research
Research themes and current directions
Geometry and Topology of Large Language Models
We study the internal representations of transformer models using tools from geometry and topological data analysis. By treating token embeddings as evolving point clouds across layers, we characterize how models organize and process information. This geometric perspective reveals interpretable structure in the latent space and provides practical tools for model interpretability and safety. Applications include pre-output monitoring, layer pruning, and understanding uncertainty propagation in neural networks.
Topological Analysis of Neural Dynamics
We develop methods to characterize temporal evolution in neural population recordings using persistent homology. By tracking topological features (loops, connected components) in time-varying activity patterns, we extract compact representations of spatiotemporal dynamics. This framework applies to several types of high-dimensional time series from neuroscience experiments.
Learning Optimal Topological Summaries
Applying topological data analysis requires choosing filtrations and vectorization schemes. We introduce methods to learn these components by maximizing relevant information about the system. This enables automated, task-specific optimization of the topological pipeline for scientific inference problems. The framework is implemented in an open-source library and applies to point clouds, fields, and time series.