Content I Consume - 12/30/2024

Past weeks editions can be found here 

Hello all,

My senior fall semester is officially over and all 10 of my PhD applications are submitted! Even after returning home to North Carolina, it’s hard to leave behind the level of stress these couple of months have normalized.

At MIT, we have the month of January effectively off, so I’m excited to have some time to decompress and focus fully on new research projects.

Physics

Paper: Product Manifold Machine Learning for Physics V1 by Nate S. Woodward et al.

I began this project my sophomore year and I’m excited to finally have it publically available.

In this paper, we explore new data representations for hierarchical datasets in physics. Hierarchies in nature are often formed by processes that evolve through a splitting. For example, a tree grows originally from the trunk but successively splits into smaller and smaller branches. In this evolution, there is a clear hierarchy with the trunk as the most fundamental aspect with each splitting one level lower in the hierarchy.

As you might imagine, for datasets formed through hierarchical processes finding a way to represent our data in a model that also optimally represents the hierarchical structure is key to capturing all the available features of the dataset.

To accomplish this, we leverage non-Euclidean manifolds. In our case, these are curved surfaces. It’s been proven mathematically that some non-Euclidean surfaces can optimally represent the hierarchical structure. In our approach, instead of fully representing data in non-Euclidean manifolds, we consider a combination of several representations on several manifolds, forming a Product Manifold. Specifically, Product Manifolds are Cartesian products of constant curvature Riemannian manifolds (for this paper, we only consider hyperbolic, Euclidean, and spherical geometries).

We develop MLP and transformer models employing product manifold representations and benchmark their performance on particle jets. Read the paper to see why particles are hierarchical objects and how our models perform!

Miscellaneous

Podcast: Beauty in Knowledge

For my final project Producing Podcasts in the spring of my Junior year, I made a 12 minute podcast exploring how learning more about a subject changes our preception. This topic was motivated by questions such as, does the muscian apprechaite music more before or after they are trained in the theory and structures? To me this was never an obvious question and something I’ve discussed before in a blog post here.

In this podcast, I interview three people in different fields at different stages of mastery. I think it’s a great exploration of the topic with some interesting people and all at about 12 min.