School of Science Department of Mathematics 41 Applications of Large Language Models in Special Sectors Supervisor: CHEN Kani / MATH Student: LIU Xingyuan / QFIN Course: UROP 1100, Fall Recently Whisper Model has approached human-level robustness and accuracy in English speech recognition (ASR), while in minor language and mixed-language speech recognition, there remains a compelling need for further improvement. In this work, we present the impressive results of Whisper-MCE, our fine-tuned Whisper model, which was trained using our self-collected dataset, Mixed Cantonese and English (MCE) audio dataset. Our Whisper-MCE achieved an impressive Character Error Rate (CER) in Common Voice zhHK, positioning it as state-of-the-art. However, CER poses challenges when it comes to evaluating its effectiveness in mixed-language contexts. To address this, we proposed a novel evaluation metric, FAL, which evaluates an ASR system from fidelity to the original audio, accuracy, and latency. In this evaluation metric, our Whisper-MCE also beats other models, further highlighting its exceptional performance. Geometric Flows Supervisor: FONG Tsz Ho / MATH Student: HO Chiu Ming Chatwin / MATH-IRE Course: UROP 1000, Summer In 1986, M. Gage and R. Hamilton published a paper on curve-shortening flows, where a 1- parameter family of curves flows according to a form of the heat equation. They showed that an embedded convex curve stays convex and embedded and develops no singularity as it evolves, until it eventually shrinks to a point, and the shape of the curve will converge to a circle in some strong geometric and uniform sense. In this paper, we will move the curve-shortening flow to a more general setting and begin a brief preliminary investigation on how much of these geometric properties will still hold. Geometric Flows Supervisor: FONG Tsz Ho / MATH Student: RIZVI Syed Momin Ahmed / COMP Course: UROP 1000, Summer In this report we study the Curve Shortening Flow (CSF). We first see why convex shapes are special, then we study some properties of the flow - namely it’s affect on the arclength, area and the overall shape, and finally we conclude with some time bounds on CSF to show that inscribed curves remain inscribed. Geometric Flows Supervisor: FONG Tsz Ho / MATH Student: WANG Daci / MATH-GM Course: UROP 1000, Summer We introduce the tensor maximum principle to show the positivity of Ricci curvature is preserved in dimension three. We use the geodesic normal coordinates to show the variation equations of the Riemann, Ricci and scalar curvature. We give a lower bound for the scalar curvature and prove a finite time for the scalar curvature to blow up. Finally, we adopted Bernstein’s trick to show an inequality of the gradient.
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