inference. Training and…

Large language models (LLMs) are powerful AI tools that can generate and comprehend natural language text and other complex information. However, the field lacks a mathematical framework to systematically describe, compare and improve LLMs.…

Large language models (LLMs) demonstrate impressive multilingual capability, but their performance varies substantially across different languages. In this work, we introduce a simple yet effective method, called cross-lingual-thought…

Convex analysis is a modern branch of mathematics with many applications. As Large Language Models (LLMs) start to automate research-level math and sciences, it is important for LLMs to demonstrate the ability to understand and reason with…

Large language models (LLMs) exhibit remarkable capabilities across diverse tasks, yet aligning them efficiently and effectively with human expectations remains a critical challenge. This thesis advances LLM alignment by introducing novel…

Despite demonstrating impressive capabilities, Large Language Models (LLMs) still often struggle to accurately express the factual knowledge they possess, especially in cases where the LLMs' knowledge boundaries are ambiguous. To improve…

Existing research predominantly focuses on developing powerful language learning models (LLMs) for mathematical reasoning within monolingual languages, with few explorations in preserving efficacy in a multilingual context. To bridge this…

Large language models (LLMs) have revolutionized various domains but still struggle with non-Latin scripts and low-resource languages. This paper addresses the critical challenge of improving multilingual performance without extensive…

When using large language models (LLMs) in high-stakes applications, we need to know when we can trust their predictions. Some works argue that prompting high-performance LLMs is sufficient to produce calibrated uncertainties, while others…

Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (e.g., LLaMA-2) are still far away from…

Large Language Models are increasingly used by students to explore advanced material in computer science, including graph theory. As these tools become integrated into undergraduate and graduate coursework, it is important to understand how…

Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but the quality bar for medical and clinical applications is high. Today, attempts to assess models' clinical knowledge…

Counterfactual reasoning is widely recognized as one of the most challenging and intricate aspects of causality in artificial intelligence. In this paper, we evaluate the performance of large language models (LLMs) in counterfactual…

The widespread adoption of large language models such as ChatGPT and Bard has led to unprecedented demand for these technologies. The burgeoning cost of inference for ever-increasing model sizes coupled with hardware shortages has limited…

Large language models (LLMs) have demonstrated broad utility across molecular domains, spanning drug discovery and materials design. Analyzing LLMs' latent representations is crucial for elucidating their underlying mechanisms, improving…

Large language models (LLMs) are increasingly used in decision-making contexts, but when they present answers without signaling low confidence, users may unknowingly act on erroneous outputs. Prior work shows that LLMs maintain internal…

Recent advancements in Large Language Models (LLMs) have showcased striking results on existing logical reasoning benchmarks, with some models even surpassing human performance. However, the true depth of their competencies and robustness…

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…