Camilo Brown-Pinilla's senior project: A new approach to AI translation

Fourth-year applied mathematics concentrators at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) have the option to write senior theses. These theses use mathematical, statistical or computational modeling methods to explain a phenomenon, going beyond data analysis to answer questions of mechanism and causation.

On Translation as a Symmetry of Language

Camilo Brown-Pinilla, A.B. '26, Applied Mathematics

Advisors: Melanie Weber

• Please give a brief summary of your project.

When you translate a sentence into another language, the surface form that sentence takes on varies, but the underlying meaning remains unchanged. Using the language of group theory, Geometric Deep Learning describes relationships such as these as symmetries. By treating symmetries as a foundational design principle, we are able to create models that are especially robust and data efficient. This thesis approaches Natural Language Processing, which allows artificial intelligence agents to understand human languages, from this geometric perspective, treating translation as a symmetry of language and asking whether this approach can be used to improve the translation ability of AI systems. 

• How did you come up with this idea for your final project?

I have been thinking about this project ever since my junior year when I took a class on Geometric Machine Learning. Starting with a background in Natural Language Processing, I was amazed by the mathematical elegance and real-world utility of the geometric learning philosophy. This project emerged as my attempt at finding a bridge between these mostly disjoint fields. 

• What was the timeline of your project?

I started working on this project in April 2025. Over the summer, I conducted a thorough literature review and refined the formulation of my problem. From August to March 2026, I completed the implementation of this idea, which stitches together three distinct machine learning pipelines. 

• What part of the project proved the most challenging?

The hardest part of the project was refining my initial interest in a bridge between Geometric Deep Learning and Natural Language Processing into an actionable research question. I had to dig through linguistic literature that was unfamiliar to me and think outside of the box to see how different tools and perspectives were really just instances of the same overarching idea. From there, the engineering pipeline was a challenge, requiring me to optimize and orchestrate several large models and datasets. 

• What part of the project did you enjoy the most?

I thoroughly enjoyed the opportunity to spend a lot of time thinking very deeply about a problem that interests me. Every part of the project felt like working my way through the wild west. It was very exciting getting to work with so many different techniques and finding a way to link them all together.

• What did you learn, or skills did you gain, through this project?

I learned more skills than I can count. Most importantly, I learned how to think like a scientist and channel curiosity and excitement into real results.