Improving Convergence and Generalization Using Parameter Symmetries
This work addresses optimization challenges in machine learning by exploiting symmetries, offering incremental improvements to existing algorithms.
The paper tackled the problem of understanding and leveraging parameter symmetries in neural networks to improve optimization and generalization, showing that teleportation accelerates convergence and enhances generalization by moving to minima with different curvatures.
In many neural networks, different values of the parameters may result in the same loss value. 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 show that teleportation not only speeds up optimization in the short-term, but gives overall faster time to convergence. Additionally, teleporting to minima with different curvatures improves generalization, which suggests a connection between the curvature of the minimum and generalization ability. Finally, we show that integrating teleportation into a wide range of optimization algorithms and optimization-based meta-learning improves convergence. Our results showcase the versatility of teleportation and demonstrate the potential of incorporating symmetry in optimization.