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Poster
Geometric Clifford Algebra Networks
David Ruhe · Jayesh K. Gupta · Steven De Keninck · Max Welling · Johannes Brandstetter

Tue Jul 25 02:00 PM -- 04:30 PM (PDT) @ Exhibit Hall 1 #534
in Poster Session 1 »
We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the $\mathrm{Pin}(p,q,r)$ group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable geometric templates that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods.
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Author Information

David Ruhe (University of Amsterdam)
Jayesh K. Gupta (Stanford University)
Steven De Keninck (University of Amsterdam)
Max Welling (University of Amsterdam & Qualcomm)
Johannes Brandstetter (Microsoft)

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