The Geometric Intelligence Lab @ UC Santa Barbara

We reveal the geometric signatures of natural and artificial intelligence.

Understanding the brain is one of greatest scientific challenges of our time. We still don't know how thoughts emerge from neural activity, how our memories are stored and retrieved, or how our brain so flexibly adapts to new situations.

Meanwhile, today, an equally profound challenge has arisen: understanding the artificial intelligence (AI) emerging in machines of our own making.

In our lab, we believe that these challenges are linked.

Geometric Intelligence Research

We are physicists, neuroscientists, mathematicians and computer scientists who study intelligence in biological and artificial neural networks and use our findings to build better AI models.

Just as physics unified forces through symmetry and geometry, we show mathematically and empirically that human and machine intelligence can be studied under a common framework: geometric intelligence.

Geometric Intelligence in Machines

We study the mathematical properties of top-performing AI models. Using these properties, we design novel AI that succeeds where most models fail—delivering up to +66% higher accuracy or the same accuracy with 10× faster models—even when datasets are small, noisy, or complex (e.g., networks, and 3D shapes). Learn more.

Geometric Intelligence in Brains

We study how geometric patterns of neural activity obey mathematical principles across diverse cognitive functions—from navigation and memory to vision. Learn more.

Building Brain Digital Twins

We leverage shared mathematical principles of intelligence in brains and machines to build multiscale digital twins of the brain, simulating its function in both health and disease. 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 Are Awarded the NSF SCALE MoDL Grant on Mathematical and Scientific Foundations of Deep Learning

We are excited and honored that our group was awarded the NSF SCALE MoDL Grant "Stimulating Collaborative Advances Leveraging Expertise in the Mathematical and Scientific Foundations of Deep Learning". We aim to provide a unified geometric and topological framework grounded in cell complex neural networks to explain and enhance deep learning architectures, with applications to biological shape analysis.

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!