Stochastic Flows and Geometric Optimization on the Orthogonal Group

Understand

We present a new class of stochastic, geometrically-driven optimization algorithms on the orthogonal group $O(d)$ and naturally reductive homogeneous manifolds obtained from the action of the rotation group $SO(d)$.

• We theoretically and experimentally demonstrate that our methods can be applied in various fields of machine learning including deep, convolutional and recurrent neural networks, reinforcement learning, normalizing flows and metric learning.
• We show an intriguing connection between efficient stochastic optimization on the orthogonal group and graph theory (e.g.
• matching problem, partition functions over graphs, graph-coloring).