Project title: Abstract Babble to Categories: A Mathematical Model of Human and LLMs
Project description: For both children and large language models (LLMs), learning unfolds through an iterative loop of prediction, comparison, and adjustment. However, there is a critical difference: while infants “actively” engage with linguistic input, an LLM learns “passively” from vast corpora and generates predictions. Category theory, an area of mathematics which studies abstracted structures and the relationships between them, can discover common patterns across different areas, even outside of math. In 2022, mathematicians Tai-Danae Bradley, John Terilla, and Yiannis Vlassopoulos created a mathematical “category of language” to understand LLM language acquisition. Thus, I believe it is possible to develop a mathematical framework through category theory for human language that mirrors principles of human language acquisition. To do so, I will either extend Bradley’s category of language by incorporating how infants—perhaps later on, learners of any age—may understand word relations from environmental feedback, or develop a new mathematical model (not necessarily categorical) based on these principles. A derivation of this proposal would be to power LLMs to acquire linguistic, and perhaps even broader conceptual knowledge through child-like learning, whether or not on the basis of a mathematical framework. Besides the implications of fostering cross-disciplinary connections between mathematics, linguistics, neurosciences, and artificial intelligence, this project could provide insight in two directions: a deeper understanding of human language acquisition, and of LLM language acquisition.
Most important achievement: I hope that it will be my decision to pursue my love of mathematics, which will become my most important accomplishment through the fulfillment of my mathematical career.
Reflections on the College Scholar Program: My greatest takeaway from the program so far has been learning from my peers. Their projects, so different from what I typically think about, have broadened my perspective in so many ways and have been so wonderful to learn about. I am very excited to see where their work, and mine, will lead us.