Our work spans the theoretical foundations of geometric deep learning to practical applications in science and medicine.
We build the mathematical foundations for symmetry-preserving neural networks. By embedding the symmetries of physics (equivariance) into the architecture, we ensure data efficiency and generalization.
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Representing signals not as discrete pixels, but as continuous functions grounded in geometry. This allows for resolution-independent processing and rigorous handling of manifold data.
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Applying geometric deep learning to complex medical data. From histopathology to MRI, we use equivariance to robustly analyze biological structures and improve diagnostic reliability.
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Developing generative models that operate on non-Euclidean spaces (manifolds). We explore stochastic differential equations and flow matching on geometric domains.
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Modeling atomic systems and molecular structures as geometric point clouds. Our methods help predict properties and simulate interactions conformant with physical laws.
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