My interests include mathematics, cognitive science, art, Chinese philosophy, and related fields.
➰ Topology and Geometry
Topology and geometry are both powerful tools commonly used in machine learning research.
Topology studies properties that remain invariant under continuous transformations in topological spaces (such as gluing or loops), while geometry examines properties like distance, shape, and size of a space.
In my view, topology approaches problems in a more global and coarse manner, whereas geometry uses more local and detailed methods.
Although topology and geometry are closely related in mathematics, they have branched into two separate areas in machine learning research.
Geometry primarily investigates many interesting properties of ML models, such as the Hessian matrix and curvature, while topology is mainly applied in data analysis through a specialized branch called Topological Data Analysis (TDA).
TDA is highly effective in studying the overall structure of data, making it useful for understanding how models process data.
However, the methods used in TDA to compute the topological structures of data are often computationally expensive, which has limited the widespread application and research of TDA.
For more information about TDA, check out Prof. Gunnar Carlsson's work. I also provided a brief introduction in my paper.
I believe that combining these two branches could be an interesting direction, as it would provide a comprehensive perspective on both the local and global properties of data and models.
🧠 Psychology and Neuroscience
As two major branches of cognitive science, psychology and neuroscience are closely interconnected.
Psychology primarily studies behavior and mental processes, helping us understand human cognition and emotional activities.
Neuroscience, on the other hand, explores the biological and neural mechanisms underlying these processes, focusing on the structure and function of the brain.
I feel their relationship is somewhat akin to that of topology and geometry: psychology takes a more macroscopic approach, emphasizing overarching patterns, while neuroscience delves into the microscopic mechanisms.
I am particularly interested in their mathematical foundations and their connections with machine learning models.
For example, one article employs deep neural networks to investigate spatial cognition in infants,
while another uses artificial neural networks to model the hippocampal subfield CA3 and explore its role in memory formation.
I believe that leveraging machine learning or other mathematical tools to forge stronger links between psychology and neuroscience is also a fascinating and promising research direction.
👘 Fashion Design
Coming soon...
🎬 Film
Among all movie genres, my top three favorites are sci-fi films like The Matrix, comedies such as The Girl Who Leapt Through Time, and historical/biographical films like Hidden Figures and Green Book. I also enjoy most of Marvel's works since many of them incorporate comedic elements (though not all). Additionally, I like to connect movies with real-life reflections. For example, during a film studies lecture, I wrote a final paper analyzing a sociology book and its connection to Japanese society through Japanese films, earning the highest score among over 200 students. Read more
⚖️ Divination (命理学)
Coming soon...
☯︎ Chinese Geomancy (Feng Shui, 风水)
Coming soon...