Improving Convergence and Generalization Using Parameter Symmetries

In overparametrized models, different parameter values may result in the same loss. Parameter space symmetries are loss-invariant transformations that change the model parameters. Teleportation applies such transformations to accelerate optimization. However, the exact mechanism behind this algorithm's success is not well understood. In this paper, we prove that teleportation gives overall faster time to convergence. Additionally, teleporting to minima with different curvatures improves generalization, which suggests a connection between the curvature of the minima and generalization ability. Finally, we show that integrating teleportation into optimization-based meta-learning improves convergence over traditional algorithms that perform only local updates. Our results showcase the versatility of teleportation and demonstrate the potential of incorporating symmetry in optimization.