Research Interests
Theory of Deep Neural Networks
Despite their astonishing performance, deep neural networks have proven to be incredibly difficult to understand. I am interested in finding intuitive descriptions that manage to explain their inner workings, especially in the overparametrized regime. My current approach to this problem involves establishing connections between network representations and topological spaces. This is done by leveraging tools from polyhedral geometry, quotient spaces and homology. However, I strive to expand my toolbox and am also interested in questions about inductive biases, expressivity, mechanistic interpretability and kernel limits.
Topological Data Analysis of Neural Representations
The notion of a neural manifold is a fundamental component for our understanding of how the brain represents and transforms information. Such manifolds can be highly non-linear and of very high dimension, this often means that simply applying dimensionality reduction to visualize them can often lead us astray. My goal is to overcome these limitations by developing tools from Topological Data Analysis (TDA) specifically intended for the high-dimensional, non-linear and low sampling setting that neural data exists in.
De novo Protein Design with Machine Learning
Machine learning for the generation of de novo protein design is a rapidly evolving field. In my current work I apply and develop machine learning algorithms for de novo protein design. This work combines evolutionary algorithms, statistical modeling and neural networks to create and simplify existing proteins with the goal of improving gene therapy.
I am also interested in using tools from geometry, shape analysis and topological data analysis to understand how the space of protein representations in protein language models relates to the space of amino acid sequences and the actual structure of proteins.