Understanding Generalization through Visualizations

TL;DR

This paper explores the phenomenon of neural network generalization using visualization techniques to provide more intuitive insights into loss landscape geometry and the effects of high-dimensionality on optimizer behavior.

Contribution

It introduces visualization methods to better understand neural network generalization, loss landscape geometry, and the role of dimensionality in optimizer convergence.

Findings

Visualizations reveal the geometry of loss landscapes.

High-dimensionality influences optimizer settling into good minima.

Insights into why neural networks generalize well despite loose bounds.

Abstract

The power of neural networks lies in their ability to generalize to unseen data, yet the underlying reasons for this phenomenon remain elusive. Numerous rigorous attempts have been made to explain generalization, but available bounds are still quite loose, and analysis does not always lead to true understanding. The goal of this work is to make generalization more intuitive. Using visualization methods, we discuss the mystery of generalization, the geometry of loss landscapes, and how the curse (or, rather, the blessing) of dimensionality causes optimizers to settle into minima that generalize well.