UROP Proceedings 2022-23

School of Science Department of Mathematics 40 Applications of Large Language Models in Special Sectors Supervisor: CHEN, Kani / MATH Student: LIU, Xingyuan / SBM Course: UROP1000, Summer This report presents a novel approach to finetuning large language models by leveraging self-instructed corpus. The method utilizes ChatGPT, a powerful language model, to generate targeted data for training, enabling improved performance in specific domains. We discuss the key points of self-instructed data and use as well as compare different finetuning methods on different large language models. Our experimental results demonstrate the effectiveness of our approach in enhancing the language model's performance on domain-specific tasks. This report provides valuable insights into the potential of self-instructed data for finetuning large language models, highlighting its significance in advancing natural language processing applications. Applications of Large Language Models in Special Sectors Supervisor: CHEN, Kani / MATH Student: XIA, Haonan / SBM Course: UROP1100, Spring This report basically introduces about the Dark Forest Theory and its related case study, the main arbitrage strategies in MEV attack and the possible application of the backrun strategy in the forward market, its implication and limitation. Geometric Flows Supervisor: FONG, Tsz Ho / MATH Student: CHAU, Yu Hei / DSCT Course: UROP3100, Fall This UROP report is to document some of the research and self learning I have done after the last report. Unfortunately, there are no meaningful new results. This would document attempts on removing the concavity assumption on Gerhardt’s convergence Theorem, understanding and trying out the technique of considering flows in terms of the dual body with Andrews’ et. al. paper, and some miscellaneous topics I have spent time on. The general concepts will be mainly focused on, so not all details of the proofs will be written out; some of the proofs will be sketched or skipped, and the theorem statement will simply be written.