Geodesic Mode Connectivity

TL;DR

This paper explores the concept of mode connectivity in neural networks through the lens of Information Geometry, proposing geodesic paths as a means to connect different trained models with low loss.

Contribution

It introduces a novel geometric perspective by framing mode connectivity as geodesics in the space of neural network distributions, along with an algorithm to approximate these paths.

Findings

Geodesic paths effectively connect trained models with low loss.

The proposed algorithm successfully approximates geodesics in the parameter space.

Geometric interpretation enhances understanding of neural network loss landscapes.

Abstract

Mode connectivity is a phenomenon where trained models are connected by a path of low loss. We reframe this in the context of Information Geometry, where neural networks are studied as spaces of parameterized distributions with curved geometry. We hypothesize that shortest paths in these spaces, known as geodesics, correspond to mode-connecting paths in the loss landscape. We propose an algorithm to approximate geodesics and demonstrate that they achieve mode connectivity.