Timezone: »

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
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.

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)

More from the Same Authors