Statistical Gems in AI: Toward Reliable and Efficient Intelligence

The rapid rise of large language models (LLMs) has reshaped how humans create, reason, and communicate, yet their reliability and efficiency remain imperfectly understood. This dissertation develops statistical tools to evaluate and enhance these systems. We demonstrate how hypothesis testing, coupling methods, and conformal inference can ensure that advanced artificial intelligence (AI) models operate with safety, fairness, and efficiency. First, we design hypothesis-testing frameworks that distinguish genuine reasoning from token bias, revealing fundamental limits in LLMs’ ability to generalize logically. Next, we introduce statistically principled watermarking methods for detecting AI-generated content and safeguarding digital integrity. Building on this, we explore the application of conformal inference to ensure fair and robust detection of excessive AI use in classrooms while embracing the evolving world of human–AI collaboration. Finally, we propose statistical early stopping rules that enhance generative efficiency while maintaining accuracy. Together, these studies uncover key “statistical gems” that bridge AI technology with trustworthy and efficient real-world deployment.

Author dc:creator

• Xie, Yangxinyu

Advisor dc:contributor.advisor

• Su, Weijie

• Statistics and Probability

Language dc:language.iso

en

Repository record dc:identifier.uri

https://repository.upenn.edu/handle/20.500.14332/62676

OAI identifier oai:identifier

oai:repository.upenn.edu:20.500.14332/62676