The Geometric Intelligence Lab @ UC Santa Barbara

We reveal the geometric signatures of natural and artificial intelligence.

We are physicists, neuroscientists, statisticians, mathematicians and computer scientists who develop methods to understand intelligence in human and artificial neural networks.

We use tools from geometry, topology, computer vision, machine learning and deep learning to reveal the structures of intelligence. Our findings inspire us to build next–generation intelligent systems: Geometric AI.

By creating geometric computational representations of human and artificial brains at different scales, we aim to transform theoretical, computational and clinical brain sciences. For the latter, we work with clinicians to advance medical knowledge and AI-assisted medical practice for brain sciences.

Geometric Intelligence Research

Geometry

The concepts of geometry and shapes are very intuitive to the human eye. How can we express and quantify geometries and shapes mathematically and in a computer? Learn more.

Artificial Intelligence

We research foundations of geometric deep learning and topological deep learning and ask: what is the geometry of a deep learning model? Can we build a geometric model of the (artificial) mind? Learn more.

Natural Intelligence

We explore the neural manifold hypothesis which postulates that the activity of (biological) neurons forms low-dimensional geometric subspaces -- the neural manifolds -- that reflect the structure of the outside world. Learn more.

Intelligence-Based Medicine

What are the geometric signatures of neurodegenerative diseases: what does a brain shape tell us about the progression of Alzheimer's disease? Why are women are twice at risk of Alzheimer's compared to men? Learn more.

Latest News

News

We Are Awarded a NIH R01 Grant for Biological Shape Reconstruction

We are excited and honored that our group was awarded a NIH R01 grant for the introduction of geometric and deep learning methods to enhance 3D biological shape reconstruction. We aim to reveal the shapes of membrane proteins, these biomolecules targeted by over 50% of the pharmaceutical drugs, yet still difficult to image.

We win the 1st Prize in the C3.ai Covid-19 Grand Challenge!

In the C3.ai COVID-19 Grand Challenge, developers, data scientists, students, and creative minds around the world developed meaningful data-driven insights to inform decision makers and change how the world is fighting this pandemic.

Our solution "Modeling Population Heterogeneity by Providing Personalized Covid-19 Diagnostics" with C. Donnat and F. Bunbury won the first prize of $100,000!

Our software Geomstats is in the news! Open-Source Bridges the Gap between Mathematical Research and Industry

Ovio starts a new series of blog posts showcasing the extraordinary #maintainers and #communities that are making #opensource.