Loss Surface Simplexes for Mode Connecting Volumes and Fast Ensembling

TL;DR

This paper introduces a method to construct multi-dimensional low-loss manifolds called simplicial complexes that connect multiple trained models, enabling fast ensembling with improved accuracy and robustness.

Contribution

It presents a novel approach to build mode-connecting simplicial complexes for efficient ensembling, outperforming traditional deep ensembles.

Findings

Constructed mode-connecting simplicial complexes for multiple models.

Achieved faster ensembling with higher accuracy and robustness.

Requires only a few training epochs to find low-loss simplices.

Abstract

With a better understanding of the loss surfaces for multilayer networks, we can build more robust and accurate training procedures. Recently it was discovered that independently trained SGD solutions can be connected along one-dimensional paths of near-constant training loss. In this paper, we show that there are mode-connecting simplicial complexes that form multi-dimensional manifolds of low loss, connecting many independently trained models. Inspired by this discovery, we show how to efficiently build simplicial complexes for fast ensembling, outperforming independently trained deep ensembles in accuracy, calibration, and robustness to dataset shift. Notably, our approach only requires a few training epochs to discover a low-loss simplex, starting from a pre-trained solution. Code is available at https://github.com/g-benton/loss-surface-simplexes.