Going Beyond Linear Mode Connectivity: The Layerwise Linear Feature Connectivity

TL;DR

This paper introduces Layerwise Linear Feature Connectivity (LLFC), a stronger form of linear connectivity in neural networks, providing empirical evidence that LLFC holds across various settings and deepening understanding of neural network training dynamics.

Contribution

The paper proposes LLFC as a new concept extending linear mode connectivity to layerwise feature maps, supported by comprehensive empirical evidence and analysis of underlying factors.

Findings

LLFC holds across diverse training scenarios when LMC is observed.

LLFC provides new insights into neural network training and feature representations.

Spawning and permutation methods influence LLFC and deepen understanding of network connectivity.

Abstract

Recent work has revealed many intriguing empirical phenomena in neural network training, despite the poorly understood and highly complex loss landscapes and training dynamics. One of these phenomena, Linear Mode Connectivity (LMC), has gained considerable attention due to the intriguing observation that different solutions can be connected by a linear path in the parameter space while maintaining near-constant training and test losses. In this work, we introduce a stronger notion of linear connectivity, Layerwise Linear Feature Connectivity (LLFC), which says that the feature maps of every layer in different trained networks are also linearly connected. We provide comprehensive empirical evidence for LLFC across a wide range of settings, demonstrating that whenever two trained networks satisfy LMC (via either spawning or permutation methods), they also satisfy LLFC in nearly all the layers. Furthermore, we delve deeper into the underlying factors contributing to LLFC, which reveal new insights into the spawning and permutation approaches. The study of LLFC transcends and advances our understanding of LMC by adopting a feature-learning perspective.