Gradient-based optimization drives most modern machine learning, but the connection between gradient dynamics and uncertainty is still not well understood. This project focuses on developing a theoretical framework for uncertainty quantification that treats gradient descent as a dynamical system. The approach involves decomposing gradients into certainty-preserving and uncertainty-inducing components and using second-order structure to analyze how uncertainty evolves during training. The goal is to improve the interpretability of model uncertainty and enable more trustworthy models. Results will be evaluated via training and testing on well-known datasets.

I’m doing SuperUROP to gain experience with carrying out a year-long independent project. This is a really exciting opportunity to study more of the mathematical foundations of ML and contribute to more trustworthy ML models.