School of Science Department of Mathematics 46 Intelligent Tutoring Systems for University Math Foundation Subjects Supervisor: HU Jishan / MATH Student: LI Aaron Branson Cigres / MATH-STAT Course: UROP 1100, Spring This project aims to develop a tutoring system for university-level foundation mathematics, with a focus on a large language model capable of handling mathematics at this level. Existing large language models have shown promise in natural language processing, but mathematical reasoning remains a challenging task. Specifically, university-level foundation mathematics, including topics from courses like Calculus 1, Calculus 2, and Calculus 3, presents a unique subset of mathematical reasoning. To address this, the research team decided to fine-tune the DeepSeekMath-RL model using a high-quality calculus dataset. Most contributions of this paper to the project was on model evaluation, specifically accuracy determination on test datasets consisting of past papers from foundation mathematics courses. Extracting data from these past papers posed challenges as they were primarily in PDF format, which couldn’t be directly converted to the required LaTeX format. To overcome this, open-source optical character recognition (OCR) models were utilized to streamline the extraction process. Algorithms for PDF segmentation and syntax cleaning were built around the OCR model as a workaround to the implicit limitations of the OCR model. The resulting approach provides a streamlined process for converting PDFs into text files with LaTeX syntax, significantly decreasing the need for manual data cleaning. Modeling the Statistical Structures of Brain-wide Activity Using Recurrent Neural Circuits Supervisor: HU Yu / MATH Student: LIU Minghao / COMP Course: UROP 1100, Fall In this project, we aim to build up a model to study the statistical structures of neural population activity. As a progress report, firstly, we present a review of our learning path in understanding basic models of neural circuits in computational neuroscience. This review encompasses the fundamental concepts and principles that form the foundation of our implementation. Then we showcase our approach to constructing and simulating a data-driven recurrent circuit model using Partial In-Network Training (PINning). The main idea behind PINning is to selectively modify a desired fraction of the initial random connections within a network by utilizing a synaptic change algorithm. By training the interaction matrix that represents synaptic connections between each neuron, we can reproduce the firing rates of neurons over a defined time period. Modeling the Statistical Structures of Brain-wide Activity Using Recurrent Neural Circuits Supervisor: HU Yu / MATH Student: YANG Dongjie / DSCT Course: UROP 1100, Fall This project aims to model the statistical structures of brain-wide activity by utilizing neural circuits and a provided dataset that includes recent experimental data from the zebrafish whole brain. One first objective of the project is to gain a good understanding of the background and conduct an extensive review of relevant literature, particularly in the context of recurrent neuron networks in computational neuroscience. This report outlines the progress achieved thus far, including the exploration of model components, examination of formulas, and identification of parameters requiring tuning, and implementing the algorithm on a computer. This abstract provides a concise overview of the project’s objectives, methodology, and progress.
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