Xin Wang

Xin Wang

he/his

Trying to build something cool

Universal Approximation Theorem

less than 1 minute read

Published:

The most important application of neural networks is in machine learning, where neural networks are “trained” to approximate a function. Thus, a fundamental question for neural networks is whether they can approximate reasonable functions to an arbitrary degree of accuracy. This depends on the activation function \(\sigma\) and is the subject of many papers, including the paper studied for this project. This project was mentored by Zach Wagner and supported by UCSB’s Directed Reading Program. We won the People’s Choice Award luckily. You can access our presented poster via this link if you are interested.

Leshno et al. proved in their paper “Multilayer Feedforward Networks With a Nonpolynomial Activation Function Can Approximate Any Function” that, under modest assumptions, a broad class of activation functions are suitable for building neural networks to approximate continuous functions. We studied this paper to understand the mathematics underlying the result.

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Molecules as Cellular Complexes

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The molecule is a complex system characterized by intricate relationships between its components, such as atoms, bonds, and rings. Topological Deep Learning (TDL) utilizes domains beyond graphs and constructs a comprehensive framework to process and extract knowledge from data associated with this kind of system. In this study, I introduce a novel representation of molecules as cellular complexes, specifically designed to accommodate ring structures. I rebuilt a topological neural network (TNN), the Cell Attention Network (CAN), and conducted a comparative analysis with standard Graph Neural Networks (GNNs) as baselines. This comparison highlighted both the strengths and limitations of our approach, offering insights into the potential and challenges of using cellular complexes for molecular modeling.

Measuring Visual Acuity in Bees from High-Resolution Images

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Visual acuity, the ability to perceive detail, is ecologically important, as it dictates what aspects of a visual scene an animal can resolve. The study of visual acuity in bee species helps biologists understand their evolutionary history and gain insight into their foraging strategies and navigation abilities. Sponsored by the Caves Lab, this project aims to design a pipeline that uses high-resolution 2D photos taken by the NSF-funded Big Bee Project to estimate visual acuity across different bee species. In the pipeline, we develop algorithmic approaches to measure the diameter of the ommatidia and estimate the interommatidial angles on the eyeʼs surface. By achieving a significant level of automation and accuracy, our pipeline will facilitate more efficient data collection for biologists. You can access the code and poster, if you are interested.