The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks
This work addresses a foundational problem in machine learning with implications for lottery ticket hypothesis, distributed training, and ensemble methods, though it is incremental as it builds on existing concepts.
The paper investigates whether considering permutation invariance in neural networks leads to no barrier in linear interpolation between SGD solutions, and presents empirical and preliminary theoretical support for this conjecture.
In this paper, we conjecture that if the permutation invariance of neural networks is taken into account, SGD solutions will likely have no barrier in the linear interpolation between them. Although it is a bold conjecture, we show how extensive empirical attempts fall short of refuting it. We further provide a preliminary theoretical result to support our conjecture. Our conjecture has implications for lottery ticket hypothesis, distributed training, and ensemble methods.